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This is to certify that the

dissertation entitled

DEVELOPMENT AND TESTING OF A
FREEWAY RECURRING CONGESTION MEASURE

presented by

Mousa F. Abbasi

has been accepted towards fulfillment
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Ph.D. Civil Engineering

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DEVELOPMENT AND TESTING OF
A FREEWAY RECURRING CONGESTION MEASURE

By

Mousa F. Abbasi

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Civil and Environmental Engineering

1998

ABSTRACT
DEVELOPMENT AND TESTING OF
A FREEWAY RECURRING CONGESTION MEASURE
By

Mousa F. Abbasi

Selecting the most appropriate measure for evaluating Advanced Traffic
Management Systems (ATMS) is vital in detecting the true impact of this technology.
This study developed a freeway recurring congestion measure that is sensitive to short
term fluctuations in traffic speed and can be used in evaluating ATMS systems. The
measure quantifies recurring congestion on a location, segment, or system basis. . The
analysis used data from detectors in a freeway system in the Detroit, Michigan
metropolitan area. Models were developed to predict start time and duration of recurring
congestion, and values were assigned to congestion on each of the study segments. The
study recommends a sampling plan for measurements over Space, weekdays, seasons, and
the data collection frequency to quantify congestion. A sensitivity analysis was
performed to compare the developed measure with an existing recurring congestion
measure, and to determine the ratio of recurring and non-recurring congestion. Future

research topics were also recommended.

iii

Dedicated to my wife Bushra,

and my sons Omar and Osama

ACKNOWLEDGMENT

I would like to express my sincere appreciation and gratitude to my advisor Dr.
Virginia P. Sisiopiku and my guidance committee member Dr. William C. Taylor, for
their invaluable continuous advice, support, and guidance throughout my studies at
Michigan State University. My experience with them will never be forgotten.

My appreciation and gratitude are also extended to Dr. Thomas Maleck and Dr.
Vince Melfi for serving as members of the guidance committee and for their assistance
and professional suggestions. My appreciation is also extended to all faculty and students
in the Department of Civil and Environmental Engineering at Michigan State University.
Their assistance, suggestions, support, and encouragement were also crucial to the
completion of this research.

My love and appreciation to my wife Bushra. Without her love, patience, and
constant support I could not have finished this endeavor. My gratitude is also extended to
my sons Omar and Osama who gave me inspiration to finish this study. I wish to thank
my parents Fare’ and Noufa, and my parent-in-laws late Adeeb and Shoufa for their
support and constant sacrifice. My thanks are also extended to my brothers, especially
Karam, Mackram, and Hytham, my sister, and brother-in-law for their support.

I would like to thank the Michigan Department of Transportation for supporting

this research financially and provided necessary data and information.

iv

TABLE OF CONTENTS

LIST OF TABLES .......................................................................................................... vii

LIST OF FIGURES ......................................................................................................... ix
CHAPTER 1

INTRODUCTION ............................................................................................................. 1

1.1 Overview ......................................................................................................... 1

1.1.1 Congestion Definition and Characteristics ...................................... 2

1.1.2 Measure to Alleviate Congestion ..................................................... 3

1.1.3 Congestion Measurement ................................................................. 5

1.2 Description of the Problem ............................................................................. 5

1.3 Research Objective ......................................................................................... 6

1.4 Research Approach ......................................................................................... 6

1.5 Summary ......................................................................................................... 7
CHAPTER 2

LITERATURE REVIEW .................................................................................................. 9

2.1 Current Congestion Measurement Methodologies ......................................... 9

2.1.1 Congestion Severity Index ............................................................. 10

2.1.2 Roadway Congestion Index ........................................................... 12

2.1.3 Lane-Mile Duration Index ............................................................. 14

2.1.4 Traffic Intensity Index ................................................................... 15

2.1.5 Speed and Delay Rate Indices ........................................................ 17

2.1.6 Minute-Miles of Congestion .......................................................... 17

2.1.7 Freeway Congestion Index ............................................................ 19

2.1.8 California Department of Transportation Methodology ................ 20

2.2 Discussion on the Current Congestion Measures ......................................... 21

2.3 Summary ....................................................................................................... 22
CHAPTER 3

METHODOLOGY .......................................................................................................... 24

3.1 Study Site ...................................................................................................... 24

3.2 Data Collection ............................................................................................. 26

3.3 Study Approach ............................................................................................ 26

CHAPTER 4

DEVELOPMENT OF FREEWAY CONGESTION MEASURE ................................... 30
4.1 Definition of Congestion ............................................................................... 30
4.2 Definition of Recurring Congestion .............................................................. 32
4.3 Methodology for Smoothing Recurring Congestion Duration ..................... 33
4.4 Preliminary Analysis ..................................................................................... 35
4.5 Modeling Start Time and Duration of Recurring Congestion ...................... 37
4.6 Development of Recurring Congestion Freeway Measures ......................... 40
4.6.1 Probabilistic Recurring Congestion Indices ................................... 40
4.6.2 Probabilistic Recurring Congestion Severity Indices .................... 42
4.6.3 Freeway System Recurring Congestion Measure .......................... 44
4.7 Summary ....................................................................................................... 45
CHAPTER 5
ANALYSIS AND RESULTS .......................................................................................... 47
5.1 Freeway Recurring Congestion Speed Thresholds ....................................... 47
5.2 Data Availability ........................................................................................... 53
5.3 Freeway Recurring Congestion Probability .................................................. 57
5.4 Start Time and Duration of Freeway Recurring Congestion ........................ 60
5.5 Freeway Recurring Congestion Indices and Measures ................................. 64
5.5.1 Probabilistic Location Recurring Congestion Indices ................... 64
5.5.2 Probabilistic Freeway Recurring Congestion Indices ..................... 71
5.5.3 Freeway System Recurring Congestion Measure .......................... 73
5.6 Summary ....................................................................................................... 73
CHAPTER 6 -
SENSITIVITY ANALYSIS AND VALIDATION .......................................................... 79
6.1 Weekday Variations ...................................................................................... 79
6.2 Seasonal Variations ....................................................................................... 86
6.3 Model Validation .......................................................................................... 93
6.4 Comparison of Recurring and Nonrecurring Congestion ............................. 97
6.5 Comparison of Study and CALTRANS Methodologies .............................. 99
6.6 Summary ..................................................................................................... 101
CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS ........................................................ 102
7.1 Conclusions ................................................................................................. 102
7.2 Recommendations ....................................................................................... 105
BIBLIOGRAPHY .......................................................................................................... 107

vi

LIST OF TABLES

Table 2.1 Current Congestion Methodologies Characteristics ....................................... 23
Table 4.1 Customized Sample Output (6/ 16/97, 6:00-10:00 am.) ................................. 37
Table 5.1 Mean Recurring Congestion Indices Comparison (WB I-94 AM Peak) ........ 48
Table 5.2 Mean Recurring Congestion Indices Comparison (NB M-10 PM Peak) ....... 49
Table 5.3 Comparison of Recurring Congestion Index (Mi) by Using Three Speed
Threshold (Station 19) .................................................................................... 51
Table 5.4 Data Availability on the I-94 Study Segment ................................................. 55
Table 5.5 Data Availability on the M-lO Study Segment ............................................... 56
Table 5.6 Summary of Recurring Congestion Probability (%) ....................................... 60
Table 5.7 Probabilistic Location Recurring Congestion Indices (WB I—94) .................. 67
Table 5.8 Probabilistic Location Recurring Congestion Indices (EB I-94) .................... 68
Table 5.9 Probabilistic Location Recurring Congestion Indices (NB M-lO) ................. 69
Table 5.10 Probabilistic Location Recurring Congestion Indices (SB M-10) ................ 70
Table 5.11 Probabilistic Freeway Recurring Congestion Indices ................................... 72
Table 5.12 Vehicle Delay (WB I-94) .............................................................................. 74
Table 5.13 Vehicle Delay (EB I-94) ................................................................................ 75
Table 5.14 Vehicle Delay (NB M-10) ............................................................................. 76
Table 5.15 Vehicle Delay (SB M-lO) .............................................................................. 77
Table 5.16 Study Segments Vehicle Delay ..................................................................... 78
Table 6.1 Weekday Data Distribution (WB I-94 AM Peak Period) ............................... 80

vii

Table 6.2 Weekday Data Distribution (NB M-10 PM Peak Period) .............................. 81

Table 6.3 Weekday Data Distribution (SB M-lO AM Peak Period) .............................. 82
Table 6.4 Summary of Weekday Data Distribution ........................................................ 84
Table 6.5 Weekday Comparison of Recurring Congestion Index (Mi) .......................... 85
Table 6.6 Seasonal Data Distribution (WB I-94 AM Peak Period) ................................ 87
Table 6.7 Seasonal Data Distribution (NB M-10 PM Peak Period) ............................... 88
Table 6.8 Seasonal Data Distribution (SB M-IO AM Peak Period) ............................... 89
Table 6.9 Summary of Seasonal Data Distribution ........................................................ 90
Table 6.10 Seasonal Comparisons of Recurring Congestion Index (Mi) ....................... 91
Table 6.11 Total and Recurring Congestion Comparison (WB I-94 AM) ..................... 98
Table 6.12 FRSCM vs. CALTRANS Methodologies (WB I-94 AM) ......................... 100

viii

Figure 3.1
Figure 3.2
Figure 3.3
Figure 4.1
Figure 4.2
Figure 4.3

Figure 4.4

Figure 4.5

Figure 5.1

Figure 5.2

Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6

Figure 5.7

Figure 5.8

LIST OF FIGURES

Study Site Area Map ..................................................................................... 25
Schematic Diagram of Detector Locations in the I-94 Freeway ................... 27
Schematic Diagram of Detector Locations in the M-10 Freeway ................. 28
Speed Profile on West Bound I-94 at Gratiot Road ...................................... 31
Congested and Uncongested Traffic Conditions Scenarios .......................... 34
Examples on the Smoothing Methodology ................................................... 36
Start and Duration of Congestion and Recurring Congestion Before and

After Smoothing by using a 35 mph threshold (WB I-94) ............................ 38
Functionality of Data Collection Stations on West Bound 1-94 Freeway
Segment During AM Peak Periods (12/ 1996-5/ 1 997) ................................... 39
Speed Profiles for Stations 2 and 19 (12/ 1996-7/1997) ................................ 52
Average Speed on the WB I-94 and SB M-lO Freeways (AM Peak

Periods) .......................................................................................................... 54
Recurring Congestion Probability on the M-10 Freeway Segment ............... 58
Recurring Congestion Probability on the I-94 Freeway Segment ................. 59
Recurring Congestion Start Time and Duration on the M-lO Freeway ........ 61
Recurring Congestion Start Time and Duration on the I-94 Freeway ........... 62
The M-10 Freeway Recurring Congestion Start Time and Duration

Groups ............................................................................................................ 65
The 1-94 Freeway Recurring Congestion Start Time and Duration

Groups ............................................................................................................ 66

ix

Figure 6.1 Recurring Congestion Index (M) at Stations 19 and 72 (AM

Spring/Summer) ............................................................................................. 92
Figure 6.2 Recurring Congestion Index (M) at Stations 19 and 72 (AM

Fall/Winter) .................................................................................................... 94
Figure 6.3 Recurring Congestion Index (M) at Station 48 (PM in both Seasons) .......... 95
Figure 6.4 Recurring Congestion Start Time and Duration (SB M-10) ......................... 96

Chapter 1

INTRODUCTION

1.1 Overview

Traffic congestion is recognized as a major problem in urban areas with
significant effects on the economy, travel behavior, and land use. Although traffic
congestion is not a new problem for the central city, it has spread to cover suburban
areas. Schrank and Lomax (1997) estimated that the annual cost of congestion in 50
urban areas in 1994 exceeded $53 billion. They also estimated that 90 percent of total
congestion costs in major urban area are attributed to travel delay, with the other 10
percent attributed to fuel cost.

The decline in urban mobility resulting from congestion has become a major
concern to the transportation and business community and to the public. Measuring
congestion assists the transportation professionals and policy makers in communicating
problems, developing transportation system improvement strategies, and formulating new
policies and programs.

Several methods, based on travel time and delay, have been used for measuring
congestion. Despite the importance of these methods, there is no generally accepted
congestion measure for use by public agencies. Moreover, current methods neither

produce comparable results for various systems with similar congestion conditions nor

2

are they appropriate for evaluating the effect of Intelligent Transportation Systems
applications such as traffic management systems. There is a need for a new congestion
measure that accounts for small variations in traffic speed and can be used in evaluating
traffic management systems.
A review of the literature on the definition, measurement, and methods to alleviate
congestion, are presented in the following subsections.
1.1.1 Congestion Definition and Characteristics

Traffic congestion reflects an increase in delay or travel time beyond a threshold
acceptable to users. This threshold may vary by type of transportation facility,
geographic location, and time of day (Lomax, Turner, and Shunk, 1997). For example,
freeway congestion usually results when the road system is unable to accommodate
traffic at an acceptable speed and extends over both space and time (Turner, Lomax, and
Levinson, 1996).

Congestion can be divided into two major categories based on its occurrence

predictability:

a. Recurring congestion usually occurs at a predictable location during specific
periods of the day due to normally heavy traffic during these periods (e.g.
during peak commute periods).

b. Nonrecurring congestion takes place when an incident or special event results
in lane closure, increased demand, and/or reduced capacity.

The magnitude and duration of the nonrecurring congestion is difficult to quantify

because of limited information on incidents. Although many methodologies have been

developed to identify incidents, no one has been able to indicate a clear differentiation

3

between recurring and nonrecurring congestion. As a result, recurring congestion
databases partially still include congestion due to incidents.

The current practice of some transportation agencies, for example the California
Department of Transportation (CALTRANS), assumes that congestion is divided equally
into recurring and nonrecurring congestion (Epps, Cheng, and May, 1994). Lindley
(1986) reported that nonrecurring congestion accounted for more than 61 percent of all
urban congestion in 1984. He proposed a model to measure recurring and nonrecurring
congestion based on the Federal Highway Administration (FHWA) Highway
Performance Monitoring System (HPMS) database. His model estimates an average split
of 33 percent recurring and 67 percent nonrecurring congestion. When Epps, Cheng, and
May (1994) applied Lindley’s model to a sample of freeway sections in California, they
found that the ratio is highly variable between different segments at different congestion
levels. Understanding congestion definition, types, and splits is important in selecting
measures to alleviate it. For example, measures to alleviate recurring congestion are not
necessarily the same as for non-recurring congestion. A summary of these measures is
presented next.

1.1.2 Measures to Alleviate Congestion

Techniques for reducing traffic congestion can be divided into three categories
(Rathi and Lieberman, 1989 and Lindley, 1986):

a. Increase of roadway system capacity through construction of additional

facilities or other physical improvements to provide additional capacity.

b. Maximization of the use of available capacity through traffic management

practices aimed at more efficient use of existing capacity.

4

c. Reduction of traffic demand through behavioral changes, travel demand

management or traffic restraints.

Traffic management has received considerable attention since constructing more
freeway facilities (for example, lane addition) to relieve recurring congestion is often
politically and socially unacceptable and economically infeasible. Traffic surveillance,
ramp metering, network optimization and integration, and incident management are
major components of a traffic management system.

Travel demand management techniques may include congestion pricing, parking
restrictions, high occupancy vehicles (HOV) lane dedication, and ride sharing. In this
study, we are developing a congestion measure to evaluate a system designed to improve
the efficiency of an existing freeway system.

Advancement in computer, communication, and information technologies in the
past decade enhanced the ability to improve performance of transportation systems in
many parts of the world. In the United States, Intelligent Transportation Systems (ITS)
was initiated in 1992 to enhance performance of the transportation system through the
use of new technologies (U .S. Department of Transportation, 1992).

The implementation of Advanced Traffic Management System (ATMS) and
Advanced Traveler Information System (ATIS) components creates the potential for
congestion relief in urban areas. The primary feature of these systems is the provision of
real time information and control to respond to changing traffic conditions. There are
several pilot ATMS/ATIS programs currently being implemented in the US, Europe, and

Japan.

1.1.3 Congestion Measurement

Congestion information can be used in a variety of policy, planning, and
operational situations. It may be used by public agencies in assessing facility or system
adequacy, identifying problems, developing and assessing improvements, and
formulating programs, policies, and priorities. It may also be used by the private sector
in making location and investment decisions.

Four important attributes of roadway congestion should be quantified (Lomax,
Turner, and Shunk, 1997). These are duration, extent, intensity, and reliability. More
specifically, duration is defined as the length of time the travel system experiences
congestion. Extent refers to the number of people or vehicles affected by congestion.
Intensity is the severity of the congestion that affects travel, and reliability is measured in
terms of the variation in the other three elements.

Congestion methodologies assign quantitative values to congestion. These
methodologies provide a tool that assists the transportation professional, general public,
policy makers, business community to communicate with each other, introduce
transportation system improvements, and adopt new policies and programs.

Currently, existing congestion measures can be classified according to (a)
congestion type (total, recurring, or nonrecurring), (b) roadway type (freeway or arterial),
and (c) methodology used for their development (field, surrogate, or simulation). A
description of current congestion measures is provided in Chapter 2.

1.2 Description of the Problem
Several methods have been developed to measure congestion. However, many of

these methods are not sensitive to variations in traffic speed over time resulting from a

6

traffic management system. They also lack the ability to produce comparable results for
various systems with similar congestion levels. Therefore, there is a need for the
development of a new measure for quantifying recurring congestion, which is capable of
overcoming these limitations if the measure is to be appropriate for measuring the change
in congestion resulting from the implementation of ITS components.
1.3 Research Objective
This research addresses the development and testing of a measure to quantify
freeway recurring congestion. The scope of the research includes:
3. Identification of speed thresholds for identifying congestion.
b. Development of a methodology for identifying recurring congestion.
c. Development and validation of models to estimate the start time and duration
of recurring congestion.
d. Development and application of a measure for quantifying recurring
congestion.
e. Investigation of the sensitivity of the measure for seasonal and weekday
variations, and data collection frequency.
f. Comparison of the recurring and non-recurring congestion values in addition
to the study and CALTRANS estimates of recurring congestion.
1.4 Research Approach
This research was based on analysis of 24-hour, l-minute loop detector traffic
data. The Statistical Package for Social Sciences (SPSS) Version 7.5 (SPSS, 1997) and
F ortran PowerStation Version 4.0 algorithms (Microsoft, 1995) were used to analyze and

model recurring congestion.

The research was based on 8-month (December 1996 to July 1997) data obtained
from loop detectors embedded in two freeway segments (I-94 and M-lO) in the Detroit,
Michigan metropolitan area. Speed and congestion duration thresholds were developed
to detect recurring congestion. Further, a methodology was developed to identify start
time and duration of recurring congestion at each detector location. The methodology
identifies recurring congestion and smoothes variations below the defined recurring
congestion duration threshold. Statistical modeling was used to group the locations that
have the same start time and duration. A recurring congestion measure was developed
and values were assigned to each location and segment, and the whole system.

Seasonal and weekday variations of the developed measure were tested in
addition to the measure’s stability over data collection frequency. Moreover, the start
time and duration of recurring congestion models were validated using data obtained
during August 1997. The recurring and non-recurring congestion estimates were
compared in addition to the study and CALTRANS estimates of recurring congestion.

1.5 Summary

Major urban areas suffer from excessive traffic congestion. Several remedies,
including traffic management techniques, have been explored and implemented to
alleviate congestion. Advanced Traffic Management System (ATMS) applications are
being implemented in many parts of the world to test their effectiveness in reducing
congestion. The evaluation of these projects is critical for justifying widespread
deployment of such technologies.

The existing methods for assigning quantitative values to congestion are not

sensitive to variations in traffic speed over time resulting from a traffic management

system. More specifically, traffic management techniques are expected to affect average
freeway traffic speed rather than volume. There is a need for the development of a new
measure for quantifying recurring congestion, which is capable of quantifying the change

in congestion resulting from traffic improvements.

Chapter 2

LITERATURE REVIEW

Congestion measures have been described in the literature Since the 19505. The
early efforts toward measuring congestion were centered on empirical relationships.
Greenshields (1955) proposed an indicator of the “traffic roughness” of roadway sections.
The indicator was equal to the product of speed and direction changes over a section of a
roadway.

Several other methods have been proposed for assigning a quantitative measure to
congestion. Level of Service (LOS) is a widely used measure among traffic agencies. It
is defined in the Highway Capacity Manual (HCM) in terms of density for freeways,
average travel speed for arterial roads, and average stopped delay for signalized
intersections (HCM, 1994). Other queuing-related, travel time, delay, and speed
measures have also been used to quantify congestion. Congestion indices have also been
developed to quantify traffic congestion on an areawide basis. A summary of congestion
measurement approaches follows.

2.1 Current Congestion Measurement Methodologies

As mentioned previously, there are currently several methods for quantifying

total, recurring, and nonrecurring congestion. In this chapter, a review of these

methodologies is presented with emphasis on total and recurring congestion aspects.

10
Measuring nonrecurring congestion is beyond the scope of this research. The
methodologies are presented in this chapter in a chronological order of evolution and
interconnection.
2.1.1 Congestion Severity Index

The Congestion Severity Index (CSI) is a measure of freeway delay per million
vehicles-miles of travel (Lindley and McDade, 1988). The methodology uses the
Highway Performance Monitoring System (HPMS) database in urban areas with
populations of 50,000 or more (Lindley, 1986). Congested conditions occur when the
volume to capacity ratio (v/c) exceeds the 0.77 threshold value (which represents the
boundary between LOS C and D), and travel speed is less than 55mph (HCM, 1985).
The methodology's v/c threshold corresponds to the boundaries between LOS D and E in
the 1994 HCM. The methodology uses the 1965 HCM to estimate freeway capacity
based on number of lanes and adjustment factors for lane width, lateral clearance, truck
presence, and terrain (Lindley, 1986).

Based on traffic data collected on the Washington, DC. freeways, the
methodology developed twelve 24-hour volume profiles that represent typical urban
freeway traffic patterns for various peak hour percentage and directional factors (Lindley,
1986). By using these volume profiles, the HPMS data (peak hour data) were expanded
to give hourly traffic volume estimates of each freeway section.

This methodology assumes that recurring congestion occurs 260 days per year in
order to calculate the total annual congested vehicle miles of travel. Nonrecurring
congestion conditions were estimated by using total incident rates. The rates associated

with freeways with adequate shoulders and freeways with no Shoulder are 200 and 79

11

incidents per million vehicle miles of travel, respectively (Lindley, 1986). Delays are
calculated based on average travel speed varying between 30 and 54 miles per hour for
v/c ratios between of 1.0 and 0.77. An average speed of 20 mph is assumed for v/c ratios
greater than 1.0 (Lindley, 1986).

The C81, in vehicle hours of delay per million miles of travel, can be summarized

as shown in the following equation:

C S I _ Total Freeway Delay (Vehicle — Hours) (1)
Freeway Vehicle — Miles of Travel (Millions)

 

Turner (1992) concluded that a CSI value greater than 24,000 vehicle hours of
total delay per million miles of travel represents undesirable area congestion.

The CSI methodology is capable of measuring total, recurring, and nonrecurring
congestion from a readily available data (HPMS database). It is also simple to use and
neither time consuming nor labor extensive. It can be used to study both statewide
networks and individual road sections.

However, there are some questions regarding the accuracy of the results (Epps,
Cheng, and May, 1994). First, nationwide, only about 50 percent of road sections are
included in the HPMS database. Expansion factors and assumed hourly distributions are
used to convert the results obtained from the database into statewide estimates. A third
source of error involves the estimation of hourly directional traffic volumes from the

twelve 24-hour volume profiles based on the traffic characteristics of two Washington,

12

DC. freeways. Fourth, the measure is based upon the assumption that the maximum free
flow speed is 55 mph, while higher free flow speeds occur in real freeway traffic
conditions. The fifth source of error rises from the measure's assumption that a linear
relationship between v/c (from 0.77 to 1.00) and speed (from 30 to 55 mph) exists during
LOS E (operations at capacity) traffic conditions. Finally, the methodology does not
allow comparison with more severe congestion condition (LOS F) when it truncates
analysis at v/c ratio equal to one (Boamet, Kim, and Parkany, 1998). The methodology
also does not account for small variations in speed so it cannot be used in evaluating
ATMS.
2.1.2 Roadway Congestion Index

The Roadway Congestion Index (RC1) is based on the daily vehicle-miles of
travel (VMT) per lane-mile for freeways and principal arterial street systems combined
(Schrank and Lomax, 1997). This index quantifies congestion by comparing the existing
value to values identified under congested conditions. The RC1 is an empirically derived
formula that uses HPMS data. The RC1, which is dimensionless, can be represented as

shown in the following equation:

(VMT/lane - mi * VMT)Fuy + (VMT/lane - mi * VMT)Art

RC] =
(13, 000 * VMT)Fwy + (5, 000 * VMT)Art

(2)

 

where: VMT = Daily vehicle-miles of travel,
VMT/Lane-mi = Daily vehicle-miles of travel per lane-mile,

Fwy = Freeway, and

13

Art = Arterial street.

The basic assumption in calculating the RC1 is that congestion begins to occur at
LOS D as defined in the 1985 HCM (Turner, 1992). Based on historical traffic data fiom
Houston, Texas and an assumed hourly distribution, it was also determined that
congestion conditions are equivalent to approximately 15,000 and 5,750 vehicles per lane
per day (average annual daily traffic per lane) on individual freeway and principal arterial
street sections, respectively (Turner, 1992). The values of 13,000 and 5,000 vehicles per
day per lane thresholds for freeways and arterial streets, respectively, were used as an
areawide basis for congestion threshold (Turner, 1992).

A RC1 value greater than 1.0 represents undesirable level of roadway congestion.
Although this index gives an areawide indication of congestion, it is not a measure
applicable to segment or site specific evaluation of traffic conditions or variations in
travel patterns. An urban area with a RCI of less than 1.0 may still have specific
locations that experience congestion, despite the fact that the average level of mobility
within the urban area is characterized by uncongested conditions.

The methodology is useful if comparative studies between urban areas are needed.
However, this methodology does not distinguish between recurring and nonrecurring
congestion. It is only applicable to areawide congestion estimation. It also cannot be
used to evaluate ATMS because neither variable (VMT or VMT per lane-mile) changes
with the implementation of ATMS components. This methodology also uses the HPMS
database and an assumed hourly distribution, which raises the same concerns that have

been discussed in previous section.

14
2.1.3 Lane-Mile Duration Index
The freeway Lane-Mile Duration Index (LMDI) is a measure of the extent and
duration of recurring freeway congestion. The LMDI value for each urban area is the
sum of the product of congested freeway lane-miles and congestion duration (hours) for
individual roadway segments. A congestion travel condition exists if average annual
daily traffic volume (AADT) to hourly capacity ratio (AADT/C) is greater than 9.0

(Cottrell, 1991). The LMDI equation is:

n
LMDI = Z [(Congestea' Lane - Miles)i * (Congestion Duration)i] (3)

i=1

where: i = Individual freeway segment,
n = Total number of freeway segments, and
Congestion duration = Duration obtained from an assumed hourly traffic
distribution and AADT/C greater than 9.0 as a congestion
threshold (hours).

The methodology utilizes the HPMS database, just as the previous two
approaches, but uses a different threshold for congested and uncongested conditions.
This new threshold corresponds to LOS F where the volume to capacity ratio is greater
than 1.0 and the average travel speed is less than 30 mph (HCM, 1985). This
methodology also assumes an hourly traffic distribution similar to the previous two

approaches.

15

This methodology only addresses the estimation of recurring congestion delay
because of insufficient data for estimating nonrecurring congestion delay was found in
the database used (Cottrell, 1991). It is a useful tool if comparative studies between
different urban areas are needed. The LMDI methodology also uses the HPMS database,
which raises the same concerns that had been discussed in Section 2.1.1.

2.1.4 Traffic Intensity Index

The Traffic Intensity Index (T1) was developed using a database from the Traffic
Accident Surveillance and Analysis System (TASAS) in California to represent the
traffic demand as a fraction of the supply provided by the freeway facility (Epps, May,

and Cortelyou, 1993). The TI index is defined as follows:

1- way ADT

T1 = (4)
(I - way # of lanes)* 1,000

 

where: T1 = Traffic Intensity Index (dimensionless),

ADT = Average Daily Traffic (vehicles/day),

l-way # of lanes = Number of lanes in a one way direction, and

1,000 = A reduction factor (vehicles per day per lane).

Using this methodology, freeway segments are classified by the level of recurring
congestion. Segments with TI values greater than 20 were defined as experiencing

congestion. This methodology does not account for nonrecurring congestion.

16
Epps, Cheng, and May (1994) modified the equation to include the HCM peak

(K) and directional (D) factors. The modified measure, named Directional Peak Hour

Demand per Lane, equation is as follows:

_ at: at:
Directional Peak Hour Demand per Lane = (2 way AADT) K D (5)
# of lanes in l — way

 

where: AADT = Annual Average Daily Traffic (vehicles),

K = Peaking Factor, and

D = Directional Factor.

The modified measure is an estimate of the traffic demand per hour per lane
during a peak period which can be compared with an acceptable lane capacity (vehicles
per hour per lane) to give a demand-capacity ratio (D/C). Demand-capacity ratios near
1.0 indicate near-capacity flow conditions, and D/C values greater than 1.0 indicate
recurring congestion conditions.

Freeway sections with directional peak hour demand per lane greater than 2,000
vehicles are defined as congested sections. Recurring congestion and incident levels are
also stratified into three levels: low, medium, and high. Then, a 3 x 3 matrix is created to
classify freeway sections into nine categories.

The methodology is a modification of the CSI and measures both recurring and
nonrecurring congestion based on a surrogate database. However, there are some

questions regarding the accuracy of the surrogate database Similar to ones that had been

17

discussed in Section 2.1.1. The measure also neither accounts for small variations in
traffic speed nor can be used in evaluating ATMS since none of the variables would
change with the implementation of ATMS components.

2.1.5 Speed and Delay Rate Indices

The Speed and Delay Rate Indices (SR1 and DRI) are based on the HCM free-
flow conditions (HCM, 1985 and 1994). Both the SR] and DRI quantify congestion
based on a continuous scale with numerical values from 0 to 10. The SRI values
correspond to the percentage decrease in speed relative to assumed free-flow condition
speed (Lomax, Turner, and Shunk, 1997). On the other hand, DRI values correspond to
the increase in travel time relative to travel time under free-flow conditions (Levinson
and Lomax, 1996). For example, a SR1 value of 5 corresponds to a 50% speed drop due
to congestion while a DRI value of 5 corresponds to a time loss of 1 minute per mile (30
mph) on freeways with a free flow speed of 60 mph.

The two indices can be used for freeway or arterial roadways. They are capable
of measuring total congestion but not able to distinguish between recurring and
nonrecurring congestion. Moreover, these two indices are not able to account for small
variations in speed or suitable for evaluating ATMS. The use of a surrogate database and
an assumed hourly distribution raises the concerns that have been discussed in Section
2.1.1.

2.1.6 Minute-Miles of Congestion

The Minute-Miles of Congestion (MMC) is a measure of the average section

congestion during a given time period and is used by the Illinois Department of

Transportation for estimation of congestion on Chicago-area expressways (Polus, 1996).

18

The measure is based on percent occupancy, which measures the percentage of time each
detector is occupied by vehicles. A 30% occupancy, which is equivalent to a density of
about 90 vehicles per mile and speed of 25 mph (based on freeway capacity of 2,300
vehicles per hour per lane), is selected as a dividing threshold between the congested and
uncongested states.

Therefore, the MMC (in minute-miles) is the sum of the congestion duration
multiplied by the length of the corresponding congested section. The MMC equation is

as follows:

It
MMC = ZDi Li (6)
i=1

where: i = One-way freeway segment,

n = Total number of freeway segments,

Di = Average duration of congestion for a freeway section i (minutes), and

Li = Length of a freeway section i (miles).

The threshold value of congestion, in MMC units, was arbitrarily selected as 10.
This means that the start of the peak period occurs when occupancies of 30% or more are
measured for 5 minutes or longer on a two mile section (Polus, 1996).

The methodology measures total congestion and does not distinguish between
recurring and nonrecurring congestion. The 5-minute threshold eliminates short-term

incidents, which results in under estimation of total congestion. The MMC methodology

19

does not give a measure of the percentage of all traffic subjected to congestion in a day.
It also does not account for small speed variations.
2.1.7 Freeway Congestion Index

The Freeway Congestion Index (F CI) was developed to quantify the severity of
recurring congestion on Utah freeways by using a speed of 40 mph as a congestion

threshold (Thurgood, 1995). Its mathematical expression is:

M* .
FCI= Zlc—L—M D j (7)

where: F CI = Freeway Congestion Index (lane-mile-hours per lane-mile),

i = One-way freeway segment,

n = Total number of freeway segments,

CLM, = Total congested lane-miles in freeway segment i (miles),

D = Duration of congestion (hours), and

LMi = Total lane miles in freeway segment i (lane-miles).

To determine the start time of congestion, duration, and extent (lane-miles), the
study used instrumented vehicles during defined morning and afternoon peak periods.
The study also suggests using aerial photography and employing 1994 HCM density
criterion for defining congestion and its extent.

The methodology measures recurring congestion but does not account for

nonrecurring congestion. The data collection method (instrumented vehicles) is

20

expensive. Moreover, the methodology only defines recurring congestion when traffic
speed falls below 40 mph without specifying a minimum congestion duration threshold.
2.1.8 California Department of Transportation Methodology

The California Department of Transportation (CALTRANS) identified congested
freeway segments where speeds less than 35 mph are experienced for at least 15 minutes
(Epps, Cheng, and May, 1994). Two methods were used for data collection; namely,
loop detectors and vehicles equipped with tachometers. Incident-free weekdays were
selected, based on speed plots generated from data collected by loop detectors. In the
case of the tachometer-equipped vehicles, data were collected twice a year (in the spring
and fall) during incident-free peak periods. From these outputs, maps were created
indicating the duration of congestion, average speed, and average travel time.
Congestion delay (person-hours of delay) was calculated as the product of the number of
vehicles delayed, additional travel time per vehicle due to traveling below 35 mph, and

average occupancy (persons per vehicle). The delay equation is as follows:

" . . . 1 1
Delay = 2V1 * P1 * L1 ”(SE—3?] (8)

i=1

where: i = Freeway segment i ,
n = Number of freeway segments,
Vi = Average congested traffic volume along segment i during a typical incident-
free weekday (vehicles),

Pi = Average vehicle occupancy along segment i (persons per vehicle),

21

Li = Length of freeway segment i (miles),

35 = Speed congestion threshold (mph), and

Sci = Average speed during congestion along segment i (mph).

This method measures total and recurring congestion. The speed (35 mph) and
minimum recurring congestion interval (15 minutes) are reasonable, but the method
neither accounts for small variations in traffic speed nor gives information regarding the
probability of congestion occurrence.

2.2 Discussion on the Current Congestion Measures

From the perspective of the data source used in the development of the current
congestion methodologies, two major data sources are used: historical and real. The
methodologies that are based on already available historical databases use an assumed
hourly traffic distribution in order to quantify congestion, while the other techniques use
real time speed and hourly traffic distribution data. The first four measures presented
above (CSI, RCI, LMDI, and TI) use historical databases. CSI, RC1, and LMDI use the
Highway Performance Monitoring System (HPMS) database, while the TI measure uses
the Traffic Accident Surveillance and Analysis System (TASAS) in California. The last
three measures (MMC, EC], and CALTRANS) use real time data, from loop detectors or
instrumented vehicles.

The first four measures are all derived from the 1985 HCM definition of LOS.
The CSI and RCI use LOS D (55 mph) as a threshold value between congested and
uncongested conditions, while LMDI uses a LOS F (30 mph). The TI methodology uses
a directional peak hour capacity per lane threshold of 2,000 vehicles, which corresponds

to LOS D. On the other hand, the MMC uses 30 percent detector occupancy as a

22
congestion threshold, which is generally equivalent to a HCM density threshold of 90
vehicles per lane per mile (severe congestion conditions). The last two measures (FCI
and CALTRANS) use slightly higher speed thresholds than the LOS F, namely they use
thresholds of 40 and 35 miles per hours, respectively.

With respect to specifying a minimum time interval threshold to define recurring
congestion, only the MMC and CALTRANS methodologies do so (5 and 15 minute
thresholds, respectively). Finally, none of the current measures is sensitive to short term
speed fluctuation within an hour, account for small traffic speed variations or spikes, or
estimate the probability of recurring congestion, or can be used to evaluate ATMS. In
general, the current recurring congestion measures use data from typical days in order to
quantify congestion.

It is also worth mentioning that the DRI and SR1 measures are just a variation of
the RC1 methodology. They are developed to provide measures that are perceived by the
public better than the RC1 measure. The current recurring congestion measures
assumptions and characteristics are summarized in Table 2.1.

2.3 Summary

Several indicators are used to identify recurring congestion based on either travel
time, delay, or speed. There are currently many available measures to assign quantitative
values to congestion. These measures fall into two major groups based on the databases
used; surrogate or real time data. The surrogate models are not sensitive to short term
traffic flow fluctuations within the hour. Moreover, some of the current real time data
measures account for the Short term fluctuations within the hour, but none of them

account for the traffic speed spikes or probability of recurring congestion.

23

Table 2.1 Current Congestion Methodologies Characteristics.

 

 

 

Current Congestion Measure
Characteristic
CSI RC1 LMDI Tl MMC F CI CALTRANS

Data Source Hist. Hist Hist Hist Real Real Real
Threshold Source HCM HC M HCM HCM Exp. Exp Exp
Threshold Measure v‘/c‘ V/C AADT'/c c o’ D‘ S‘ s D
Threshold Value 0.77 0.77 9.0 2.000 30 5 40 35 15
Equivalent S 55 55 30 55 25 40 35
Equivalent LOS D/E D/E F D/E F F F
Sensitivity to AS No No No No No No No
Probability Factor No No No No No No No
Evaluate ATMS No No No No No No No

 

 

 

 

 

 

 

 

 

 

Note: Hist = Historical.

Exp = Professional experience.

V = Traffic flow (vehicles per hour per lane).

C = Freeway capacity (vehicles per hour per lane).

AADT = Average Annual Daily Traffic (vehicles per day).
0 = Detector occupancy (%).

S = Speed (mph).

D = Minimum continuous duration (minutes).

Chapter 3

METHODOLOGY

This study is designed to develop a methodology to identify and quantify
recurring freeway congestion. The methodology is based on statistical modeling using
real time data from freeways in the Detroit, Michigan metropolitan area. The steps used
in this process are: 1) The peak traffic periods are identified from 24-hour l-minute
interval data, 2) Three speeds (30, 35, and 40 mph) and a minimum time interval (15
minutes) are selected as thresholds for defining recuning congestion, 3) The start time
and duration of congestion are then determined, 4) A measure for quantifying recurring
congestion is developed and applied to the freeway segments studied, and 5) sensitivity
analysis and validation of these models are also conducted.

3.1 Study Site

Data were obtained from two freeway segments in the Detroit metropolitan area
(Figure 3.1), where an extensive loop detector system is in place. The first segment, on
the 1-94 interstate freeway, extends between Moross and Van Dyke road (6.0 miles
East/West). The second segment, on the M-lO freeway, extends between Grand

Boulevard and Meyers Road (8 1/3 miles North/South).

24

25

 

 

Figure 3.1 Study Site Area Map.

26

The Annual Average Daily Traffic (AADT) for the first and second study
segments is 129,000 and 137,000 vehicle per day, respectively (MDOT, 1996). These
two segments were selected because continuous 24-hour l-minute aggregated data along
each segment were available from existing detectors in both directions. Schematic
diagrams of the study site detectors distribution on the 1-94 and M-lO freeways are
illustrated in Figures 3.2 and 3.3, respectively. A total of ninety one loop detectors are
embedded in the study segments with an average spacing of one third of a mile.

3.2 Data Collection

Data from ten typical weekdays in each month of an eight-month period between
December 1996 and July 1997 were used. Four F all/Winter months (December 1996 —
March 1997) and four Spring/Summer months (April 1997 — July 1997) were chosen as
these two groups have a monthly average daily traffic less than or similar to, respectively,
the annual average daily traffic (Turner, Lomax, and Levinson, 1996). One more month
of data (August, 1997) was collected to test and validate the developed congestion
models.

A detector's data file includes the following variables: detector location
identification, calendar date, military time, detector station type (mainline or ramp),
number of lanes, number of working detectors at a location, traffic volume (vehicles),
detector occupancy (%), and speed (miles per hour).

3.3 Study Approach

The approach used in this study is based on comparative statistical analysis of

data obtained from loop detectors. First, thresholds of speed, the minimum continuous

time interval to define recurring congestion, and the severity of congestion are defined

27

 

NQZD

Moross

Cadleux

Whittier

i

i

A //E\ A
N V N V V

Outer Rd. ‘1 l
W

 

Conner

M
V

French Rd.

 

w
Gratiot w
<

-1. > Van Dyke

 

 

 

Not to Scale

Figure 3.2 Schematic Diagram of Detector Locations in the I-94 Freeway.

28

 

M-lO N

Cl: Meyers fi
Cl:

CD.

mfim
an

El:

—lu:l

a: a:

Cl: Cl:

:11: Livemois

 

 

 

 

i.
i
HHHHEH

f—VV

Davison

 

 

 

Glendale

Webb

Chicago

CIairmount

Seward
Pallister

Grand
Blvd. T

 

 

r-EH

WAR/JAR
HBHHB BBB EIH
*HBHBBHHBHH 88
WW

 

 

 

Not to Scale

Figure 3.3 Schematic Diagram of Detector Locations in the M-10 Freeway.

29

based on the literature review and experience. A methodology to smooth the data from
Short interval incident-related traffic spikes is also developed. Using this methodology
and the defined thresholds, an algorithm is developed to identify start time and duration
of congestion at each detector location.

By using this algorithm, a preliminary analysis is conducted to assess the quality
and availability of data obtained from detectors and the adequacy of the sample size.
This analysis is used to define the AM and PM traffic peak time intervals and limit the
study to these intervals. SPSS is used to produce data files that only include the detector
locations that have continuous data during the defined peak time intervals.

The start time and duration of recurring congestion are recalculated based on the
selected refined database. The Analysis of Variance (ANOVA) statistical tests are used
to model recurring congestion at statistically similar locations. The developed models
allow for locations that have statistically similar start time and duration of recurring
congestion to be grouped together.

Indices are developed to measure and assign quantitative values to congestion. An
analysis of seasonal and weekday variations of the developed models are conducted. By
using one month of data, these models are tested. A comparison between recurring and
nonrecurring congestion estimates is performed. Finally, a comparison between the
congestion estimates of the developed and CALTRANS measures is also performed. The
development of the freeway congestion measure is presented in detail in the following

chapter.

Chapter 4

DEVELOPMENT OF FREEWAY CONGESTION MEASURE

In the previous chapter, a general description of the research methodology was
introduced. In this chapter, the methodology is presented in more detail and a freeway
recurring congestion measure is developed.

4.1 Definition of Congestion

Several congestion indicators and definitions were introduced in the literature
review chapter. Many of these methods define congestion based on the v/c ratio used in
the HCM to identify LOS thresholds. A few of them define congestion based on a traffic
speed threshold. In this study, congestion is defined when the traffic speed falls below a
specific threshold value. This definition is illustrated in Figure 4.1 based on a real speed
profile from a data collection station on the I-94 study segment. Further, severity of
congestion is defined based on the speed increment drop below the specified threshold.
In other words, the severity of congestion increases as the speed decreases.

The congestion speed threshold in the 1994 HCM is defined at the LOS E/F
breakpoint on freeways (HCM, 1994). This threshold seems to occur at significantly
higher speeds (50 instead of 35 mph) and lower densities than in the 1985 edition (HCM,
1985 and 1994). Some states use a congestion speed threshold that is lower than the

value specified in the 1994 HCM. For example, a 35 mph speed threshold is used by

30

31

 

70 1994 HCM
LOS E/F

Breakpoint

Speed (mph)

 

 

 

 

 

0200 3:00 6:00 9:00

Time (Wednesday, 2/ 12/1997)

Figure 4.1 Speed Profile on West Bound 1-94 at Gratiot Road.

12:00

32

CALTRANS to define congestion (Epps, Cheng, and May, 1994). Some other
congestion measurement methods use a speed of 30 mph as a threshold based on the LOS
F boundary as defined in the 1994 HCM. It is also believed that a traffic stream speed
below 40 mph is a strong indicator that flow is falling into the LOS F (forced-flow) realm.
The precise value of the threshold may not be critical, as one study has concluded, in most
cases, once speed fell below 50 mph, it also fell below 40 mph (Thurgood, 1996). The
speed profiles performed as part of this research also support this conclusion as illustrated
in the sample speed profile of Figure 4.1. Based on this discussion, the study proposed
testing three speed thresholds: 30, 35, and 40 mph.
4.2 Definition of Recurring Congestion

One of the issues to be resolved in developing a recurring congestion measure is
the definition of recurring congestion. The literature review presented in Chapter 2
identified one methodology (CALTRANS) that uses 15 minutes of continuous low-speed
operation as a time threshold for defining recurring congestion. In other words, recurring
congestion is assumed to occur when the average traffic speed falls below the congestion
speed threshold (35 mph in the CALTRANS methodology) for a continuous 15-minute
time interval (Epps, Cheng, and May, 1994).

This threshold was adopted for defining recurring congestion. Data from this
study Show that there is a significant variation in average speed calculated on a minute by
minute basis (Figure 4.1). A methodology is needed to smooth the data from short time

spikes. This methodology is described in the following section.

33

4.3 Methodology for Smoothing Recurring Congestion Duration

When the recurring traffic congestion state occurs, short term interruptions are
possible where an increase in speed above the congestion speed threshold is observed. A
similar situation is encountered during the uncongested traffic state, where this state is
interrupted by short term decreases in speed below the congestion Speed threshold.
Based on this understanding, a methodology has been developed to account for these
spikes in the traffic speed and smooth the data.

The methodology will be explained using two scenarios, often encountered during
data collection, as examples. The first scenario is characterized by the fact that a
congested condition occurs first, followed by an uncongested one, and then congested
and uncongested conditions are alternating. The second scenario refers to a situation
where uncongested conditions occur first, followed by congested conditions, and then
uncongested and congested conditions are alternating. Both scenarios and terminology
are illustrated in Figure 4.2.

The methodology’s rules are summarized as follows:

IfCl Z 15and NCI <15,thean = NC1+C1andCNj =0

IfCl 215andNC1 215,thean =ClandCNf = NCI

IfC1<15,thean = OandCNf = NC1+C1
where: C1 = Congested interval (minutes),

CN; = Uncongested interval (minutes),

Cf = Final combined congested interval (minutes), and

34

First Scenario

 

Congested
Interval of
C1 minutes

 

 

Uncongested
Interval of
NC] minutes

 

up to n alternating intervals

 

b

 

l

Beginning of Analysis Period

Second Scenario

 

Uncongested
Interval of
NC] minutes

 

 

Congested
Interval of
C1 minutes

 

up to n alternating intervals

 

b

 

l

Beginning of Analysis Period

Figure 4.2 Congested and Uncongested Traffic Conditions Scenarios.

 

 

35

CNf = Final combined uncongested interval (minutes).

Then, the resulting combined traffic conditions are tested against the third consecutive
traffic condition by using the same defined rules. Two illustrative examples are
presented in Figure 4.3 to explain how the developed methodology works.

The methodology is automated through a FORTRAN program. At each location,
the program identifies the following (a customized sample of the program’s output is
shown in Table 4.1):

1. Duration of congested and uncongested intervals (minutes),

2. Total traffic volume that does not experience recurring congestion (vehicles),

3. Total traffic volume that experiences recurring congestion (vehicles), and

4. Recurring congestion severity value that is defined as the summation of the

product of traffic volume and speed difference between the actual and the
recurring congestion threshold speed at each minute (vehicle miles per hour).

The methodology was tested on pilot data collected during September, 1996. The
start time and duration of congestion for a segment of west bound I-94 during the
morning peak period on 9/9/1996 are shown in Figure 4.4. The diagram shows how the
methodology smoothes the recurring congestion data and accounts for the small spikes in
traffic speed.

4.4 Preliminary Analysis

AS part of the preliminary analysis, the methodology was used to calculate the
start time and duration of recurring congestion at each detector location along the west
bound 1-94 freeway test section by using a 6-month database (12/96-5/97). The results

indicated that less than two percent of the cases have recurring congestion outside the

36

(3) Example 1:

Real Traffic Conditions

 

C1=18 NC1=7 C2=15 NC2=20

 

 

 

 

 

 

Smoothed Traffic Conditions

 

Cf = 40 NCf = 20

 

 

 

 

 

 

 

 

 

 

 

 

(b) Example 2:
Real Traffic Conditions
Cl=8 NC1=17 C2=15 NC2=3O
Smoothed Traffic Conditions
NCf= 25 Cf: 15 NCf: 30

 

 

 

 

 

Note: Time Interval, Minutes.

Figure 4.3 Examples on the Smoothing Methodology.

37

Table 4.1 Customized Sample Output (6/ 16/97, 6:00-10:00 am.)

 

 

8‘; 2.222281%. .
(vehICICS) (vehicles-mph)
14 NC 241 17931 0
15 NC 95 8311 0
15 C 50 3888 19035
15 NC 96 5657 0

 

 

 

 

 

 

 

identified AM and PM peak periods (6:00-10:00 am. and 3:00-7:00 pm, respectively).
Therefore, the analysis was limited to these defined peak intervals and data files were
reduced only to include records from detectors that were working continuously during
this extended AM and PM peak periods.

The preliminary analysis indicated that twelve of the data collection loop
detectors were not working during all data collection days. As an example, Figure 4.5
shows the functionality of the loop detectors on the west bound 1-94 freeway segment
during the six-month period (sixty 24-hour weekdays of data). A value of -1 in the graph
is assigned to stations with malfunctioning loop detectors.

4.5 Modeling Start Time and Duration of Recurring Congestion

A ninety five percent confidence interval is used to calculate the mean start time

and duration at each detector location. The lower limit of the start time and the upper

limit of the duration are used to plot the extended congestion interval at each location.

38

Duration of Congestion on WB I-94
Before Smoothing

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

22 - .I.I=I.
15 ; '.'. _
g I c I
'g 12 3
a l -| . —
7 3 .'_.
1 l ‘_I_ __ fl _. I F I n __ "r‘fi' 1 7M __ 7 .‘
6:00 7:12 8:24 9:36 10:48 12:00
Time (Monday 9/9/96)
Duration of Recurring Congestion on WB 1-94
After Smoothing
22 1;
i
16 i
g :
g 12 l
(I) .'
7 l
11- __ __ “V--- _ ‘ ._ L
6:00 7:12 8:24 9:36 10:48 12:00
Time (Monday 9/9/96)

Figure 4.4 Start and Duration of Congestion and Recurring Congestion Before and After
Smoothing by using a 35 mph threshold (WB 1—94).

39

39
. 34: ‘
29. l
1' 1
.l
l 4,‘ ll
. ‘ ‘
1 1‘
l 1
l1
1 ‘ .
. 9, ‘ 1
1 ‘ ‘ ‘
.l 1
. 1 - 1
l
, 1 1 .1
.1 W " ' 'I'I I I
12 3 4 5 6 7 8 9

10 11 12 13 I4 15 16 17 18 19 20 21 22
Station

 

5

Number of Days w1th Fuctional Detectors
— N
A

 

 

 

Note: -1 denotes that detector was not functioning during data collection period.

Figure 4.5 Functionality of Data Collection Stations on West Bound 1-94 Freeway
Segment During AM Peak Periods (12/1996-5/1997).

40

By using these extended congestion interval plots and ANOVA analysis, stations that
are statistically similar are grouped together over space. A minimum of five recurring
congested days is used as a threshold for defining start time or duration at a location.
4.6 Development of Recurring Congestion Freeway Measures
4.6.1 Probabilistic Recurring Congestion Indices

Based on the discussion throughout this chapter, congestion indices and measures

are developed. First, the Probabilistic Location Recurring Congestion Index (PLRCI) is

defined as follows:

Ni
2M7-

PLRCIs = P.- j" (1)

I

 

where: PLRClS = Probabilistic Location Recurring Congestion Index at a speed
threshold of s mph (dimensionless),
Mij = Recurring congestion index at location i during a time period T in a
congested day j (dimensionless),
= VCij/VTij

VCU = Volume of vehicles that have speed less than or equal to the speed
threshold at location i during a time period T in a congested day j
(vehicles),

an = Total volume of vehicles at location i during a time period T in a congested

day j (vehicles),

41
Pi = Probability of recurring congestion at location i,
= ni/Ni
ni = Total number of congested days at location i, and
N1 = Total number of available days at location i.

Equation 1 can also be expressed as follows:

m M V1“
PLRCI. = -—2 c’ (2)
. VTi'
l j=l J

 

The PLRCIS is a probabilistic index of the traffic volume that experiences
recurring congestion below speed threshold 8 relative to the corresponding total traffic
volume at a specific location and during a defined time interval. In other words, it is an
indicator of the probability of a vehicle experiencing recurring congestion at a specific
location.

Equation 1 can be expanded to calculate a Probabilistic Freeway Recurring

Congestion Index (PFRCI) as follows:

k-l
Z PLRCIi(O. 5(X1- 1.1+ X11+ 1))

PFRCI = ’=2 3
S X1-I.k-0.5(X1-1,1+Xk-l.k) ()

 

42
where: PFRCIs = Probabilistic Freeway Recurring Congestion Index at a speed

threshold of 3 mph (dimensionless),

PLRCIS = Probabilistic Location Recurring Congestion Index at location i and
speed threshold of 3 mph (dimensionless),

Xi_1,i = Distance between detector i and the immediate upstream detector i - 1

(miles),
X1. 1 + 1 = Distance between detector i and the immediate downstream detector
i + 1 (miles),
Xi.”‘ = Total distance between detectors i - 1 and k (miles), and
k = Total number of detectors included in the freeway segment.

By assuming equal spacing of loop detectors, Equation 3 can be simplified as

follows:

k —1
ZPLRCIi (4)

i=2

1

PFRCIs = ——
k —2

The PF RC1s is an index of the probability of recurring congestion along a freeway
segment during a specified time interval. It is an indicator of the extent of freeway
recurring congestion.

4.6.2 Probabilistic Recurring Congestion Severity Indices
A Probabilistic Location Recurring Congestion Severity Index (PLRCSI) is

defined as follows:

43

N1
zu-

PLRCSIs = P.- F‘ (5)

l

 

where: PLRCSIs = Probabilistic Location Recurring Congestion Severity Index at a
speed threshold of S mph (mph),
Sij = Speed drop below the threshold 5 at location i and during a time period
T in a congested day j (mph), and
Pi = as defined above.

The PLRCSIS is an index of the probabilistic Speed drop of the traffic below the
speed threshold s at a specific location and during a defined time interval. It is an
indicator of the severity of recurring congestion at a specified location.

Equation 5 can be expanded to calculate a Probabilistic Freeway Recurring

Congestion Severity Index (PFRCSI) as follows:

k—l
ZPLRCSIi(0.5(Xi-I,i+Xi,i+I))

PFRCSIs = i=2 (6)
X7). —0.5(X.--/.1+Xk - 1,1)

 

where: PFRCSIS = Probabilistic Freeway Recurring Congestion Severity Index (mph),

and other variables as defined above.

44

By also assuming equal spacing of loop detectors, Equation 6 can be simplified as

follows:

I k-l

PFRCSI. =— PLRCSI' 7
. [(42% , (2

4.6.3 Freeway System Recurring Congestion Measure

A Freeway System Recurring Congestion Measure (FSRCM) is defined as

follows:

 

k—l
FSRCMszZPi*0.5(X1—1.1+X1,1+1)*Vci*[ 1 J) (8)

. S—Si S
122

where: FSRCMS = Freeway System Recurring Congestion Measure (vehicle-hours),
Pi = Probability of recurring congestion at location i,
X - 1.1 = Distance between detector i and the immediate upstream detector i -— 1
(miles),
X, 1 + 1 = Distance between detector i and the immediate downstream detector
i+ 1 (miles),
s = Speed threshold (mph),

Vci = Total volume of vehicles that have speed less than or equal to 3 (vehicles),

45
Si = Average speed drop below the threshold 5 at location i, and
k = Total number of locations in the freeway segment.
By assuming equal detectors spacing (1/3 of a mile for the study segments),

Equation 8 can be simplified as follows:

 

k—l
FSRCMs = L1* 2101* Vci*( 1 J) (9)

. S— St S
1:2

where: L = Average spacing of data collection locations (miles).

The FSRCM is a freeway recurring congestion measure of delay over time and
Space. It provides a quantitative value to freeway recurring congestion on a segment or
areawide basis.
4.7 Summary

Definitions of congestion and recurring congestion were developed based on a
speed threshold (30, 35, and 40 mph). A methodology was also developed to detect and
smooth recurring congestion duration based on speed and minimum congestion duration
thresholds.

The AM and PM peak period intervals of 6:00-10:00 and 3:00-7:00 p.m.,
respectively, were identified based on a preliminary analysis. Further analyses in the

following chapters are limited to these peak intervals.

46

A methodology for modeling the start time and duration of recurring congestion
of a freeway segment was introduced. Location and freeway recurring congestion indices
and measures were also developed.

These indices and measures are capable of identifying and quantifying freeway
recurring congestion on a location, segment, or areawide basis. They also account for
small variations in traffic speed within the peak periods and utilize a recurring congestion
probability factor. These measures are also suitable for use in evaluating ATMS because
they account for small variations of traffic speed. The following chapter presents the

analysis and results of implementing this methodology.

Chapter 5

ANALYSIS AND RESULTS

The testing was based on real time data from loop detectors embedded in an urban
freeway network. Analyses were performed on two freeway segments during both the
AM and PM peak periods. Testing recurring congestion index (M) equality at three
speed thresholds is introduced in the first section and data quality and results follow.

5.1 Freeway Recurring Congestion Speed Thresholds

The hypothesis that the recurring congestion index (M) values are equal for three
speed thresholds (30, 35, and 40 mph) is tested. This test is used to determine the
sensitivity of this index to the selected speed threshold and accordingly, select threshold
or thresholds for M measurement.

Tables 5.1 and 5.2 show the results of testing the hypothesis on two freeway
segments. The recurring congestion index is the percentage of vehicles that experience
speed below the speed threshold relative to the total volume of vehicles during a peak
period. The analysis was performed by using records from congested stations on the WB
1-94 AM and NB M-10 PM freeways (a minimum sample size of 5 congested days was
used as a selection threshold). ANOVA was performed to compare the three M mean
values at each station. The recurring congestion index (M) is not statistically different at

Significance level of 5% (Tables 5.1 and 5.2) when using each of the three proposed

47

48

Table 5.1 Mean Recurring Congestion Indices Comparison (WB I-94 AM Peak).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Standard Deviation of
Mean Ml
Sample M
Station (%) P-value2
Size (%)
I.D. (%)
(N) Threshold (mph) Threshold (mph)
30 35 4O 30 35 4O
2 7 26 28 29 20 21 21 95.6
3 5 32 34 41 21 24 24 78.7
4 8 36 37 42 23 23 23 84.7
7 5 26 36 41 14 17 18 39.6
9 8 36 41 49 23 21 23 48.6
10 8 39 48 56 22 2O 22 30.2
12 7 42 49 57 22 22 20 42.4
13 5 43 58 6O 16 l3 13 17.1
14 8 28 35 40 l8 17 17 38.4
15 16 26 32 35 16 15 17 22.4
16 23 23 29 32 l6 16 16 17.1
18 19 21 28 34 17 16 18 7.8
19 39 29 36 41 15 l6 17 0.4
20 25 33 38 44 16 16 17 6.8
21 27 44 47 49 14 13 13 35.0
Note: 1 Mean recurring congestion index.

2 P-value = Probability of (F-statistic > F-observed) assuming that the observed means are statistically equal
at the three speed thresholds.

49

Table 5.2 Mean Recurring Congestion Indices Comparison (NB M-lO PM Peak).

 

Standard Deviation of

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mean M'
Sample M
Station (%) P-value2

Size (%)
1.1). (%)

(N) Threshold (mph) Threshold (mph)

30 35 40 30 35 40
45 13 28 33 34 16 18 18 59.8
46 16 29 36 40 l7 l9 18 23.1
47 14 25 33 37 19 20 20 25.0
48 19 26 31 36 l6 17 18 20.2
49 8 45 54 56 13 16 17 33.7
51 13 28 38 49 21 23 25 8.2
52 9 31 45 52 20 21 25 13.3
59 5 13 18 23 7 7 4 8.1
Note: 1 Mean recurring congestion index.

2 P-value = Probability of (F -statistic > F -observed) assuming that the observed means are statistically equal
at the three speed thresholds.

50
speed thresholds at 22 of 23 stations. Station 19 is the exception.

Further analysis of the three M mean values by using the Bonferroni multiple
comparison tests indicates the same previous results. Table 5.3 Shows the Bonferroni
multiple comparison tests for station 19 which indicates that the M mean value obtained
by using a 35 mph threshold is not statistically different than that obtained by using 30 or
40 mph threshold at a level of significance of 5%. The table also shows that the M mean
values obtained by using a 30 mph threshold is statistically different than that obtained by
40 mph threshold at any reasonable significance level.

The above analyses Show that if the traffic speed drops below 40 mph it nearly
always falls below 30 mph. The differences in the mean M values at station 19 may be
attributed to the location of the station in the upstream area of an exit ramp to a major
road (Van Dyke Road).

To study station 19 in more detail, the average speed profiles for station 19 and
another station (station 2) where the M mean values, by using either one of the three
thresholds, are not statistically different (Figure 5.1). The average slope of the speed
profile curve where the speed falls from 40 to 30 mph is approximately the same (-0.7
mph per minute) for stations 2 and 19. On the other hand, the average slope of the speed
profile curve where the speed rises from 30 to 40 mph for station 2 (2.0 mph per minutes)
is approximately three times that of station 19 (0.7 mph per minute). This indicates that
both stations 2 and 19 have the same pattern when the speed falls under 40 mph. The
patterns of these stations are different when the speed rises from 30 to 40 mph. This
indicates that station 19 has a unique congestion pattern different than other stations.

It can be concluded that the recurring congestion index (M) is not statistically

51

Table 5.3 Comparison of Recurring Congestion Index (Mg) by Using Three Speed
Threshold (Station 19).

 

 

 

 

 

 

 

 

 

 

 

Speed Threshold 1 Speed Threshold 1 Mean Difi‘ 1-1' Std. Err.2
P-value3
(mph) (mph) (mph) (mph)
30 35 -007 0.04 0.14
40 -012‘ 0.04 0.00
35 30 0.07 0.04 0.14
40 -005 0.04 0.48
40 30 0.12‘ 0.04 0.00
35 0.05 0.04 0.48
Note: 1 Difference between mean Mi by using thresholds l and J.

2 Standard error between mean Mi by using speed thresholds l and J.

3 P-value = Probability of (t-statistic > t-observed) assuming that the observed mean differences are
statistically equal at the corresponding speed thresholds.

* The mean difference of Mi is significant at the 0.05 level.

52

Average Speed (mph)

 

 

 

10 Station 19 ----- Station 2 .
o _ __ 2 - 2— _ - . . __..s
o o o o o o o o o
so so I\ l\ 00 00 as as C
Time (AM)

Figure 5.1 Speed Profiles for Stations 2 and 19 (12/1996-7/1997).

53

different for each of the three selected speed thresholds of 30, 35, and 40 mph. In other
words, to measure recurring congestion it is sufficient to use any one of these speed
thresholds. Accordingly, the analyses and results throughout the rest of this study will be
presented by using one speed threshold (35 mph).

Figure 5.2 Shows the average speed profile during the AM peak periods on the
WB 1-94 and SB M-10 freeways. This figure shows that the average speed on these two
segments during the AM congestion ranges between 25 to 30 mph, except for a few
stations. This pattern also confirms the previous conclusion in this regard; the recurring
congestion index is the same regardless of speed threshold values of 30 mph and above.
5.2 Data Availability

The functionality of the detectors varies from station to station, freeway to
freeway, and the AM to PM peak periods as shown in Tables 5 .4 and 5.5. Twelve of the
ninety one detectors (13%) were not operational during the test period. The total
available data on each of remaining 79 detectors ranged from one day to seventy two
days (of the 80 days in the sample). The average number of days of data are 37 and 42
per detector during the AM and PM peak periods, respectively. The average number of
days of data are 38, 29, 31, and 56 days per detector on the WB 1-94, EB [-94, NB M-lO,
and SB M-lO freeways, respectively.

In general, congestion occurs on west bound 1-94 (inbound to the city center)
during the morning peak period. Non-congested traffic conditions prevail on both west
and east bound [-94 during the PM peak period. Congestion exists on both south and

north bound M-10 during the AM and PM peak periods.

54

35 . , , 2, _ __

 

20 l i, 7

Average Speed (mph)

15...-.._
69717375

1 _ T ‘ '— T

77 79 81 83 85 87 89
Station (SB M-10)

35 . WW.

Average Speed (mph)

 

15+ 1 ‘ ‘1": 1 1’1 1 1 ‘7 7*1‘ 'Vr ' lira 12
l 3 5 7 9 ll l3 l5 l7 19 21

Station (WB 1-94)

Figure 5.2 Average Speed on WB 1-94 and SB M-10 Freeways (AM Peak Periods).

Note:

55

Table 5.4 Data Availability on the I-94 Study Segment.

 

 

 

 

 

 

West Bound East Bound
Functional Rec. Cong. Functional Rec. Cong.
Station Station
Days Days Days Days
ID. ID.
AM PM AM PM AM PM AM PM
1 35 44 3 0 23 -1 -l -l -l
2 45 52 7 1 24 55 58 0 l7
3 42 51 8 0 25 8 12 0 l
4 37 40 10 l 26 -l -l -1 -1
5 -I -l -l -l 27 3 1 0 0
6 -l -l -l -l 28 7 8 0 0
7 32 44 5 l 29 64 67 0 12
8 -l -l -l -1 30 64 67 0 2
9 42 45 IO 2 31 -l -l -l -l
10 50 55 14 2 32 -l -l -1 -l
11 49 55 7 2 33 54 56 0 O
12 50 62 l l 0 34 36 37 0 1
13 49 63 7 0 35 5 6 0 0
14 44 59 I7 2 36 9 9 0 0
15 49 62 26 1 37 60 63 0 l
16 53 60 33 2 38 26 30 0 2
I7 -1 -1 -l -1 39 I3 12 0 0
18 50 54 30 2 40 61 63 0 2
I9 50 53 48 4 41 36 35 0 3
20 50 54 29 2 42 -l -l -l -1
21 26 31 23 8 43 60 63 0 3
22 8 l 1 4 2 44 54 6O 0 8

 

 

 

 

 

 

 

 

 

 

-1 denotes that detectors did not function during the active data collection period (80 days).

 

Note:

56

Table 5.5 Data Availability on the M-lO Study Segment.

 

 

 

 

 

 

North Bound South Bound
Functional Rec. Cong. Functional
Station Station RFC: Cong. Days
Days Days Days
ID. ID.
AM PM AM PM AM PM AM PM

45 45 50 0 I7 69 l7 l9 1 l
46 65 63 0 24 70 l6 l8 2 0
47 13 50 0 21 71 58 69 34 0
48 39 58 0 26 72 62 72 40 0
49 34 42 0 20 73 46 52 10 8
50 -l -l -l -l 74 70 75 26 0
51 59 70 0 I6 75 61 70 27 l
52 59 70 0 I7 76 67 74 31 2
53 56 60 0 I l 77 18 28 10 7
54 67 69 0 4 78 68 71 32 l
55 l l 21 l l 79 67 73 16 3
56 66 70 O 4 80 8 l l 3 0
57 -l -l -l -l 81 10 10 2 O
58 -l -l -l -l 82 70 76 4 0
59 48 55 0 10 83 70 75 3 0
60 34 44 l 4 84 72 75 3 0
61 9 12 0 l 85 28 29 2 l
62 57 62 l 2 86 70 72 2 2
63 39 45 l 3 87 72 74 2 l
64 35 46 l l 88 51 54 l l
65 4 5 0 0 89 70 74 l I 0
66 7 8 0 0 90 65 69 IS 0
67 8 8 0 0 91 66 69 16 l
68 26 31 0 l _ _ _ _ -

 

 

 

 

 

 

 

 

 

 

-1 denotes that detectors did not function during the active data collection period (80 days).

 

57

5.3 Freeway Recurring Congestion Probability

The probability of recurring congestion at a data collection station is defined as
the ratio of the number of congested days at that station over the number of days with
valid data. The probability of congestion on south and north bound M-10 during the AM
and PM peak period is shown in Figure 5.3. In general, the probability of congestion
during the AM peak period increases as far as station 77, then decreases as traffic flow
approaches the city center (south of Milwaukee Rd.). The same pattern applies during
the PM peak period as traffic flow departs the city center. This pattern can be explained
by the fact that suburban commuters destination is to the city center during the AM peak
period and out of the city center during the PM peak period. Deviation of stations 71 and
72 (SB M-10) from this pattern during the AM peak period is recommended for further
analysis in future studies by collecting detailed lane-by-lane data.

The above pattern also applies to the I-94 freeway segment as shown in Figure
5.4, except that congestion only occurs in one direction, namely west bound, during the
AM peak period. In general, east bound I-94 does not experience congestion either
during the AM or PM peak periods. Deviation of stations 19 and 21 (WB 1-94) from this
pattern during the AM peak period is attributed to the locations of these stations upstream
an exit ramp to a major road (Van Dyke Rd.) that results in a different congestion pattern.

Table 5.6 summarizes the recurring congestion probabilities of the freeway
segments. The table shows that the average probability of recurring congestion on both
segments during the AM peak interval is higher than that of the PM peak interval. The

difference in the average recurring congestion probability between the AM and PM peak

58

80

701

LII
o
Milwaukee Rd.

 

 

8°.
C‘.
.9
273
Q)
00
t:
8
w 404
.E
t:
g 30
O
E‘.
o 20“.
f?
E 10
m
.0
g 0

45 47 49 51 53 55 57 59 61 63

-10 1
Station ID. (NB M-lO/PM)

80 1
f; 70 -
°\
5 60 J
2;» 50
8 .
so 40 1 1 l
.s »
:3: 30 «1 :2 y 1
32 i9 1 l

” 1

“5 204 «’2‘ 1 . i ~ l
e E ‘ , 1
a 10 « ll 1 1 l
2 1
:2? 0 l. . l .

10 69 71 73 75 77 79 81 83 85 87

 

Station ID. (SB M-lO/AM)

Note: Negative value denotes that a station was not functioning during the data collection period.

Figure 5.3 Recurring Congestion Probability on the M-10 Freeway Segment.

65

89

Meyers Rd.

Milwaukee Rd.

91

59

100
A 90
5 80-:
8
a 70
O
E“ 60
U '0'
E" 50 ‘ M
5 4o 3
8 E
55 301 2
O
s 20‘
”III I I I
E 0- - -—- .-. a " ' - - -
-10 1 3 5 7 9 11 13 15 17 19 21
Station ID. (WB l-94/AM)
100
90.
$3 80.
C
.2 70
a
:5)“ 60 g
D .
go 501-; a
.E Q m
:1 40- g 8
,_ 301 2
0
g 20.
g 103 I I
t. l
9- 0l_. ,l,_ . , .-._.._,7..I. , .J .-.I._,l.,
_10 23 25 27 29 31 33 35 37 39 41 43

Station ID. (EB I-94/PM)

Note: Negative value denotes that a station was not functioning during the data collection period.

Figure 5.4 Recurring Congestion Probability on the 1—94 Freeway Segment.

Van Dyke Rd.

60

Table 5.6 Summary of Recurring Congestion Probability (%).

 

 

 

Freeway M- 1 O I-94
SB/AM NB/PM WB/AM EB/PM
Minimum 2 0 9 0
Maximum 65 48 96 29
Average 25 1 6 39 6

 

 

 

 

 

 

 

periods on the I-94 freeway is higher than that on M-lO. The table also Shows that the I-
94 freeway is more congested than M-10 during the AM peak period.
5.4 Start Time and Duration of Freeway Recurring Congestion

Figures 5.5 and 5.6 show the start time and duration of recurring congestion on
M-10 and I-94 freeways during the peak periods. The average AM peak period recurring
congestion on the I-94 freeway starts 34 minutes earlier than on the M-lO. The average
AM peak period recurring congestion start times on the 1-94 and M-10 freeways are 7:04
and 7:38 am, respectively. However, the average AM peak period recurring congestion
on both freeways ends approximately at the same time with a difference of 5 minutes
(8:55 and 8:50 am. for the 1-94 and M-10 freeways, respectively). This is because the
AM peak period recurring congestion on the 1-94 freeway lasts longer than that of the M-

10, namely 111 and 72 minutes, respectively.

89 j
87 "I
85 j
33 ‘

811

Station (SB M-lO/AM)

 

300 400 500 600

Time (Accumulative Minutes Starting from Midnight)

Station (NB M-lO/PM)

 

900 1000 110 1200

3
,3.
1

Time (Accumulative Minutes Starting from Midnight)

Figure 5.5 Recurring Congestion Start Time and Duration on the M-10 Freeway.

62

Station (WB I-94/AM)

 

 

300 400 500 600

Time (Accumulative Minutes Starting from Midnight)

 

31‘

Station (EB I-94/PM)

29' —
271

25
—
2.1

1“” “ '—'— —‘ " r _— fiq—‘m _ ' — '" — ”"

900 1000 1100 1200

 

Time (Accumulative Minutes Starting from Midnight)

Figure 5.6 Recurring Congestion Start Time and Duration on the I-94 Freeway.

63

The average start time and duration of the PM peak period recurring congestion
on the M-IO freeway are 4:20 pm. and 86 minutes, respectively. This average PM peak
period recurring congestion lasts 14 minutes longer than that of the average AM peak
period (86 and 72 minutes, respectively). The PM peak period recurring congestion on
the I-94 freeway is not significant.

The average AM peak period recurring congestion extends for a greater distance
on the I-94 freeway than on M-lO. In other words, the AM peak period recurring
congestion covers more distance (miles) on the 1-94 freeway than on M-lO.

The study of the AM peak period recurring congestion pattern reveals the
following: (a) as the traffic flow moves toward the city center, recurring congestion on
both freeways starts at a later time, and (b) the upstream half of both freeways has a
recurring congestion duration longer than the downstream half. In other words, the AM
peak period recurring congestion decreases as the traffic flow moves towards the city
center. The same pattern applies to the PM peak period on the M-lO freeway when the
traffic flow moves away from the city center; i.e. recurring congestion starts at a later
time and lasts for a shorter duration. No specific pattern can be applied to the PM peak
period recurring congestion on the 1-94 freeway because it is not significant.

The development of a data sampling plan involves: (a) establishing a baseline for
future analyses, (b) determining the most appropriate time intervals and threshold speed to
define congestion, and (c) testing the stability of this measure of congestion over time and
distance. The sampling plan was established by grouping locations based on the statistical
similarity of the freeway recurring congestion start time and duration (a minimum sample

size of five congested days).

64

Figures 5.7 and 5.8 Show that the freeway locations can be grouped based on the
statistical similarity of the recurring congestion start time and duration. A significance
level of 5% is used as an analysis threshold (a minimum sample size of five congested
days was used). Figures 5.7 and 5.8 support the same recurring patterns that were
discussed throughout this section.

In summary, this plan allows reduction of (a) the number of data collection
locations, and (b) the frequency of data collection during the peak period necessary for
recurring congestion measurement. For example, sampling at one location between
stations 7 and 13 (Figure 5.8) during the AM peak period is sufficient to estimate the
recurring congestion along that freeway segment (at a 5% significance level).

5.5 Freeway Recurring Congestion Indices and Measures
5.5.1 Probabilistic Location Recurring Congestion Indices

The Probabilistic Location Recurring Congestion and Severity Indices (PLRCI
and PLRCSI) were calculated for the study freeway segments and are presented in Tables
5.7 through 5.10. The calculations are based on the mean values of the probability of
congestion, recurring congestion index, and severity of recurring congestion index at
each station (using Equations 2 and 5 in Chapter 4).

A sample calculation of the PLRCI and PLRCSI values for station 1 during the
AM peak period (Table 5.6) is provided as follows:

Mean recurring congestion probability = Pi = 8.6 %

Mean recurring congestion index = Mi = 27.8 %

Mean recurring congestion severity index = 31 = 10.1 mph

PLRCI = Pi * Mi = 0.086 * 0.278 = 239 x 10“1

65

91 ‘

 

74-79

7. -

Y ___ . i _

300 400 500 600

Grouped Stations (SB M-lO/AM)

 

Time (Accumulative Minutes Starting from Midnight)

51-53 I

 

4549 l

Grouped Stations (NB M-lO/PM)

 

900 1000 1100 1200

Time (Accumulative Minutes Starting from Midnight)

Figure 5.7 The M-10 Freeway Recurring Congestion Start Time and Duration Groups.

21

19-20

7-13 '

Grouped Stations (WB l-94/AM)

 

1* fi _ ..
300 400 500 600

Time (Accumulative Minutes Starting from Midnight)

Figure 5.8 The 1-94 Freeway Recurring Congestion Start Time and Duration Groups.

Note:

67

Table 5.7 Probabilistic Location Recurring Congestion Indices (WB I-94).

 

 

 

 

P,‘ M? sf PLRCI‘ PLRCSI’
Station
(%) (%) (mph) x 10“ (mph) x 10'2
1.1).

AM PM AM PM AM PM AM PM AM PM

1 8.6 0.0 27.8 0.0 10.1 0.0 239 0 86 0
2 15.6 1.9 28.3 6.8 12.1 9.5 441 13 188 18

3 19.0 0.0 29.7 0.0 8.4 0.0 566 0 160 0
4 27.0 2.5 31.8 7 8 12.1 20.2 860 19 328 51
5 21.3 2.4 34.0 11.0 10.5 20.2 726 26 223 48
6 21.3 2.4 34.0 11.0 10.5 20.2 726 26 223 48
7 15.6 2.3 36.2 14.2 8.8 20.2 566 32 138 46
8 15.6 2.3 36.2 14.2 8.8 20.2 566 32 138 46
9 23.8 4.4 36.8 18.4 9.4 18.2 875 82 224 81
10 28.0 3.6 34.4 35.6 8.2 19.3 963 129 228 70
11 14.3 3.6 39.9 44.3 6.4 20.5 570 161 91 75

12 22.0 0.0 38.3 0.0 7.5 0.0 843 0 164 0

13 14.3 0.0 50.0 0.0 8.1 0.0 714 0 116 0
14 38.6 3.4 24.8 10.7 6.9 15.9 958 36 265 54
15 53.1 1.6 25.8 11.1 8.0 16.9 1367 18 424 27
16 62.3 3.3 25.8 11.7 7.1 16.4 1605 39 440 55
17 62.3 3.3 25.8 11.7 7.1 16.4 1605 39 440 55
18 60.0 3.7 24.5 17.9 6.4 14.8 1471 66 382 55
19 96.0 7.5 33.0 15.6 9.8 16.6 3165 118 942 125
20 58.0 3.7 35.6 22.2 9.8 19.2 2063 82 566 71
21 88.5 25.8 46.9 24.3 14.1 13.6 4144 628 1250 350
22 50.0 18.2 24.8 11.1 6.6 7.1 1241 201 330 130

 

 

 

 

 

 

 

 

 

 

 

1 Pi = Probability of recurring congestion at location i (%).
2 M, = Mean recurring congestion index at station i (%).

3 s; = Mean recurring congestion severity at station i (mph).
4 PLRCI = Probabilistic Location Recurring Congestion Index (dimensionless).
5 PLRCSI = Probabilistic Location Recurring Congestion Severity Index (mph).

 

Note:

68

Table 5.8 Probabilistic Location Recurring Congestion Indices (EB I-94).

 

 

 

 

Pl‘ Mil sf PLRCI“ PLRCSI3
Station
(%) (%) (mph) x 104 (mph) x 10'2
ID.
AM PM AM PM AM PM AM PM AM PM
23 0.0 12.5 0.0 10.6 0.0 7.1 0 133 0 89
24 0.0 29.3 0.0 26.2 0.0 9.5 0 768 0 278
25 0.0 8.3 0.0 20.6 0.0 2.6 0 I72 0 22
26 0.0 8.3 0.0 20.6 0.0 2.6 0 172 0 22
27 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0 0
28 0.0 0.0 0.0 0.0 0.0 0.0 0 0 O 0
29 0.0 17.9 0.0 40.1 0.0 4.1 0 718 0 73
30 0.0 3.0 0.0 19.3 0.0 8.8 0 58 0 26
31 0.0 3.0 0.0 19.3 0.0 8.8 0 58 0 26
32 0.0 0.0 0.0 0.0 0.0 0.0 O 0 0 0
33 0.0 0.0 0.0 0.0 0.0 0.0 0 0 O 0
34 0.0 2.7 0.0 15.7 0.0 7.4 0 42 0 20
35 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0 0
36 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0 0
37 0.0 1.6 0.0 25.9 0.0 3.9 0 41 0 6
38 0.0 6.7 0.0 18.9 0.0 8.2 0 126 0 55
39 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0 0
40 0.0 3.2 0.0 34.7 0.0 7.7 0 110 O 24
41 0.0 8.6 0.0 31.9 0.0 10.9 0 273 0 94
42 0.0 6.7 0.0 29.6 0.0 9.1 0 197 0 60
43 0.0 4.8 0.0 27.3 0.0 7.2 0 130 0 34
44 0.0 13.3 0.0 25.8 0.0 7.6 0 344 0 101

 

 

 

 

 

 

 

 

 

 

 

1 Pi = Probability of recurring congestion at location i (%).
2 M; = Mean recurring congestion index at station 1 (%).

3 83 = Mean recurring congestion severity at station 1 (mph).
4 PLRC1= Probabilistic Location Recurring Congestion Index (dimensionless).
5 PLRCSI = Probabilistic Location Recurring Congestion Severity Index (mph).

 

69

Table 5.9 Probabilistic Location Recurring Congestion Indices (NB M-lO).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P.‘ MK s." PLRCI‘ PLRCSI’
Station 0 / 4 _2

(/o) ”76) (mph) x 10 (mph) x 10

ID.
AM PM AM PM AM PM AM PM AM PM
45 0.0 34.0 0.0 29.6 0.0 11.9 0 1006 0 403
46 0.0 38.1 0.0 28.6 0.0 9.2 0 1091 0 349
47 0.0 42.0 0.0 27.1 0.0 8.6 0 1140 0 361
48 0.0 44.8 0.0 25.9 0.0 9.5 0 1162 0 426
49 0.0 47.6 0.0 31.8 0.0 6.7 0 1515 0 321
50 0.0 22.9 0.0 33.5 0.0 7.1 0 765 0 163
51 0.0 22.9 0.0 33.5 0.0 7.1 0 765 0 163
52 0.0 24.3 0.0 29.4 0.0 5.2 0 713 0 125
53 0.0 18.3 0.0 20.1 0.0 5.4 0 369 0 98
54 0.0 5.8 0.0 13.0 0.0 6.6 0 75 0 38
55 9.1 4.8 18.9 17.6 10.0 2.1 171 84 91 10
56 0.0 5.7 0.0 13.1 0.0 8.8 0 75 O 50
57 0.0 5.7 0.0 13.1 0.0 8.8 0 75 0 50
58 0.0 5.7 0.0 13.1 0.0 8.8 0 75 0 SO
59 0.0 18.2 0.0 16.6 0.0 5.6 0 303 0 102
60 2.9 9.1 22.5 20.4 17.8 8.1 66 185 52 73
61 0.0 8.3 0.0 26.9 0.0 7.6 0 224 0 63
62 1.8 3.2 29.1 19.9 16.9 11.8 51 64 30 38
63 2.6 6.7 36.9 24.2 21.1 9.3 95 161 54 62
64 2.9 2.2 21.7 14.4 16.8 13.0 62 31 48 28
65 0.0 0.0 21.7 0.0 0.0 0.0 0 0 0 0
66 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0 0
67 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0 0
68 0.0 3.2 0.0 17.1 0.0 23.0 0 55 0 74
Note: 1 P; = Probability of recurring congestion at location i (%).

2 M = Mean recurring congestion index at station 1 (%).
3 s; = Mean recurring congestion severity at station i (mph).
4 PLRCI = Probabilistic Location Recurring Congestion Index (dimensionless).
5 PLRCSI = Probabilistic Location Recurring Congestion Severity Index (mph).

 

Note:

70

Table 5.10 Probabilistic Location Recurring Congestion Indices (SB M-10).

 

 

 

 

P.‘ M? s.-‘ PLRCI“ PLRCSI“
Station % (%) (mph) x 10“ (mph) x 10'2
1.1).
AM PM AM PM AM PM AM PM AM PM
69 5.9 5.3 15.9 35.2 10.2 23.2 94 185 60 122
70 12.5 0.0 6.9 0.0 5.9 0.0 86 0 74 0
71 58.6 0.0 30.4 0.0 8.1 0.0 1780 0 474 0
72 64.5 0.0 31.8 0.0 8.4 0.0 2052 0 543 0
73 21.7 15.4 12.2 11.1 5.0 6.1 266 170 109 93
74 37.1 0.0 28.3 0.0 7.5 0.0 1052 0 279 0
75 44.3 1.4 30.2 8.3 8.7 6.2 1338 12 386 9
76 46.3 2.7 30.0 15.8 8.6 15.8 1386 43 397 43
77 55.6 25.0 17.8 15.7 8.5 10.6 991 393 475 264
78 47.1 1.4 30.0 41.9 7.3 16.5 1410 59 342 23
79 23.9 4.1 28.3 43.1 3.9 13.7 676 177 93 56
80 37.5 0.0 30.9 0.0 2.6 0.0 1161 0 98 0
81 20.0 0.0 14.8 0.0 3.7 0.0 296 0 75 0
82 5.7 0.0 10.0 0.0 6.5 0.0 57 0 37 0
83 4.3 0.0 10.6 0.0 6.3 0.0 45 0 27 0
84 4.2 0.0 16.5 0.0 9.7 0.0 69 0 40 0
85 7.1 3.4 22.1 10.4 7.5 13.2 158 36 53 46
86 2.9 2.8 22.5 10.4 8.5 13.0 64 29 24 36
87 2.8 1.4 18.1 18.3 8.0 20.6 50 25 22 28
88 2.0 1.9 25.0 22.2 4.5 23.6 49 41 9 44
89 15.7 0.0 29.1 0.0 6.9 0.0 457 0 108 0
90 23.1 0.0 26.6 0.0 10.2 0.0 614 0 235 0
91 24.2 1.4 33.3 7.1 9.2 14.3 807 10 223 21

 

 

 

 

 

 

 

 

 

 

 

1 Pi = Probability of recurring congestion at location i (%).
2 Mi = Mean recurring congestion index at station 1 (%).

3 s) = Mean recurring congestion severity at station 1 (mph).
4 PLRCI = Probabilistic Location Recurring Congestion Index (dimensionless).
5 PLRCSI = Probabilistic Location Recurring Congestion Severity Index (mph).

 

71

PLRCSI = Pi * si = 0.086 * 10.1: 86 x104 mph

The PLRCI is an indicator of the frequency of recurring congestion while
PLRCSI is an indicator of its severity. For example, stations 61 and 63 (Table 5.9) have
almost the same recurring congestion severity value during the PM peak period (63 and
62, respectively) but station 61 is more congested than station 63 by a factor of two. This
situation indicates that when recurring congestion occurs at stations 61 and 63 during the
PM peak period, the traffic experiences almost the same speed drop below the 35 mph
speed threshold, but the average volume of congested vehicles is twice as great for station
61 compared to station 63.

The PLRCI and PLRCSI quantify congestion at a specific location. Thus, these
measures do not capture the extent of recurring congestion along a freeway segment or
compare the levels of recurring congestion on different freeway segments. For these
purposes, PF RC1 and PFRCSI are developed next.

5.5.2 Probabilistic Freeway Recurring Congestion Indices

The Probabilistic Freeway Recurring Congestion and Severity Indices (PFRCI
and PF RCSI) are indicators of the extent of freeway recurring congestion and its severity
along a freeway segment. Table 5.11 shows PF RC1 and PFRCSI values for the study
segments.

Table 5.11 shows that even though both the WB I-94 and SB M-lO freeway
segments are congested during the AM peak, I-94 is more congested than M-10 by a
factor of 2. This ratio also applies to congestion severity on these two freeway segments
during the AM peak period. This an indication that the level of congestion on WB [-94

during the AM peak period is twice as much as on SB M-10.

72

Table 5.11 Probabilistic Freeway Recurring Congestion Indices.

 

 

 

 

 

 

 

 

 

 

 

PFRCI2 PFRCSI3 (mph)
Freeway Kl
x 10" x 10'2
AM PM AM PM
EB 1-94 21 0 151 0 39
WE 1-94 22 1240 77 347 64
SB M-10 22 703 49 195 32
NB M-10 23 21 423 13 122
Note: 1 k = Total number of data collection stations.

2 PFRCI = Probabilistic Freeway Recurring Congestion Index (dimensionless).
3 PFRCSI = Probabilistic Freeway Recurring Congestion Severity Index (mph).

73

The table also shows the NB M-IO freeway segment is the most congested
segment during the PM peak period. Even though this congestion is less than half of
what is experienced on the SB M-1 0 freeway segment during the AM peak period, its
severity is relatively high.
5.5.3 Freeway System Recurring Congestion Measure

The Freeway System Recurring Congestion Measure (FSRCM) is a measure of
the average daily traffic delay over a freeway system (vehicle-hours). Vehicle delay
(vehicle-hours) values were calculated for the freeway study stations (based on Equation
8 in Chapter 4). Tables 5.12 through 5.15 summarize the results. The maximum values
of the vehicle delay, excluding the odd stations 19-21 (WB I-94) and 71-72 (SB M-IO),
range from 223 to 246 vehicle-hours.

A summary of the study freeway segments' vehicle delay values is presented in
Table 5.16. The FSRCM of the freeway system is calculated as the summation of the
vehicle delays shown in this Table. Accordingly, the study FSRCM is calculated as
5,728 vehicle-hours during both the AM and PM peak periods (12/96-7/97).
5.6 Summary

A freeway recurring congestion speed threshold was defined based on statistical
analysis of the recurring congestion index means at three selected speed thresholds. The
data availability and probability of recurring congestion at each data collection location
were also presented.

The start time and duration of recurring congestion at each study segment location
were identified. The locations that have statistically similar start time and duration were

grouped together to produce models that can be used in future data collection strategies.

74

Table 5.12 Vehicle Delay (WB I-94).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P,‘ Vciz 5,3 Vehicle Delay
Station

(%) (vehicles) (mph) (vehicle-hours)

I.D.
AM AM AM AM PM PM AM PM
I 8.6 0.0 12323 0 10.1 0.0 NA NA
2 15.6 1.9 27839 776 12.1 9.5 21.8 0.1
3 19.0 0.0 38346 0 8.4 0.0 22.0 0.0
4 27.0 2.5 46035 697 12.1 20.2 62.8 0.2
5 21.3 2.4 39215 1186 10.5 20.2 34.0 0.4
6 21.3 2.4 39215 1186 10.5 20.2 34.0 0.4
7 15.6 2.3 32395 1674 8.8 20.2 16.2 0.5
8 15.6 2.3 32395 1674 8.8 20.2 16.2 0.5
9 23.8 4.4 59082 3096 9.4 18.2 49.3 1.4
10 28.0 3.6 79191 5860 8.2 19.3 64.2 2.5
11 14.3 3.6 50688 8861 6.4 20.5 15.3 4.4
12 22.0 0.0 77744 0 7.5 0.0 44.2 0.0
13 14.3 0.0 62702 0 8.1 0.0 25.9 0.0
14 38.6 3.4 77503 2436 6.9 15.9 69.5 0.7
15 53.1 1.6 127303 1372 8.0 16.9 190.6 0.2
16 62.3 3.3 163998 2836 7.1 16.4 245.8 0.8
17 62.3 3.3 163998 2836 7.1 16.4 245.8 0.8
18 60.0 3.7 143002 5313 6.4 14.8 181.6 1.4
19 96.0 7.5 289212 8067 9.8 16.6 1029.8 5.2
20 58.0 3.7 189223 6564 9.8 19.2 403.8 2.8
21 88.5 25.8 174285 27649 14.1 13.6 994.0 43.1
22 50.0 18.2 18365 3083 6.6 7.1 NA NA

Note: 1 Probability of recurring congestion (%)

2 V, = Total volume of vehicles with speeds less than or equal to the 35 mph speed threshold at location i.
3 s, = Mean recurring congestion severity at station 1 (mph).

75

Table 5.13 Vehicle Delay (EB I-94).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P" Vc,‘ 5? Vehicle Delay
Station
(%) (vehicles) (mph) (vehicle-hours)
10.
AM AM AM AM PM PM AM PM
23 0.0 12.5 0 2199 0.0 7.1 NA NA
24 0.0 29.3 0 87799 0.0 9.5 0.0 91.0
25 0.0 8.3 0 4349 0.0 2.6 0.0 0.3
26 0.0 8.3 0 4349 0.0 2.6 0.0 0.3
27 0.0 0.0 0 0 0.0 0.0 0.0 0.0
28 0.0 0.0 0 0 0.0 0.0 0.0 0.0
29 0.0 17.9 0 103606 0.0 4.1 0.0 23.3
30 0.0 3.0 0 7316 0.0 8.8 0.0 0.7
31 0.0 3.0 0 7316 0.0 8.8 0.0 0.7
32 0.0 0.0 0 0 0.0 0.0 0.0 0.0
33 0.0 0.0 0 0 0.0 0.0 0.0 0.0
34 0.0 2.7 0 2701 0.0 7.4 0.0 0.2
35 0.0 0.0 0 0 0.0 0.0 0.0 0.0
36 0.0 0.0 0 0 0.0 0.0 0.0 0.0
37 0.0 1.6 0 4785 0.0 3.9 0.0 0.1
38 0.0 6.7 0 6751 0.0 8.2 0.0 1.3
39 0.0 0.0 0 0 0.0 0.0 0.0 0.0
40 0.0 3.2 0 11083 0.0 7.7 0.0 0.9
41 0.0 8.6 0 15632 0.0 10.9 0.0 5.8
42 0.0 6.7 0 14478 0.0 9.1 0.0 3.2
43 0.0 4.8 0 13323 0.0 7.2 0.0 1.6
44 0.0 13.3 0 36564 0.0 7.6 NA NA
Note: 1 Probability of recurring congestion (%)

2 Va = Total volume of vehicles with speeds less than or equal to the 35 mph speed threshold at location i.
3 s, = Mean recurring congestion severity at station 1 (mph).

76

Table 5.14 Vehicle Delay (NB M-IO).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P.I Vc,‘ 51’ Vehicle Delay
Station (%) (vehicles) (mph) (vehicle-hours)
I.D.
AM AM AM AM PM PM AM PM
45 0.0 34.0 0 85432 0.0 11.9 NA NA
46 0.0 38.1 0 120161 0.0 9.2 0.0 154.7
47 0.0 42.0 0 115680 0.0 8.6 0.0 150.9
48 0.0 44.8 0 139908 0.0 9.5 0.0 222.3
49 0.0 47.6 0 139607 0.0 6.7 0.0 151.0
50 0.0 22.9 0 102846 0.0 7.1 0.0 57.3
51 0.0 22.9 0 102846 0.0 7.1 0.0 57.3
52 0.0 24.3 0 105023 0.0 5.2 0.0 42.0
53 0.0 18.3 0 44671 0.0 5.4 0.0 14.1
54 0.0 5.8 0 11293 0.0 6.6 0.0 1.5
55 9.1 4.8 2145 3175 10.0 2.1 0.7 0.1
56 0.0 5.7 0 10858 0.0 8.8 0.0 2.0
57 0.0 5.7 0 10858 0.0 8.8 0.0 2.0
58 0.0 5.7 0 10858 0.0 8.8 0.0 2.0
59 0.0 18.2 0 32991 0.0 5.6 0.0 10.9
60 2.9 9.1 1771 15869 17.8 8.1 0.5 4.1
61 0.0 8.3 0 5680 0.0 7.6 0.0 1.3
62 1.8 3.2 2056 7567 16.9 11.8 0.3 1.2
63 2.6 6.7 2749 13579 21.1 9.3 1.0 3.1
64 2.9 2.2 2427 3180 16.8 13.0 0.6 0.4
65 0.0 0.0 0 0 0.0 0.0 0.0 0.0
66 0.0 0.0 0 0 0.0 0.0 0.0 0.0
67 0.0 0.0 0 0 0.0 0.0 0.0 0.0
68 0.0 3.2 0 2780 0.0 23.0 NA NA
Note: 1 Probability of recun'ing congestion (%)

2 Va = Total volume of vehicles with speeds less than or equal to the 35 mph speed threshold at location i.
3 s, = Mean recurring congestion severity at station i (mph).

77

Table 5.15 Vehicle Delay (SB M-10).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P.I Va" si'T Vehicle Delay
Station (%) (vehicles) (mph) (vehicle-hours)
1.D.
AM AM AM AM PM PM AM PM
69 5.9 5.3 2369 3620 10.2 23.2 NA NA
70 12.5 0.0 2546 0 5.9 0.0 0.6 0.0
71 58.6 0.0 153257 0 8.1 0.0 256.9 0.0
72 64.5 0.0 216608 0 8.4 0.0 421.7 0.0
73 21.7 15.4 5941 1676 5.0 6.1 2.1 0.5
74 37.1 0.0 116245 0 7.5 0.0 112.3 0.0
75 44.3 1.4 129865 1035 8.7 6.2 181.4 0.0
76 46.3 2.7 155459 4206 8.6 15.8 222.6 0.9
77 55.6 25.0 31138 15212 8.5 10.6 53.3 15.6
78 47.1 1.4 168267 6034 7.3 16.5 197.9 0.7
79 23.9 4.1 87104 19313 3.9 13.7 24.8 4.9
80 37.5 0.0 18256 0 2.6 0.0 5.3 0.0
81 20.0 0.0 5753 0 3.7 0.0 1.3 0.0
82 5.7 0.0 8011 0 6.5 0.0 1.0 0.0
83 4.3 0.0 6614 0 6.3 0.0 0.6 0.0
84 4.2 0.0 7412 0 9.7 0.0 1.1 0.0
85 7.1 3.4 8706 1512 7.5 13.2 1.6 0.3
86 2.9 2.8 5969 3000 8.5 13.0 0.5 0.5
87 2.8 1.4 7539 2769 8.0 20.6 0.6 0.5
88 2.0 1.9 2275 3301 4.5 23.6 0.1 1.2
89 15.7 0.0 68393 0 6.9 0.0 25.1 0.0
90 23.1 0.0 62907 0 10.2 0.0 56.7 0.0
91 24.2 1.4 84712 1038 9.2 14.3 NA NA
Note: 1 Probability of recurring congestion (%)

2 Va = Total volume of vehicles with speeds less than or equal to the 35 mph speed threshold at location i.
3 S, = Mean recurring congestion severity at station i (mph).

78

Table 5.16 Study Segments Vehicle Delay.

 

 

 

 

 

 

 

 

Vehicle Delay

Freeway kl (vehicle-hours)
AM PM
EB [-94 21 O 129
WB 1—94 22 3367 65
SB M-10 22 1567 25
NB M-10 23 3 572

Note: 1 k = Total number of data collection stations.

The probabilistic recurring congestion location and freeway indices were applied
to the study segments that allowed numerical comparisons of the recurring congestion

levels on the different study segments.

identified in an urban freeway traffic environment.

Average daily freeway traffic delay (vehicle-hours) due to recurring congestion
was also quantified on a location, segment, and system bases through calculating the

F SRCM values.

Comparisons between the recurring congestion level on the study

segments during the AM and PM peak periods were performed.

 

Recurring congestion patterns were also

Chapter 6

SENSITIVITY ANALYSIS AND VALIDATION

The previous chapter presented bases to establish a sampling plan for future data
collection to measure congestion. This chapter focuses on testing the reliability of the
proposed plan. This analysis is used to establish a sampling plan that minimizes the
number of locations and frequency of data collection required to obtain a reliable
congestion measure.

The analyses in the previous chapter were based on a common database that
combined 8 months of data (December 1996 — July 1997). In this chapter, the differences
in the congestion measure over days of the week and seasons of the year are studied. The
developed models are then validated using one month of data (August 1997). The
congestion values are also compared to the CALTRANS methodology values. Finally, a
comparison between recurring and nonrecurring congestion values is conducted.

6.1 Weekday Variations

Tables 6.1 through 6.3 show total number of days for which data are available and
the number of congested days on the three most congested freeway segments (WB I-94
AM, NB M-10 PM, and SB M-10 AM, respectively) distributed by weekday. Only one
station (station 19) out of 69 stations has a sample size of five or more congested days on

each weekday. This was not considered a sufficient sample size to conduct an analysis of

79

Note:

80

Table 6.1 Weekday Data Distribution (WB 1-94 AM Peak Period).

 

 

 

 

Station Mondays Tuesdays Wednesdays Thursdays Fridays
1.D. Total CongI Total Cong Total Cong Total Cong Total Cong
1 6 0 8 1 6 2 8 0 7 O
2 9 1 9 1 8 2 1 1 3 8 0
3 9 1 7 2 7 2 1 1 3 8 0

4 10 1 7 2 5 2 8 4 7 1
5 NA2 NA NA NA NA NA NA NA NA NA
6 NA NA NA NA NA NA NA NA NA NA
7 7 0 6 0 7 2 6 2 6 1
8 NA NA NA NA NA NA NA NA NA NA
9 10 3 8 2 7 2 9 2 8 1
10 12 3 9 2 9 4 1 1 4 9 1
I l 12 2 9 1 9 2 1 1 2 8 0
12 1 1 1 1 1 3 10 3 8 3 10 1
13 9 1 11 1 10 2 9 2 10 1
14 9 5 12 4 9 4 8 2 6 2
15 10 7 1 1 6 10 6 9 3 9 4
16 12 9 l 1 7 8 7 l 1 6 11 4
17 NA NA NA NA NA NA NA NA NA NA
18 13 8 10 7 9 6 9 6 9 3
19 12 ll 10 10 9 9 10 9 9 9
20 12 6 10 6 9 7 10 6 9 4
21 6 5 6 5 4 4 6 5 4 4
22 NA NA 3 O 2 2 1 1 2 1

 

 

 

 

 

 

 

 

 

 

 

1 Recurring Congestion.

2 Data are not available because detector is not functioning.

 

Note:

81

Table 6.2 Weekday Data Distribution (NB M-IO PM Peak Period).

 

 

 

 

Station Mondays Tuesdays Wednesdays Thursdays Fridays

I'D- Total CongI Total Cong Total Cong Total Cong Total Cong
45 9 3 11 4 10 5 10 3 10 2
46 14 4 14 6 13 5 12 5 10 4
47 12 4 11 5 10 4 9 4 8 4
48 10 4 13 5 11 6 12 6 12 5
49 7 3 10 5 9 4 8 4 8 4
50 NA2 NA NA NA NA NA NA NA NA NA
51 14 3 15 3 14 4 14 4 l3 2
52 14 2 15 3 14 5 14 5 13 2
53 12 2 13 3 11 2 12 2 12 2
54 14 0 15 0 13 2 14 1 13 2
55 5 0 5 O 3 0 2 0 6 1
56 I4 0 15 1 14 1 14 1 13 1
57 NA NA NA NA NA NA NA NA NA NA
58 NA NA NA NA NA NA NA NA NA NA
59 10 0 12 2 1 1 5 11 0 1 l 1
60 8 0 10 1 8 2 10 0 8 1
61 3 0 2 1 2 0 3 0 2 0
62 12 0 13 1 11 0 l3 0 13 1
63 10 0 10 1 8 0 9 0 9 2
64 10 0 10 0 9 0 9 0 9 1
65 2 O 1 0 NA NA 1 0 1 0
66 2 0 2 0 1 0 2 0 l 0
67 2 0 2 0 1 0 2 0 1 0
68 6 O 6 0 7 O 6 0 6 1

 

 

 

 

 

 

 

 

 

 

 

1 Recurring Congestion.

2 Data are not available because detector is not functioning.

 

Note:

82

Table 6.3 Weekday Data Distribution (SB M-1 0 AM Peak Period).

 

 

 

 

Station Mondays Tuesdays Wednesdays Thursdays Fridays
['0' Total Con gI Total Cong Total Cong Total Cong Total Cong
69 2 0 4 1 4 0 4 O 3 0
70 2 0 4 l 4 1 4 O 2 0
71 10 3 12 10 13 11 14 7 9 3
72 12 6 13 12 12 10 15 9 10 3
73 10 2 9 5 8 1 11 1 8 1
74 14 3 14 7 13 8 16 6 13 2
75 10 2 12 8 12 7 15 6 12 4
76 13 5 15 9 14 9 15 6 10 2
77 3 2 5 2 3 3 4 1 3 2
78 14 3 15 9 14 9 15 8 10 3
79 14 2 15 6 14 5 14 3 10 0
80 NA2 NA 3 0 2 1 2 2 1 0
81 2 1 2 0 2 1 2 0 2 0
82 13 0 15 3 14 0 15 1 13 0
83 13 0 15 2 l4 0 15 1 13 0
84 14 0 15 2 14 0 16 1 13 0
85 6 1 6 1 5 0 6 0 5 0
86 13 0 15 1 13 O 16 1 13 0
87 14 0 15 1 14 0 16 1 13 0
88 8 0 11 0 10 0 12 1 10 0
89 14 2 15 4 14 2 15 3 12 0
90 10 l 13 3 14 4 l6 5 12 2
91 11 2 13 3 14 4 16 5 12 2

 

 

 

 

 

 

 

 

 

 

 

l Recurring Congestion.

2 Data are not available because detector is not functioning.

 

83

weekday congestion variation on a station by station level.

Table 6.4 shows a summary of the total data collection days and congested days

on a segment basis. The percentage of congested days to total available days varies from

11 to 49 percent for the different weekdays and freeway segments. The table also shows

that this percentage varies from one weekday to another for the same freeway segment

and from one freeway segment to another on the same weekday.

Weekday Bonferroni multiple comparisons of the mean values of the recurring

congestion indices (Mi) are presented in Table 6.5. These results show that:

1.

The mean value of the congestion index (Mi) is not statistically different at a
5% significance level during the AM peak periods on Mondays and Tuesdays,
The mean value of the congestion index (Mi) is not statistically different at a
5% significance level during the AM peak periods on Wednesdays and
Thursdays,

The mean value of the congestion index (Mi) during the AM peak periods on
Fridays is also not statistically different at a 5% significance level than on
Mondays and Tuesdays,

The mean value of the congestion index (Mi) during the AM peak periods on
Fridays is not statistically different at a 5% significance level than on
Wednesdays and Thursdays except for SB M-10, and

The mean value of the congestion index (Mi) is not statistically different at a

5% significance level during the PM peak periods on all weekdays.

The above results indicate that a data collection plan should include either a

Monday or Tuesday, a Wednesday or Thursday, and a Friday in order to estimate the

84

Table 6.4 Summary of Weekday Data Distribution.

 

 

 

 

 

 

 

Segment Mondays Tuesdays Wednesdays Thursdays Fridays
Total Days
WB 1-94 AM 169 158 138 156 140
NB M-IO PM 190 205 180 187 179
SB M-lO AM 222 256 241 274 209

 

 

 

 

 

Congested Days

 

WB 1-94 AM 64 60 68 63 37
NB M-IO PM 25 41 45 35 36
SB M-IO AM 35 90 76 68 24

 

 

 

 

 

% Congestion

 

WB 1-94 AM 38 38 49 40 26
NB M-10 PM 13 20 25 19 20

SB M-IO AM 16 35 32 25 11

 

 

 

 

 

 

 

 

85

Table 6.5 Weekday Comparison of Recurring Congestion Index (Mi).

 

 

 

WB 1-94 AM SB M-lO AM NB M-10 PM
Weekday Weekday Mean Mean Mean
Std. P- Std. P- Std. P-
(1) (J) Diff' Diff Diff
Err.2 value3 Err. value Err. value
(1-1) (H) (H)
Mon Tue -0.02 0.03 1.00 -0.03 0.03 1.00 0.08 0.05 0.68

Wed -0.12' 0.03 0.00 .0.12' 0.03 0.00 0.04 0.05 1.00

 

Thu -0.13‘ 0.03 0.00 -0.12' 0.03 0.00 0.00 0.05 1.00
Fri -007 0.04 0.51 0.01 0.04 1.00 0.08 0.05 1.00
Tue Mon 0.02 0.03 1.00 0.03 0.03 1.00 -0.08 0.05 0.68

Wed -0.10. 0.03 0.01 -0.09' 0.02 0.00 -0.04 0.04 1.00

 

Thu -0.1 1. 0.03 0.00 -0.09' 0.02 0.00 -0.08 0.04 0.50
Fri -0.05 0.04 1.00 0.04 0.03 1.00 -0.01 0.04 1.00
Wed Mon 0.12' 0.03 0.00 0.12' 0.03 0.00 -0.04 0.05 1.00

Tue 0.10 0.03 0.01 0.09 0.02 0.00 0.04 0.04 1.00
Thu -0.02 0.03 1.00 0.00 0.02 1.00 -0.04 0.04 1.00

Fri 0.05 0.04 1.00 0.13 0.03 0.00 0.03 0.04 1.00

 

Thu Mon 0.13' 0.03 0.00 0.12' 0.03 0.00 0.00 0.05 1.00

Tue 0.1 l 0.03 0.00 0.09. 0.02 0.00 0.08 0.04 0.50

Wed 0.02 0.03 1.00 0.00 0.02 1.00 0.04 0.04 1.00

O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fri 0.06 0.04 0.90 0.13 0.04 0.00 0.07 0.04 0.88
Fr Mon 0.07 0.04 0.51 -0.01 0.04 1.00 -0.08 0.05 1.00
Tue 0.05 0.04 1.00 ~0.04 0.03 1.00 0.01 0.04 1.00
Wed -0.05 0.04 1.00 -0. 13' 0.03 0.00 -0.03 0.04 1.00
Thu -0.06 0.04 0.90 -0.13' 0.04 0.00 -0.07 0.04 0.88
Note: 1 Difference between mean Mi on weekdays I and .1.

2 Standard error between mean Mi on weekdays I and J.

3 P-value = Probability of (t-statistic > t-observed) assuming that the observed means are statistically equal
at the corresponding weekdays.

"' The mean difference of Mi is significant at the 0.05 level.

86

recurring congestion index on a freeway segment during the AM peak period. Collecting
data on any weekday is sufficient to estimate the recurring congestion measure the during
the PM peak period. The result from this analysis can be used to reduce the size of the
data sample in future data collection efforts. Analysis of seasonal variations in the
recurring congestion index is provided in the next section.

6.2 Seasonal Variations

Tables 6.6 through 6.8 show total and congested days on the three most congested
freeway segments (WB I-94 AM, NB M-10 PM, and SB M-10 AM, respectively)
distributed on the seasons (Spring/Summer and Fall/Winter). The number of days on
which data are available are fairly evenly distributed across the seasons, except for the
WB I-94 freeway segment during the AM peak period (Spring/Summer to Fall/Winter
ratio is approximately 2:3). The percentage of congested to total available days varies
from 13 to 40 percent for the various seasons and congested freeway segments
considered (Table 6.9). This percentage varies from one freeway segment to another, but
the Fall/Winter value is always higher than the Spring/Summer one.

Table 6.10 shows the results of comparing the means of the recurring congestion
indices (Mi) on the freeway segments during the seasons of the year at the 0.05
significant level. The results show that:

1. The mean congestion index (Mi) is not statistically different at a 5 %

significance level on the WB 1-94 freeway during the AM peak period for the
Spring/ Summer and Fall/Winter, and

2. The mean congestion index (Mi) is statistically different on both the NB and

Note:

Table 6.6 Seasonal Data Distribution (WB I-94 AM Peak Period).

87

 

 

 

 

Station Spring/Summer Fall/Winter

l.D. Total Days Cong DaysI Total Days Cong Days
1 10 0 25 3
2 l7 0 28 7
3 14 0 28 8
4 7 0 30 10
5 NA2 NA NA NA
6 NA NA NA NA
7 4 O 28 5
8 NA NA NA NA
9 1 1 0 31 10
10 20 0 30 14
1 1 20 0 29 7
12 22 0 28 1 1
13 23 0 26 7
14 22 5 22 12
15 22 9 27 17
16 24 14 29 19
17 NA NA NA NA
18 20 18 30 12
l9 19 19 31 29
20 19 19 31 10
21 23 23 3 0
22 NA 0 8 4

 

 

 

 

 

l Recurring Congestion.

2 Data are not available because detector is not functioning.

 

Note:

Table 6.7 Seasonal Data Distribution (NB M-lO PM Peak Period).

88

 

 

 

 

Station Spring/Summer Fall/Winter

l-D- Total Days Cong Daysl Total Days Cong. Days
45 21 4 29 13
46 32 7 31 16
47 2| 7 29 14
48 26 7 32 19
49 9 1 33 19
50 NA2 NA NA NA
51 37 9 33 7
52 37 8 33 9
53 28 5 32 6
54 37 2 32 2
55 4 0 l7 1
56 37 4 33 0
57 NA NA NA NA
58 NA NA NA NA
59 27 3 28 7
60 24 2 20 2
61 12 1 NA NA
62 31 1 31 1
63 24 l 22 2
64 25 0 22 1
65 5 0 NA NA
66 8 0 NA NA
67 8 0 NA NA
68 10 0 21 1

 

 

 

 

 

I Recurring Congestion.

2 Data are not available because detector is not functioning.

 

89

Table 6.8 Seasonal Data Distribution (SB M-IO AM Peak Period).

 

 

 

 

 

 

 

 

 

 

Station Spring/Summer Fall/Winter
l'D' Total Days Cong DaysI Total Days Cong. Days
69 17 1 NA2 NA
70 16 2 NA NA
71 27 1 1 31 23
72 32 17 30 23
73 17 4 29 6
74 38 7 32 19
75 31 7 30 20
76 34 7 33 24
77 18 10 NA NA
78 35 4 33 28
79 35 4 32 12
80 NA NA 8 3
81 10 2 NA NA
82 38 2 32 2
83 38 2 32 I
84 38 2 34 1
85 28 2 NA NA
86 36 1 34 1
87 38 2 34 0
88 18 0 33 1
89 37 11 33 0
90 31 14 34 1
91 32 15 34 1
Note: 1 Recurring Congestion.

2 Data are not available because detector is not functioning.

90

Table 6.9 Summary of Seasonal Data Distribution.

 

 

 

 

 

 

 

 

 

 

 

Segment Spring/Summer Fall/W inter
Total Days
WB 1-94 AM 297 464
NB M-10 PM 463 478
SB M-10 AM 644 558
Congested Days
WB 1-94 AM 107 185
NB M-IO PM 62 120
SB M-IO AM 127 166
% Congestion
WB [-94 AM 36 40
NB M-10 PM 13 25
SB M-IO AM 20 30

 

 

 

 

91

Table 6.10 Seasonal Comparisons of Recurring Congestion Index (Mi).

 

 

 

 

 

 

 

 

 

 

 

 

 

WB 194 AM SB M-IO AM NB M-10 PM
Season Mean Std. P- Mean Std. P- Mean Std. P-
Mil Err.2 value3 Mi Err. value Mi Err. value
Spring/Summer 0.296 0.015 0.066 0.244‘ 0.011 0.001 0.183‘ 0.012 0.000
Fall/Winter 0.336 0.014 0.066 0.306‘ 0.014 0.001 0.309' 0.018 0.000

 

 

Note: I Mean recurring congestion index during a season.

2 Standard error of the mean of Mi during a season.

3 P-value = Probability of (t-statistic > t-observed) assuming that the observed means are statistically equal
at the two seasons.

"‘ The mean of Mi is significantly different from season to season at the 0.05 level.

SB M-IO freeways during the AM and PM Spring/Summer and F all/W inter
peak periods.

Accordingly, to estimate the annual congestion values during the AM and PM
peak periods on M-10 freeway, data collection is required during both the
Spring/ Summer and F all/W inter seasons.

To study the stability of the average of the recurring congestion index (M) during
the Spring/Summer and F all/Winter season, stations 19 on WB [-94 and 72 on SB M-10
are selected during the AM peak period. Station 48 on NB M-IO is selected during the
PM peak period. These stations were selected because they are the most frequently
congested stations on the corresponding freeways and peak periods. Figure 6.1 shows the
average M values for stations 19 and 72 during the AM peak period in the

Spring/Summer season (values that are less than the 85th percentile values are excluded).

By using i 1% acceptable variation in the average M value, it noticed that this value

Recurring Congestion Index ( %)

Recurring Congestion Index (%)

92

 

 

 

Average = 25%

 

 

O l’%r— —T77 7 1 1 7‘ T _ '_ ’T__——_T__' " l' ’ 1 ___—1' —‘.—:‘_—1

12345678910111213141516

Accumulative Data Collection Days at Station 19 (AM Spring/Summer)

2 5 Average = 22%

    

 

 

O ”' ___TTTW' w‘l" *7 7v ".7 'Tfi' *T' i 1“ ‘Tt—‘_—TT‘ W W T ‘777' ‘1' 7A' "A" " '

l 2 3 4 5 6 7 8 9 10 11 12 13

Accumulative Data Collection Days at Station 72 (AM Spring/Summer)

Figure 6.1 Recurring Congestion Index (M) at Stations 19 and 72 (AM Spring/Summer).

93

stabilizes after collecting 12 and 10 congested days at stations 19 and 72, respectively,
during the AM peak periods in the Spring/Stunmer season, while it stabilized after
collection 16 and 17 congested days, respectively, during the Fall/Winter season (Figure
6.2). On the other hand, the average M value starts to stabilize at station 48 after
collecting 6 and 15 congested days during the PM peak periods in the Spring/Summer
and Fall/Winter seasons, respectively (Figure 6.3).
6.3 Model Validation

To test the start time and duration of recurring congestion models that were
presented in the previous chapter, the start time and duration of recurring congestion were
calculated at each station during both the AM and PM peak. Then, data on 10 weekdays
during the month of August 1997 were collected. A minimum sample size of two
congested days was selected as a threshold to include a station in the model validation
process. By using this threshold, stations 89, 90, and 91 (SB M-10 freeway segment)
during the AM peak period were selected to test the model. Eight stations on the NB M-
10 freeway segment satisfied this threshold, but were excluded because construction was
taking place on this segment during August 1997.

Figure 6.4 shows the start time and duration of recurring congestion at stations
89-91 during (a) the 8-month (December 1996 — July 97) peak period, (b) the
spring/summer (April — July 97) peak period, and (c) August 1997 AM peak period. The
figure shows good agreement between the Spring/Summer and 8-month models, and the
validation data (August 1997 data). The start and end time of the recurring congestion
during the month of August 1997 lies within both models with a better fit with the

Spring/ Summer model. This pattern is expected because the spring/summer and

Recurring Congestion Measure (%)

Recurring Congestion Measure (%)

94

40

     

35 . Average=3l%
30 . ----------------------------------------- -‘
25 3

201;

10-

 

0 ' V —Y§V ' ‘ Y 7__T—“_ V 1 _F— V—V_— T Y ”+7 T ' # T—‘_'1 Y_‘ _1 —‘,

12 3 4 5 6 7 8 910111213141516171819202122232425

Accumulative Data Collection Days at Station 19 (AM Fall/Winter)

 

 

Average = 32%

0 l '1 7"“ " ' 'T "—”T ' " —T—""T T“ ' _'_' T _'_ '_" 'T—‘_"T‘ '_fi—_77'_ ‘_‘ T" ‘_"‘1 ""— "fi—I_~_~)

l234567891011121314151617181920

Accumulative Data Collection Days at Station 72 (AM Fall/Winter)

Figure 6.2 Recurring Congestion Index (M) at Stations 19 and 72 (AM Fall/Winter).

b.)
O

Recurring Congestion Measure (%)
U.

Recurring Congestion Measure (%)

Figure 6.3

N
M

95

 
   

Average = 22%

 

1 2 3 4 5 6 7 8 9 10 ll 12 13 14 15

Accumulative Data Collection Days at Station 48 (PM F all/Winter)

 

 

Average = 17%

 

 

 

Accumulative Data Collection Days at Station 48 (PM Spring/Summer)

Recurring Congestion Index (M) at Station 48 (PM in both Seasons).

96

 

 

 

 

 

 

 

 

 

1 l I
91 l L- 3
E l —
it
C
I l l
2
(I)
V —
E l
L5
m 1 =
89 r :4

 

 

300 400 500

Time (Accumlative Mnutes)

8-month Spring/ &11rmer Aug-97
I

Figure 6.4 Recurring Congestion Start Time and Duration (SB M-10).

97

fall/winter season were found to be statistically different in the previous section. These
results are encouraging, however, more extensive validation is recommended when
additional data become available.

6.4 Comparison of Recurring and Nonrecurring Congestion

Total congestion is defined as the vehicle-minute of travel when traffic speed
drops below the 35 mph threshold for one minute or more during a time interval. In other
words, total congestion is the summation of short and long term congestion during a time
interval.

Table 6.11 shows a comparison between a congestion index calculated based on
l-minute threshold as defined in Chapter 4 and the same index based on the IS-minute
smoothing threshold adopted in this study. The table only includes the WB I-94 stations
and days that experienced congestion. About 38% of the data collection days
experienced only short-term congestion while the rest experienced at least one congested
period lasting fifteen minutes or longer.

The total vehicle-minutes of delay occurring during the extended congestion
periods is 18,244 minutes while short term congestion accounts for only 2,193 minutes.
About 89% of the congestion duration is attributed to recurring congestion as defined in
the study.

The percentage of traffic volume that experienced recurring and non-recurring
congestion can be calculated as follows:

Traffic that experienced congestion = 100% x 4,193 x 363/30,784 x 363

= 14%

98

Table 6.11 Total and Recurring Congestion Comparison (WB I-94 AM).

 

 

 

 

 

Congested Total Congestion
Volumel
Station Total Days Volume2 Duration3
(Vehicles)
10. (Vehicles) (Minutes)
TC"1 RC5 TC RC TC RC TC RC
1 6 3 23489 23503 2458 4108 239 203
2 8 5 23390 22383 3207 4785 423 400
3 8 6 26621 25951 4070 5549 472 482
4 l6 8 23832 23088 3240 5337 794 680
7 12 4 29610 28059 3255 7408 509 398
9 21 9 27575 26522 3152 5745 944 757
10 22 14 27449 26919 4256 5657 1330 1147
11 19 7 32897 31058 3171 7241 816 693
12 20 10 32324 31142 4386 7522 1151 1003
13 19 7 32074 30051 3565 8957 923 860
14 24 13 30209 29783 3077 5011 982 871
15 28 19 31214 31216 4061 5352 1428 1283
16 31 25 31653 31576 4612 5178 1754 1590
18 36 21 33582 32649 3653 4905 1615 1284
19 36 36 31205 31205 6467 6203 3061 2938
20 36 21 34677 32930 4458 6614 2113 1865
21 14 12 30566 29469 7411 8410 1586 1554
22 7 4 34890 33838 3365 4591 297 236
T000 363 224 20437 18244
VVefiyued
30784 30129 4193 5992
Average

 

 

 

 

 

 

 

 

 

 

 

Note: 1 Average total volume of vehicles during 12:00 a.m.-11:59 p.m. 12/1996-5/1997 (vehicles per 12 hr).
2 Average congested volume of vehicles during 12:00 a.m.-11:59 a.m. 12/1996-5/1997 (vehicles per 12 hr).
3 Total duration of congestion during 12:00 a.m.-1 l :59 am. 12/1996-5/1997 (minutes).
4 Total congestion threshold of one minute or more.
5 Recurring congestion by using the study methodology.

99
Traffic that experienced recurring congestion = 100% x 5,992 x 224/3 0,784 x 363
= 12%
Traffic that experienced only non-recurring congestion = 14% - 12%
= 2%

In other words, it is estimated that about 86% of the congestion on the west bound
I-94 freeway segment during the l2-hr time interval (from midnight to noon) is attributed
to recurring congestion. In this study recurring congestion includes incident caused
congestion that occurs between the start and end time of recurring congestion as defined
for each station.
6.5 Comparison of Study and CALTRANS Methodologies

Table 6.12 shows the total recurring congestion duration and volume of the west
bound I-94 freeway segment during the AM peak period between 12/1996-7/1997 by
using the study and CALTRAN S methodologies, respectively. The table shows that the
CALTRANS methodology consistently underestimates the recurring congestion duration
and volume at various stations in comparison with the study methodology. On the
average, the CALTRANS methodology underestimates the recurring congestion duration
and volume on this segment during the AM peak period by 11 and 12%, respectively.

These findings confirm earlier observations; namely the CALTRANS
methodology is not capturing small variations or spikes in traffic speed. The above
results show that the study methodology accounts for these variations better than the
CALTRANS methodology. This feature is significant in selecting a congestion measure
to evaluate a traffic management system because it captures most of the expected

congestion reduction in the freeway system, especially due to short term duration

Note:

100

Table 6.12 F RSCM vs. CALTRANS Methodologies (WB [-94 AM).

 

Total Recurring Congestion

Total Recurring Congestion

 

 

 

 

 

 

 

 

 

 

 

 

Station
RC Daysl Duration (minutes) Volume (vehicles)

I'D. PM2 CT5 %I)iff‘ PM CT %Diff’

1 3 203 194 -4 12323 11797 -4

2 7 452 452 0 27839 27839 0

3 8 543 515 -5 38346 36155 -6

4 10 728 694 -5 46035 43555 -5

7 5 431 420 -3 32395 31453 -3

9 10 881 821 -7 59082 54375 -8
10 14 1147 961 -16 79191 64610 -18

1 1 7 693 566 -18 50688 39516 -22

12 11 1040 926 -11 77744 67897 -13

13 7 860 705 -18 62702 49794 -21

14 17 1030 825 ~20 77503 60888 -21
15 26 1606 1385 -14 127303 108191 -15
16 33 2015 1780 -12 163998 142922 -13
18 30 1769 1586 -10 143002 126658 -11
19 47 3830 3428 -10 286786 255810 -11
20 29 2567 2236 -13 189223 163510 -14
21 21 2499 2314 -7 161811 146147 -10
22 4 236 229 -3 18365 17723 -3

Total 289 22530 20037 1654336 1448840
__Weighted
.11 -12
Average

 

1 Days that experience recurring congestion.
2 Study methodology.

3 CALTRANS methodology.

4 % difference of the recurring congestion duration estimates of the study and CALTRANS methodologies.
5 % difference of the recurring congestion volume estimates of the study and CALTRANS methodologies.

 

101

congestion. In summary, the CALTRANS methodology is expected to underestimate the
reduction of congestion due to the implementation of a traffic management system
relative to the study methodology.
6.6 Summary

Weekday and seasonal variations of the recurring congestion measure were
studied. The stability of this measure over data collection frequency was analyzed in
order to establish a sampling plan. One month of data was used to validate the measure.
Comparison of recurring and nonrecurring congestion values was conducted. The
recurring congestion estimates from the study and CALTRANS methodologies were

compared.

Chapter 7

CONCLUSIONS AND RECOMMENDATIONS

7.1 Conclusions

This research developed freeway recurring congestion measures applicable to a
specific location, a freeway segment, or the entire freeway. These measures were
developed to assist in the evaluation of ATMS implementation. A methodology was
developed to identify recurring congestion using data reduction and statistical analysis
from the freeway system in the Detroit, Michigan metropolitan area. By using the
developed methodology and measure, recurring congestion was quantified on the freeway
system. Models to identify the start time and duration of recurring congestion were
developed, and weekday and seasonal variations of recurring congestion were studied.

The AM and PM peak periods used in the analysis were 6:00-10:00 am. and
3:00-7:00 pm. The results indicated that less than two percent (2%) of recurring
congestion occurred outside these identified periods in the eight months analyzed.

The impact of speed thresholds of 30, 35, and 40 mph on the value of the
recurring congestion measure was studied. The investigation showed that this measure is
not statistically different for any of these three thresholds. If freeway traffic speed falls
below 40 mph it nearly always falls below 30 mph. In other words, to measure recurring

congestion it is sufficient to use any one of these speed thresholds.

102

103

The probability of freeway recurring congestion during the AM and PM peak
periods was studied. The study found that the probability of recurring congestion on the
freeway system locations ranged between 0 and 96 percent. It was also found that the
probability of recurring congestion during the AM peak period increases then decreases
as traffic approaches the city center. The same pattern applies during the PM peak period
as traffic departs the city center. The probability of congestion occurring during the AM
peak period is higher than that of the PM peak period.

The start time and duration of recurring congestion during the AM and PM peak
period were studied. The study concluded that the AM peak period congestion starts at a
later time and lasts for a shorter duration as traffic flow moves towards the city center.
The same pattern applies to the PM peak period congestion as traffic flow moves away
from the city center.

The freeway recurring congestion indices and measures values were calculated. It
was found that the Probabilistic Location Recurring Congestion and Severity Indices
(PLRCI and PLRCSI) of the freeway locations ranged between 0 and 4,144 x 10“
(dimensionless) and 0 and 1,250 x 10'2 (mph), respectively. The Probabilistic Freeway
Recurring Congestion and Severity Indices (PFRCI and PFRCSI) of the freeway
segments ranged between 0 and 1,240 x 10'4 (dimensionless) and 0 and 347 x 10'2 (mph),
respectively. Finally, the Freeway System Recurring Congestion Measure (FSRCM) of
the whole freeway system was calculated as 5, 728 vehicle-hours.

A data sampling plan for obtaining quantitative measure of recurring congestion

was established. It was found that grouping locations based on the statistical similarity of

104
recuning congestion start time and duration would result in an accurate measure of
congestion even if the current detector spacing was increased.

Weekday and seasonal variations of recurring congestion during the AM and PM
peak periods were studied, and it was determined that the freeway segment congestion
measure is not statistically different during the AM peak period on Mondays and
Tuesdays or Wednesdays and Thursdays. The data from Fridays were not significantly
different than other weekdays except for one of the freeway segments. The measure is
not statistically different during the PM peak period on all weekdays. The freeway
segment measure is statistically different in the Spring/Summer than in the F all/Winter.
To measure recurring congestion, data sampling is needed during the AM peak periods on
Mondays or Tuesdays, Wednesdays or Thursdays, and Fridays in both seasons. While
data during the PM peak period may be obtained on any weekday but it must be collected
in both seasons.

The stability of the recurring congestion measure as a function of data collection
frequency was analyzed. This analysis was done to determine the minimum number of
congested days required for the measure to stabilize (as part of data sampling plan). It
was found that 10-12 and 16-17 congested days were required to measure congestion
during the AM peak periods in the Spring/Summer and Fall/W inter seasons, respectively.
It was also found that 6 and 15 congested days were required to measure congestion
during the PM peak periods in the Spring/ Summer and F all/W inter, respectively.

One month of data during the Spring/Summer season was used to validate the
developed start time and duration of recurring congestion models. The results showed

good agreement between the 8-month and Spring/Summer, and the validation data. The

105
start and end time of the recurring congestion during the validation month lies within
both models with a better fit with the Spring/ Summer model.

The comparison between recurring and nonrecurring congestion estimated that
about 89 and 11 percent of congestion duration in the selected time periods is attributed
to recurring and non-recurring congestion, respectively. The study also estimated that
about 86 percent of traffic that experienced congestion resulted from recurring
congestion. Recurring congestion estimates were significantly higher than other
estimates of 33-50%.

The study’s recurring congestion duration and volume estimates were compared
with estimates using the CALTRANS methodology. It was found that the CALTRANS
methodology underestimates recurring congestion duration and volume during the peak
periods, in comparison to the study’s estimates, by about 11 to 12 percent. This can be
explained by the fact that the study methodology is capturing small variations or spikes in
traffic speed better than the CALTRANS methodology.

7.2 Recommendations

This research has developed a freeway congestion measure that can be used in
evaluating ATMS implementation. The study methodology is expected to account for the
reduction of congestion due to the implementation of a traffic management system better
than existing methodologies.

Additional data are required to validate the start time and duration of recurring
congestion. It is recommended that these data be collected in both Spring/Summer and

Fall/winter, based on the sampling plan developed in this research.

106

In order to determine the minimum spacing of freeway data collection locations
required to measure congestion, it is recommended that additional data be collected at
locations where detectors were totally not reporting data or ntunber of congested days
was less than five days during the 8-month study period. A minimum of five congested
days was required to conduct this analysis.

It is also recommended that 6 and 15 additional congested days (based on the
sampling plan) be collected during the PM peak periods in the Spring/Summer and
Fall/Winter, respectively, to firrther analyze the stability of congestion during these
periods. The analysis is recommended because the study did not show a conclusive
pattern during the PM peak periods.

As the study database did not include traffic characteristics on the lane-by-lane
level, it is recommended that future studies collect such data on locations where

congestion was abnormal.

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