Institute of Transportation Studies
University of California at Berkeley
September 2005
ISSN 0192 4109
DISSERTATION SERIES
UCB- ITS- DS- 2005- 2
Understanding and Mitigating Capacity Reduction at Freeway
Bottlenecks
Koohong Chung
Understanding and mitigating capacity reductions at freeway bottlenecks
By
Koohong Chung
B. S. ( University of California at Berkeley) 1999
M. S. ( University of California at Berkeley) 2001
A dissertation submitted in partial satisfaction of the
Requirement for the degree of
Doctor of Philosophy
in
Engineering- Civil and Environmental Engineering
in the
GRADUATE DIVISION
of the
UNIVERSITY OF CALIFORNIA AT BERKELEY
Committee in charge:
Professor Michael J. Cassidy, Chair
Professor Carlos F. Daganzo
Professor Alex Skabardonis
Professor John A. Rice
Fall 2004
The dissertation of Koohong Chung is approved:
University of California, Berkeley
Fall 2004
chair Date
Date
Date
Date
Understanding and mitigating capacity reductions at freeway bottlenecks
Copyright 2004
By
Koohong Chung
1
Abstract
Understanding and Mitigating Capacity Reductions at Freeway Bottlenecks
By
Koohong Chung
Doctor of Philosophy in Engineering – Civil and Environmental Engineering
University of California at Berkeley
Professor Michael J. Cassidy, Chair
Two freeway bottlenecks, each with a distinct geometry, have been investigated in an
effort to understand traffic conditions leading to capacity losses ( i. e., breakdown). One
bottleneck is formed by a horizontal curve and the other by a reduction in travel lanes.
These bottlenecks are shown to exhibit breakdowns after queues form immediately
upstream. The vehicle accumulations that arise near these bottlenecks are shown to be
good proxies for the mechanisms that trigger breakdowns. Evidence is provided to show
that these losses can be recovered, postponed or even avoided entirely by controlling the
accumulations.
An algorithm for estimating vehicle accumulations has been developed in this
dissertation. This algorithm’s estimates are obtained from the counts made by ordinary
detectors ( e. g. inductive loops) placed in series. The accumulations estimated are those
that arise on the intervening ( freeway) segments between the detectors. These estimates
can be obtained in real- time at short intervals of a second or so.
2
The systematic errors ( i. e., bias) that invariably arise in detector counts are automatically
corrected when traffic is freely flowing. The algorithm is thus well suited for monitoring
accumulations near a bottleneck prior to capacity drops and the estimates it furnishes can,
in turn, dictate control actions ( e. g. metering rates) that prolong higher outflows from the
bottleneck. The estimates that the algorithm furnishes can also be used for incident
detection and delay estimation.
Professor Michael J. Cassidy,
Committee Chair
i
DEDICATION
This work is dedicated to my mother, Oksoo Kim. Without her extraordinary love and
support, this work would not have been possible. I also dedicate this work to my brothers
and sisters-- Sungyong, Sunghee, Koosam and Kooe-- with much love and sincere
appreciation of their support.
ACKNOWLEDGEMENT
I am grateful and indebted to my advisor Professor Michael Cassidy. His guidance, time
and tireless devotion to this work were invaluable. I would like to thank Professor Carlos
Daganzo for providing excellent advice and sharing his profound insights. I also would
like to thank; Professor Alex Skabardonis for supporting on earlier projects and his
advice; and Professor John Rice for serving on my committee.
I would like to extend my thanks to friends and colleagues here at Berkeley. It has been
my privilege to study with them. They contributed to me greatly as a friend and a
scholar. Many thanks to; Mauch Mauch for his valuable comments; Robert Bertini for
sharing his data ; Soyong Ahn, Yoonsang Hwang, Kwangrog Kim and Jittichai
Rudjanakanoknad for helping me to collect data. Special thanks to Lisa Massland at the
City of Toronto for generously supplying the data.
Last but not least, I would like to express my sincere gratitude to a special person in my
life, Yumi Oum for encouraging me when I was in doubts and supporting me with trust
and love.
ii
TABLE OF CONTENTS
1. Introduction 1
2. Related Research 3
2.1. Related to Breakdowns 3
2.2. Related to a new algorithm for estimating vehicle accumulations 7
3. Findings 9
3.1. Findings from the Gardiner Expressway, Toronto, Canada 9
3.2. Findings from SR- 24, Orinda, California 21
4. An algorithm for estimating vehicle accumulation and its applications 27
4.1. Algorithm Description 28
4.2. Algorithm Validation 34
4.3. Applications of the Algorithm 38
4.3.1. Real- time ramp metering strategy 39
4.3.2. Incident detection 39
4.3.3. Delay estimation 41
5. Conclusions 43
5.1. Summary of findings 43
5.2. Areas of further research 45
Reference 466
iii
Appendix- A 47
iv
LIST OF TABLES
3.1 Summary of breakdowns at the Gardiner Expressway, Toronto, Canada 17
3.2 Summary of breakdowns at the State Route 24, California 22
4.2 Description of the two events in Figure 4.1 41
v
LIST OF FIGURES
2.1 Breakdown mechanism described in Daganzo’s behavioral theory 6
3.1 Gardiner Expressway, Toronto, Canada 10
3.2 O- curves from detectors 50, 60, 70 and 80 ( Gardiner Expressway, Toronto,
Canada, March 5, 1997) 11
3.3 Five- minute aggregate flow- occupancy scatter plot from detector 60 ( Gardiner
Expressway, Toronto, Canada, 14: 45 ~ 16: 15, March 5, 1997) 13
3.4 O- curves for the median lane at detectors 40, 50, 60 and 70 ( Gardiner
Expressway, Toronto, Canada, March 5, 1997) 14
3.5 O- curves for the center lane at detectors 40, 50, 60 and 70 ( Gardiner
Expressway, Toronto, Canada, March 5, 1997) 15
3.6 Five- minute moving average of vehicle accumulations between detectors
60 and 70 ( Gardiner Expressway, Toronto, Canada, March 5, 1997) 17
3.7 O- curves from detectors 50, 60, 70 and 80 ( Gardiner Expressway, Toronto,
Canada, February 11, 1997) 19
3.8 Five- minute aggregate flow- occupancy scatter plot from detector 60 ( Gardiner
Expressway, Toronto, Canada, 14: 45 ~ 16: 15, March 5, 1997) 20
3.9 State Route 24, Orinda, California 21
3.10 O- curves from locations 3 and 4 ( State Route 24, Orinda, California,
August 21, 2002) 22
3.11 O- curves from locations 2 and 3 ( State Route 24, Orinda, California,
August 21, 2002) 23
3.12 Five- minute moving average of vehicle accumulations between locations
2 and 3 ( State Route 24, Orinda, California, August 21, 2002) 25
4.1 Hypothetical input- output diagram 28
4.2( a) Example of deviation curves from two neighboring detectors ( Gardiner
Expressway, Toronto, Canada, March 5, 1997) 32
4.2( b) Estimating segment travel time using cross- correlation technique
( Gardiner Expressway, Toronto, Canada, March 5, 1997) 33
vi
4.3 Eastbound Interstate 80, Berkeley, California 34
4.4 Comparison of estimated and actual vehicle accumulations between
detectors L7 and L8 ( Interstate 80, Berkeley, California, August 9, 2003) 35
4.5 Trip time comparison between detectors L7 and L8 ( Interstate 80, Berkeley,
California, August 9, 2003) 36
4.6 Vehicle accumulation between detectors 60 and 70 from 12: 30 to 18: 00
( Gardiener Expressway, Toronto, Canada, March 5, 1997) 40
4.7 Estimated travel times between detectors 60 and 70 under assumption of a
FIFO queue discipline ( Gardiner Expressway, Toronto, Canada, March 5, 1997) 42
1
1. Introduction
Two different freeway sites have been investigated to understand the reproducible traffic
conditions that accompany the capacity reductions ( i. e., breakdowns) at freeway
bottlenecks. One of the sites is located in Toronto, Canada and the other in Orinda,
California. Both sites were plagued by an active bottleneck ( i. e., a bottleneck
characterized by queues upstream and freely flowing traffic downstream) and
breakdowns were observed at these bottlenecks after they became active.
Findings from this dissertation show that the vehicle accumulations in the vicinity of
active bottlenecks are good proxies for the mechanisms that trigger breakdowns.
Breakdowns at each bottleneck were preceded by marked increases in the vehicle
accumulations and only occurred after these accumulations exceeded a certain threshold,
termed critical accumulation in this dissertation. Each site’s critical accumulation was
reproducible. Recoveries in outflows were observed when the vehicle accumulations
diminished sufficiently below the site’s critical accumulation.
These findings came to light by monitoring the vehicle accumulations in the vicinity of
the bottlenecks using an algorithm that is developed in this dissertation. This algorithm
monitors vehicle accumulations using the data from conventional loop detectors placed in
series while correcting for systematic error ( i. e., bias). The algorithm’s estimates have
been compared with the actual vehicle accumulations counted from videotape and their
differences were only 6% on an average.
2
In addition to having provided needed information for the present study, the algorithm
has a number of useful applications. It is well suited to monitoring the vehicle
accumulations in the vicinity of an active bottleneck prior to breakdown and the estimates
it furnishes can, in turn, dictate control actions ( e. g. metering rates) that prolong higher
outflows from the bottleneck. Maintaining higher outflows for a longer period will
reduce delay in the freeway system as can be readily verified from standard queuing
diagrams ( e. g. Newell, 1993).
The algorithm can also be used to detect incidents by monitoring the rate at which the
vehicle accumulations increase: an incident causes the vehicle accumulation to increase
rapidly while activation of a recurrent bottleneck causes the accumulation to increase
gradually. Although the algorithm cannot function in a self- correcting manner once a
queue arises on the freeway segment spanning the detectors in series, it can be used to
estimate total delays ( i. e., the sum of delays to each vehicle) in an off- line fashion ( e. g.
for planning purposes) after freely flowing traffic has been restored. Section 4.3
describes these applications in more detail.
The following section summarizes the previous related research. Section 3 presents the
findings from the two bottlenecks investigated in this dissertation. Section 4 presents; ( i)
the description of the algorithm for estimating vehicle accumulation; ( ii) the results of
testing the algorithm; and ( iii) applications of the algorithm. This dissertation ends with
concluding remark in section 5.
3
2. Related research
This section provides a summary of previous research related to; ( i) breakdowns at active
freeway bottlenecks in section 2.1; and ( ii) findings that lead to the new algorithm for
estimating the vehicle accumulations developed in this dissertation in section 2.2.
2.1. Past observations of breakdown.
Bertini ( 1999) investigated freeway bottlenecks using data measured by loop detectors
and found the magnitude of their discharge ( capacity) reductions varied markedly each
day. The long- run average discharge rates were as much as twelve percent lower than the
sustained outflows that had departed these bottlenecks prior to breakdowns. Moreover,
the latter of these flows were observed for many minutes.
Bertini did not investigate the traffic conditions leading to breakdowns in detail.
However, earlier work by Edie and Foote ( 1958) provides clues to the traffic conditions
that trigger breakdowns. They reported that flows departing the median lane of New
York’s Holland Tunnel ( South Tube) reached 1400 vehicles per hour ( vph) or more at
free flow speeds of about 25 mph ( the tunnel was a low- speed facility). Following the
breakdown at the tunnel’s bottleneck, its discharge rates diminished significantly to an
average of only 1175 vph.
Edie and Foote believed the breakdowns occurred due to what they called the interaction
between platoons of vehicles: perhaps the kinds of interaction they had in mind here were
drivers prematurely reacting to kinematic waves, or overreacting to waves by adjusting
4
their speeds more dramatically than their leaders. They demonstrated that greater
discharge rates could be achieved by implementing a traffic control strategy believed to
prevent these interactions from occurring. They did so by means of a so- called “ gap
experiment” 1 in the tunnel’s median lane.
Edie and Foote reported that higher discharge rates were obtained by holding down the
entry flows to rates that could be accommodated by their bottleneck. They stated that if
drivers were sufficiently spaced to create lower densities, greater discharge rates could be
achieved by preventing the driver “ interactions”. However, the traffic condition( s) to be
monitored to alter inflows to the bottleneck and deciding appropriate times to alter these
inflows were not examined.
The findings from this dissertation were consistent with Eddie and Foot’s contention:
outflows from bottlenecks can be improved by controlling inflows. Furthermore, present
findings show that by monitoring vehicle accumulations in the vicinity of a bottleneck,
one can determine the appropriate times to alter inflows so as to postpone breakdown or
prevent it from ever occurring.
Daganzo ( 2002) proposed that the changes in drivers’ motivation could cause
breakdowns and explained the breakdown mechanism using the flow- density model
shown in Figure 2.1. The bottom triangle in the figure defines the loci of the possible
1 Whenever 44 vehicles entered the tunnel in less than a two- minute period, Eddie and Foote halted flow
for the remainder of that ( two- minute) period. On some days, this strategy increased the flows from 1175
vph to around 1300 vph. The average rate for twelve test days was 1248 vph. The gap experiments thus
yielded an average increase of 72 vph-- about six percent increase in discharge rate.
5
stationary states for the shoulder lane. The discontinuous upper lines similarly define all
possible states for the median lane.
The behavioral assumptions reflected in Figure 2.1 allow for two possible traffic regimes,
termed “ 2- pipe” and “ 1- pipe” regimes. The 2- pipe regime includes freely flowing
( unqueued) traffic, whereby aggressive drivers termed “ rabbits” ( i. e., drivers with a high
desired free flow speed, Vf) and timid drivers termed “ slugs” ( i. e., drivers with a low
desired free flow speed, vf) separately occupy median and shoulder lanes respectively.
A “ semi- congested” state can also develop within the 2- pipe regime. In this traffic state,
rabbits travel in the passing lane in a fast- moving queue at speed V, with vf < V< Vf :
rabbits are restricted to a less- than- desired speed by other rabbits ahead. This is
represented in the figure by the circle labeled A1. Here rabbits choose to drive with small
headways because they are “ motivated” to pass slugs traveling in the shoulder lane. The
latter are represented by the square labeled B1.
If V eventually diminishes to the point of being equal to ( or slightly below) vf, rabbits no
longer enjoy a speed advantage by traveling in the passing lane. A change in driver
psychology takes place: rabbits loose motivation and switch from a passing to a non-passing
mode. The flow of rabbits thus changes discontinuously and traffic transitions to
a fully congested, 1- pipe regime exemplified by the points separately labeled A2 and B2
in Figure 2.1. The breakdown can be observed during this transition, and this is
6
annotated in the figure. The breakdown mechanism described by Daganzo was
qualitatively consistent with the breakdown mechanism observed at the Gardiner site 2 .
traffic states in passing lane
traffic states in shoulder lane
traffic states combined in both lanes
B 1
v f
V f A 2
B 2
V 1
V 2
A 1 + B 1
A 2 + B 2
Flow
Density
A 1
Figure 2.1 Breakdown mechanism described in Daganzo’s behavioral theory
2 The breakdown mechanism described in Daganzo ( 2002) could not be confirmed at the Orinda site
because no occupancy ( i. e., dimensionless measure of density) data were available at there.
breakdown
7
2.2. Past researches leading to a new algorithm for estimating
vehicle accumulations
The algorithm for estimating vehicle accumulations takes the vehicle count data from
ordinary loop detectors as input and processes these data using; ( i) the cross- correlation
technique; and ( ii) conservation of flow to estimate the vehicle accumulations between
the intervening detectors. The cross- correlation technique has been used by other
researchers to compute the travel times; these studies measured segment travel times
using time differences when identifiable same traffic states were observed between the
neighboring detectors.
Daily ( 1993) used vehicle counts collected over 5- sec sampling intervals in an effort to
estimate vehicle travel times and delays. Daily estimated the segment travel time by
comparing the deviations in flow from 5- min averages at neighboring detectors; the
deviation in flow from the upstream detector was shifted in 5- sec increments until the
correlation between the deviations from the upstream and the downstream detectors
became greater than 0.4. By using such a technique, however, Daily could not measure
the travel time while the traffic was congested, because the deviations in flow propagate
backward in congested traffic 3
Coifman ( 1999) devised a vehicle reidentification algorithm to estimate travel time. This
algorithm compares vehicle lengths measured from upstream detectors with the
measurements from downstream to compute travel times. These vehicle lengths were
3 Eddi and Beverez ( 1967); Lighthill and Whitham ( 1955); and Mauch ( 2002)
8
measured using vehicle occupancy and travel time over double loop detectors: the paired
loops in each double loop detector station were spaced about 20 ft apart and the data were
sampled at 60 Hz ( i. e., reporting data 60 times per second). This method performs well
even while traffic is congested, but requires high frequency data as input. Therefore, the
vehicle reidentification algorithm is not suitable for analyzing traffic data reported in 20-
sec intervals, for example.
Prior to explaining the algorithm for estimating vehicle accumulations in detail, the
findings from this dissertation are presented in the following section.
9
3. Findings
Section 3 presents the findings from having investigated multiple days of data from two
freeway bottlenecks. Data from five days were taken from a bottleneck formed by a
horizontal curve on a stretch of the Gardiner Expressway in Toronto, Canada. Three days
of data came from a bottleneck formed by a reduction in travel lanes on a stretch of State
Route ( SR) 24, in Orinda, California. Findings from the first of these two bottlenecks are
presented in section 3.1. They show that the vehicle accumulations in the vicinity of an
active bottleneck are good proxies for the mechanisms that trigger breakdowns. Also,
evidence is provided to demonstrate that breakdowns can be recovered by controlling the
accumulations. Findings from the second bottleneck on SR- 24 are presented in section
3.2 along with a description of a remarkable event observed there. This event provides
further evidence that breakdowns can be recovered.
3.1. Findings from the Gardiner Expressway, Toronto, Canada
Study of this bottleneck ( formed by a horizontal curve) showed that its breakdown
mechanism was triggered by drivers maneuvering into the freeway’s median lane and
was completed when speeds slowed in this lane, such that its drivers lost motivation to
travel at small spacings as per Daganzo ( 2002). Observations further revealed that the
vehicle accumulations in the vicinity of the bottleneck are good proxies for this
breakdown mechanism. Breakdown only occurred after the accumulation exceeded a
certain threshold ( the critical accumulation) and the capacity losses at the bottleneck
could be recovered once the accumulation dropped below this critical value.
10
Figure 3.1 shows the 2.1 kilometer ( km) segment of westbound Gardiner Expressway
used in this part of the work. The small circles in the figure represent the freeway loop
detectors, numbered 40 through 80. These detectors record vehicle counts, occupancies
( a dimensionless measure of density) and average vehicle speeds over 20- sec sampling
intervals.
Direction of Traffic
280 m
780 m
580 m 490 m
Spadina Ave
: location of detectors
40
50 60
70
80
N
Figure 3.1 Gardiner Expressway, Toronto, Canada
Flows on the Spadina on- ramp were not metered. The freeway is located on an elevated
structure and has no shoulders. The site is plagued by a recurrent active bottleneck
between detectors 60 and 70 and, as such, is an ideal location for studying the evolution
of traffic conditions leading to breakdowns: studying active bottlenecks ensures that
breakdowns are caused by endogenous effects and not by exogenous queues from
downstream or by reductions in traffic demand.
11
The bottleneck between detectors 60 and 70 becomes active during afternoon rush
periods, as exemplified by the cumulative vehicle count curves in Figure 3.2 4 . These
curves were measured during a typical afternoon rush ( on March 5, 1997) at locations
labeled 50 through 80 ( in Figure 3.1): they are denoted as O50, O60, O70, and O80.
O 70 and O 80
6500 vph
5730 vph
6180 vph
O 60
O 50
15: 52
0
500
15: 10
15: 52
16: 35
17: 17
18: 00
Time
V( t) – q 0 ×( t- t 0 ), q 0 = 5820 vph
16: 09
Direction of Traffic
50 60
70
80
Figure 3.2 O- curves from detectors 50, 60, 70 and 80
( Gardiner Expressway, Toronto, Canada, March 5, 1997)
Their key features were made more visible by plotting them in oblique coordinates so that
each displays the quantity O( t) = V( t) – q0×( t – t0), the virtual vehicle count to time, t,
4 Cassidy and Windover ( 1995); Bertini ( 1999)
12
V( t), minus a background reduction; the later is some specified rate, q0, multiplied by the
interval extending from the curves’ start time, t0, to t. This coordinate system magnifies
the figure’s vertical axis, which in turn, amplifies the curves’ vertical separations and
changes in the curves themselves. Vertical separations between two O- curves are the
excess accumulations ( queues) in the intervening segment due to vehicular delay.
Changes in the curves’ slopes indicate changes in flows at the measurement location.
( Negative slopes on the curve merely reveal time periods when flow was smaller than the
background reduction rate, q0.)
Notice how the O- curves at detectors 70 and 80, O70 and O80 remained superimposed
during the entire observation period while a queue resided upstream of detector 70.
Therefore, these curves collectively show that the bottleneck activated between detectors
60 and 70.
The figure also shows that breakdown occurred at 15: 52 as outflows from the site
dropped from 6500 vph to 5730 vph. The mechanism of this breakdown was initiated
when the vehicles in the median lane gradually slowed down for nearly a 40- min period
because of vehicles maneuvering into that lane. After speed in the median lane became
slower than that in the shoulder lane ( the vehicle speed in the median lane was faster than
that of the shoulder lane while the traffic was freely flowing), sudden and pronounced
reductions in both speed and flows were observed in the median lane at detector 60.
Figures 3.3 through 3.6 collectively show the breakdown mechanism described above.
13
Figure 3.3 displays flow- occupancy data jointly measured in the median and the shoulder
lanes of detector 60. These were sampled over consecutive 5- min intervals ( This rather
long sampling interval was used to average- out fluctuations in the data.) Each data point
is numbered in the figure in chronological order of its measurement. Measurements from
the median lane are shown with circles and those from the shoulder lane as squares. The
data from the center lanes are omitted from Figure 3.3 to avoid clutter. Had they been
presented here, the reader would observe that these data tended to fall between the circles
and the squares.
Shoulder lane: Median lane: ( 14: 45 to 15: 10)
Shoulder lane: Median lane: ( 15: 10 to 15: 50)
Shoulder lane: Median lane: ( 15: 50 to 16: 15)
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25 30 35 40
Flow ( vehicle per hour)
1
3
4
5
6
7
8
9
10
11 12 13
14
15 16
1
2
3
4
5
6
7 8
10 9
11 12
14 15
13 16
17
flow = 2,375 vph
2
flow = 1,945 vph
17
slowing down of traffic
Occupancy (%)
Direction of Traffic
60
Figure 3.3 Five- minute aggregate flow- occupancy scatter plot from detector 60
( Gardiner Expressway, Toronto, Canada, 14: 45 ~ 16: 15, March 5, 1997)
14
The data in Figure 3.3 show that traffic in both the median and the shoulder lanes were
freely flowing until 15: 10. After this time, the vehicles in the median lane gradually
slowed down. Notice how the lightly colored circles labeled 6 through 13 migrated to
lower speeds and toward the congested branch of the flow- occupancy relation; these
points moved in the direction shown by the dotted arrow in the figure. This gradual
reduction in speed was caused by traffic maneuvering into the median lane and these
maneuvers are evident in Figure 3.4 and 3.5. These figures display oblique plots of
cumulative vehicle counts measured in the median and center lanes at detectors 40, 50, 60
and 70.
- 200
400
15: 10
15: 40
16: 10
V( t) – q 0 ×( t- t 0 ), q 0 = 1835 vph
15: 52
60
50
40
2370 vph
2090 vph
1985 vph
1920 vph
1710 vph
1565 vph
Time
2530 vph
70
2170 vph
Direction of Traffic
40
50 60
70
Figure 3.4 O- curves for the median lane at detectors 40, 50, 60 and 70
( Gardiner Expressway, Toronto, Canada, March 5, 1997)
15
- 400
100
15: 10
15: 40
16: 10
15: 52
2050 vph
1765 vph
1660 vph
1820 vph
1460 vph
1360 vph
60
50
40
Time
V( t) – q 0 ×( t- t 0 ), q 0 = 1835 vph
70
2060 vph
1860 vph
Direction of Traffic
40
50 60
70
Figure 3.5 O- curves for the center lane at detectors 40, 50, 60 and 70
( Gardiner Expressway, Toronto, Canada, March 5, 1997)
The average flows measured in the median and center lanes at detectors 40 through 70
from 15: 10 to 16: 10 are annotated in Figure 3.4 and 3.5. Notice ( in Figure 3.4) how the
flows in the median lanes at detectors 40 and 50 were about the same, even though the
Spadina on- ramp resides between them. The flows measured in the center lane ( Figure
3.5) at detectors 40 and 50 only differ by approximately 100 vph: the on- ramp flow
remained about 1700 vph during the same period. Together, the figures indicate that
most of the vehicles entering the freeway via the Spadina on- ramp stayed in the shoulder
and auxiliary lanes until they passed detector 50. They maneuvered later into adjacent
16
lanes after passing detector 50: the flows measured in the median and center lanes at
detector 60 were about 400 vph and 300 vph ( respectively) greater than the flows
measured in the median ( Figure 3.4) and center ( Figure 3.5) lanes at detector 50.
Breakdown occurred at 15: 52 when the speed of the traffic in the median lane became
slower than the shoulder lane traffic. This is evident in the lightly shaded circle labeled
13 and the blackened circle labeled 14 in Figure 3.3; they are the data points measured
just before and after breakdown. The gradual slowing of vehicles in the median lane that
resulted in breakdown can also be detected by monitoring the vehicle accumulations, and
this is explained next.
The time series displayed in Figure 3.6 is constructed by taking 5- min moving averages
of vehicle accumulations 5 between detectors 60 and 70. A marked increase ( of 112 vph)
in the vehicle accumulations ( see Figure 3.6) was observed from 15: 10 to 15: 52 and this
period coincides with the time period when slowing was observed in the median lane ( see
Figure 3.3). Findings from multiple days showed that the slowing of vehicles that
initiated the breakdown mechanism coincided with a marked increase in the vehicle
accumulation. Vehicle accumulations are evidently good proxies for the mechanism
triggering breakdown at this bottleneck.
Monitoring the vehicle accumulations in the vicinity of the bottleneck further revealed
that breakdowns only occurred after the vehicle accumulations exceeded the critical value
and evidence of this is provided in table 3.1. The table presents flows observed before
5 The accumulations were estimated from the detector counts using an algorithm described in section 4.
17
and after breakdown on each study day, the durations of these flows and the vehicle
accumulation ( between detectors 60 and 70) when each breakdown was observed.
Notably, breakdown only occurred after the vehicle accumulation exceeded 89 vehicles.
We therefore treat 89 vehicles as the site’s critical accumulation.
0
20
40
60
80
100
120
140
14: 45
15: 50
16: 55
18: 00
Vehicle Accumulations ( vehicles)
Time
112 vph
( 15: 10, 35)
( 15: 52, 95)
Direction of Traffic
60
70
Figure 3.6 Five- minute moving average of vehicle accumulations between detectors 60
and 70 ( Gardiner Expressway, Toronto, Canada, March 5, 1997)
Notice the vehicle accumulation never exceeded 75 vehicles on the final day listed in
table 3.1. As an apparent consequence, breakdown did not occur. Instead, high outflows
in excess of 6,200 vph persisted for the entire rush period ( 170 mins). This remarkable
observation serves as “ a natural experiment;” i. e., it unveils the expected outcome from
18
controlling accumulation exogenously ( e. g. by metering an on- ramp), and it shows that
breakdown can be avoided entirely if the vehicle accumulation is kept under the site’s
critical accumulation.
Date
Flow before breakdown
( duration)
Flow after breakdown
( duration)
Vehicle accumulation
3/ 5/ 1997 6500 vph ( 45 min) 5730 vph ( 17 min) 95 vehicles
2/ 11/ 1997 6150 vph ( 24 min) 5670 vph ( 60 min) 104 vehicles
4/ 28/ 1998 6300 vph ( 29 min) 6090 vph ( 31 min) 100 vehicles
5/ 1/ 1998 6280 vph ( 49 min) 6035 vph ( 18 min) 89 vehicles
5/ 12/ 1998 6230 vph ( 170 min) N. A. < 75 vehicles
Table 3.1 Summary of breakdowns at Gardiner Expressway, Toronto, Canada
The capacity losses at the bottleneck after breakdown can also be recovered if the vehicle
accumulation is reduced below the site’s critical accumulation. Evidence of this kind was
observed on February 11, 1997. The following describes the traffic conditions that led to
a capacity recovery.
The O- curves for a period on that day are displayed in Figure 3.7. These curves
reconfirm that the active bottleneck resided between detectors 60 and 70. The breakdown
occurred on this day at 15: 20 and the capacity reduction became more severe at 15: 53.
The vehicle accumulations between detectors 60 and 70 during the same period are
displayed in Figure 3.8.
The recovery process observed at the site was initiated when the flows arriving at
detector 50 diminished ( to 5120 vph) at 16: 12 ( see the curves inscribed in the dotted
circle in Figure 3.7). The upstream traffic conditions that reduced flows could not be
19
Direction of Traffic
50 60
70
80
Time
V( t) – q 0 ×( t- t 0 ), q 0 = 5570 vph
- 350
150
14: 00
14: 30
15: 00
15: 30
16: 00
16: 30
6150 vph
15: 00
15: 20
5885 vph
5230 vph
5990 vph
5670 vph
15: 53
16: 10
16: 20
O 70 and O 80
O 60
O 50
16: 13 16: 12
5650 vph
16: 20
5120 vph
5120 vph
Figure 3.7 O- curves for detectors 50, 60, 70 and 80
( Gardiner Expressway, Toronto, Canada, February 11, 1997)
uncovered since no ramp data were available on this day. When these reduced flows
( 5120 vph) reached detector 60 at 16: 13 ( in the encircled portion of Figure 3.7), the
vehicle accumulation between detectors 60 and 70 started to decrease because of the
difference in flows entering and leaving the segment ( see Figure 3.8). The inflow
remained at 5120 vph and the outflow at 5650 vph until 16: 20; this too is shown in the
20
encircled portion of Figure 3.7. When the vehicle accumulation diminished to a lower
value ( shown to be 50 vehicles in Figure 3.8), the outflow from the bottleneck increased
to 5990 vph ( Figure 3.7). These findings ( i. e., correlations between critical accumulation
and the recovery of breakdown) were also reproducible at SR- 24, and they are presented
in the next section.
0
20
40
60
80
100
120
140
14: 00
14: 30
15: 00
15: 30
16: 00
16: 30
Vehicle Accumulations ( vehicles)
Time
Direction of Traffic
60
70
( 16: 13, 81)
( 16: 20, 50)
( 15: 20, 104)
Figure 3.8 Five- minute moving average of vehicle accumulations between detectors 60
and 70 ( Gardiner Expressway, Toronto, Canada, February 11, 1997)
21
3.2. Findings from SR- 24, Orinda, California
No loop detectors were present at this site. Therefore, four cameras were strategically
deployed along this freeway stretch to record individual vehicle arrival times at locations
marked as 1, 2, 3 and 4 in Figure 3.9. The vehicle arrival times were manually extracted
from the videotapes.
N
1600 m
480 m 280 m
320 m
Fish Ranch Road
Gateway
Caldecott Tunnel
Direction of Traffic
4
3
2
1
Stalled Vehicle
Figure 3.9 State Route 24, Orinda, California
The site is plagued by recurrent active bottleneck that resides between locations 2 and 3
due to the reduction in travel lanes and breakdowns were observed there on a daily basis.
Table 3.2 summarizes the findings from the three days studied here: the table presents
flows observed before and after the breakdown on each study day, the durations of these
flows and the vehicle accumulation ( between locations 2 and 3) when the breakdown was
observed. Notably, breakdowns only occurred after the vehicle accumulation exceeded
25 vehicles. We therefore treat 25 vehicles as the site’s critical accumulation
22
Date Flow before breakdown
( duration)
Flow after breakdown
( duration)
Vehicle accumulation
8/ 21/ 2002 4070 vph ( 11 min) 3860 vph ( 40 min) 27 vehicles
8/ 07/ 2004 4240 vph ( 36 min) 4025 vph ( 18 min) 25 vehicles
8/ 14/ 2004 4355 vph ( 14 min) 3985 vph ( 10 min) 26 vehicles
Table 3.2 Summary of breakdowns at SR- 24, Orinda, California
- 60
40
14: 00
14: 20
14: 40
15: 00
15: 20
15: 40
16: 00
16: 20
Time
V( t) – q 0 ×( t- t 0 ), q 0 = 3890 vph
O 3 ( with on- ramp count) and O 4
3860 vph
4070 vph
Direction of Traffic
Stalled Vehicle
3
4
Caldecott Tunnel
15: 16
Figure 3.10 O- curves from locations 3 and 4
( SR- 24, Orinda, California, August 21, 2002)
A remarkable event was observed on the first day listed in Table 3.2 ( August 21, 2002).
A disabled vehicle parked in the freeway’s median ( see Figure 3.9). This event caused
the vehicle accumulation in the vicinity of the bottleneck to return to that of a free flow
23
state. As a result, bottleneck’s outflow eventually recovered. The event is described in
detail below.
- 100
0
14: 00
14: 20
14: 40
15: 00
15: 20
15: 40
16: 00
16: 20
V( t) – q 0 ×( t- t 0 ), q 0 = 3890 vph
Time
O 3 ( without on- ramp count)
O 2 ( without off- ramp count)
3860 vph
4070 vph
3605 vph
4050 vph
15: 16
15: 52
16: 05
Direction of Traffic
Stalled Vehicle
2
3
Caldecott Tunnel
14: 43
Figure 3.11 O- curves from locations 2 and 3
( SR- 24, Orinda, California, August 21, 2002)
Figure 3.10 and 3.11 display the O- curves from locations 2, 3 and 4 on August 21, 2002;
they are drawn in pair- wise fashion so that in both figures, vehicle counts were conserved.
These curves, however, can be used collectively to verify the location of active
bottleneck. The O- curves from locations 3 and 4 shown in Figure 3.10 remained
superimposed during the entire observation period, indicating that the traffic between the
24
intervening segment was always freely flowing. The displacement between the curves
from locations 2 and 3 ( see Figure 3.11) beginning at about 14: 43 reveals the formation
of the queue upstream of location 2. Therefore, the curves from locations 2, 3, and 4
collectively show that an active bottleneck resided somewhere between locations 2 and 3.
Breakdown was observed at approximately 15: 16 ( see Figure 3.11) and it diminished
outflows from 4070 vph to 3860 vph; these changes in flows are annotated in Figure 3.11
and they do not include on- ramp flow.
At 15: 52, a passenger car made an emergency stop in the median at a location annotated
in Figure 3.9, a short distance upstream of location 2. The stalled vehicle remained there
until 16: 20; this event is documented in video.
Although the stalled vehicle did not block a travel lane, it temporarily reduced the flow
departing the site. Figure 3.11 shows that flows dropped from 3860 vph to 3605 vph.
Evidently, the vehicle stall initially caused a rubber- necking effect among passing
motorists.
The event caused the vehicle accumulations between locations 2 and 3 to return to that of
the free flow state. This is evident in the 5- min moving average of vehicle accumulations
shown in Figure 3.12. As an apparent consequence of the lower vehicle accumulation,
the outflow past location 3 rose substantially; Figure 3.11 shows that at 16: 05, the
outflow measured at location 3 increased from an average rate of 3,605 vph to 4,050 vph.
25
This new rate was higher than the queue discharge rate ( of 3,860 vph) observed prior to
the vehicle stall and this rate persisted for an extended time, as is evident in the figure.
0
10
20
30
40
50
14: 00
14: 20
14: 40
15: 00
15: 20
15: 40
16: 00
16: 20
Vehicle Accumulations ( vehicles)
Time
( 15: 16, 27)
( 15: 52, 30)
( 16: 05, 14)
Direction of Traffic
Stalled Vehicle
2
3
Caldecott Tunnel
Figure 3.12 Five- minute moving average of vehicle accumulations from
locations 2 and 3 ( SR- 24, Orinda, California, August 21, 2002)
Findings presented in section 3.1 and 3.2 show that vehicle accumulations in the vicinity
of active bottleneck are good proxies for the mechanisms triggering breakdown.
Breakdown only occurred after vehicle accumulation exceeded the bottleneck’s critical
accumulation. Breakdown could be avoided entirely or recovered by controlling the
26
vehicle accumulations. Breakdown could recover when the vehicle accumulations
diminished sufficiently below the site’s critical accumulation.
These findings came to light by monitoring the vehicle accumulations in the vicinity of
active bottlenecks. Vehicle accumulations at the SR- 24 site were monitored in accurate
fashion using individual vehicle arrival times ( at fixed locations) that were manually
extracted from videos. Vehicle accumulations at the Gardiner Expressway, however,
could not be monitored in such an accurate manner because the data were taken here
were extracted from loop detectors and these naturally exhibited bias ( i. e., systematic
count errors). The algorithm for estimating vehicle accumulation was developed, in part,
to remedy the problem of detector bias. Section 4 explains the algorithm and its
applications.
27
4. An algorithm for estimating vehicle accumulation and its
applications
This chapter presents; ( i) an algorithm for estimating vehicle accumulations from the
counts made by ordinary detectors ( e. g. inductive loops detectors) placed in series in
section 4.1; ( ii) the results of testing the algorithm in section 4.2; and ( iii) the algorithm’s
applications ( e. g. real- time traffic control, incident detection and delay estimation) in
section 4.3.
The algorithm’s estimates of the vehicle accumulations can be obtained in real- time at
short intervals of a second or so. The algorithm is, thus, well suited for monitoring the
vehicle accumulations near a bottleneck prior to breakdown and the estimates it furnishes
can, in turn, dictate control actions ( e. g. metering rates) that prolong higher outflows
from the bottleneck.
The algorithm can also be used to detect incidents by monitoring the rate at which the
vehicle accumulations increase: an incident causes the vehicle accumulation to increase
rapidly while activation of a recurrent bottleneck causes the accumulation to increase
gradually. Although the algorithm cannot function in a self- correcting manner once a
queue arises on the freeway segment spanning the detectors in series, it can be used to
estimate delays in an off- line fashion ( e. g. for planning purposes) after freely flowing
traffic has been restored. Section 4.3 describes these applications in more detail.
28
4.1. Algorithm Description
The algorithm’s logic is explained with the aid of Figure 4.1. It displays curves of
cumulative vehicle count, N, vs time, t, measured by the detectors at an upstream
location, XU, and by the detectors downstream at XD.
Number of vehicles
Time
 
N( t, XU)
Direction of Traffic
X U X D
N( t, XD)
*
j a
t0 t0− 0 t j
j a
j
) ( t, X N ˆ
D
ai
ti
Figure 4.1 Hypothetical input- output diagram
The counts at XD began a time R 0 after those at XU, where R 0 is a freely flowing vehicle’s
trip time between the two locations. At any time ti, i > 0, the accumulation between
detectors, ai, is the vertical separation between the N- curves; i. e.,
ai = N( ti, XU) – N( ti, XD), as shown in the figure.
29
The matter is made complicated by the bias that occurs in the detector counts; when left
uncorrected, errors in the estimate of ai can increase with increasing i. Bias may occur in
the detectors at XU, at XD or at both. But since the goal here is to estimate an ai, it
suffices to correct the counts at one location ( e. g. XD) relative to those at the other ( XU).
The algorithm makes these corrections automatically at various tj, j > i. Doing so
requires estimates of R j, the trip time between locations for a vehicle arriving at XD at
time tj. How the algorithm obtains these estimates will be described momentarily. Note
for now that with the R j, the corrected accumulation, aj
*, is N( tj, XU) – N( tj – R j, XU), as
shown in Figure 4.1.
The accumulation at any earlier time ti can then be corrected by proportioning the
difference between aj
* and aj; i. e.,
ai
* = N( ti, XU) – N( ti, XD) + b N( ti, XD),
where ai
* is the corrected estimate at time ti; and
b is a dimensionless correction factor computed as ( aj
* – aj) / N( tj, XD).
The j is reset to zero ( tj = t0) when an aj
* is obtained and the above process is then
repeated.
An aj
* is obtained whenever the R j can be estimated with reasonable accuracy. The
process rests on the assumption that in freely flowing traffic, disturbances ( flow changes)
30
propagate forward with vehicles. This assumption has been adopted in traffic flow
theories 6 and has been empirically verified 7 even when unqueued flows approach
capacity. Freely flowing vehicle trip times are therefore taken as the times measured for
disturbances to propagate from XU to XD in unqueued traffic.
Following from this assumption, the algorithm matches the flow deviations measured in
each freeway travel lane at XU with those measured later in time at XD. ( A similar
technique was used in Mauch ( 2002) for tracing backward- moving disturbances in
queued traffic.) The deviations are taken relative to a moving average flow. If, for
example, the detectors use 20- sec sampling intervals, the count deviation from the
average of 15 such intervals ( a 5- min average) is defined here as ( N – N15)( tk) for time tk,
where the subscript k denotes the detector’s k- th sampling interval, k = 1, 2, …, and is
computed as
( N – N15)( tk) = ( N( tk) – N( tk- 15))/ 15 + ( N – N15)( tk - 1),
and when 0 < k < 15 ( i. e., when t0 < tk < t0 + 5 mins), the deviation, ( N – Nk)( tk), is
computed as
( N – Nk)( tk) = ( N( tk) – N( t0))/ j + ( N – Nk)( tk - 1).
6 Lighthill and Whitham ( 1955); Newell ( 1993)
7 Windover ( 2001)
31
Notation referring to measurement location is omitted from the above equations. The
reader will note nonetheless that deviations over time are separately computed for each
travel lane and for each location XU and XD. These computations occur in real- time, with
no need for predicting counts in future times, and deviations can be estimated at small
time intervals ( e. g. every second) by linearly interpolating the counts measured over the
detectors’ sampling intervals.
Trip times, R j, are measured ( e. g. to a resolution of 1- sec) by matching a given lane’s
pattern of count deviations at XU with those at XD. The algorithm virtually constructs a
time series of flow deviations as described above for a lane at XD for some extended
period ( e. g. 30 mins) ending at a time tj. The time series for the same lane at XU is
measured from the same start time ( e. g. tj – 30 mins) but ends at time tj – R , where R is
some value several times larger than a feasible value of R j. In effect, the R j is estimated to
be the temporal shift that most nearly superimposes the entire curve at XU with its
corresponding curve at XD. The shift selected is the one that yields the highest
correlation coefficient.
Whenever this correlation is large ( e. g. 0.5 or more) in each of the freeway segment’s
travel lanes, the algorithm takes R j to be an average of each lane’s trip time weighted by
the flows in these lanes. This is the R j used to obtain an aj
*. The start and end times of all
time series of flow deviations are next advanced by some time step ( e. g. 5 mins) and the
process repeats.
32
Flow deviations at detector 60 shifted 20 seconds forward in time
Flow Deviations at detector 70
- 15 0 15
12: 30
12: 40
12: 50
13: 00
Time
Deviation ( vehicles)
Direction of Traffic
60
70
Figure 4.2( a) Example of deviation curves from two neighboring detectors
( Gardiner Expressway, Toronto, Canada, March 5, 1997)
Figure 4.2( a) and ( b) show how the trip time in the median lane between detectors 60 and
70 at the Gardiner Expressway was estimated by comparing the deviations in flow.
Figure 4.2( a) display the deviations in flow observed at the median lane at detector 60
and the deviations in the same lane at detector 70. The curve displayed in Figure 4.2( b)
shows how the correlation coefficient changed when the deviation curve from the
upstream detector ( 60) is shifted in forward in time by 1- sec increments. The maximum
correlation was obtained when the curve was shifted 20 second. The segment travel time
was thus estimated to be 20 seconds.
33
Deviation curves are also advanced by some time step ( i. e., 5 mins) when the correlation
in any lane is small ( e. g. below 0.5), such that an aj
* is not obtained. Low correlations
arise when disturbances are altered while propagating from XU to XD. This can be the
result of driver lane- change maneuvers or even erratic behavior on the part of a few
drivers. And low correlations almost always occur in queued traffic, since disturbances
travel backward in queues.
( 20, 0.896)
- 1
- 0.5
0
0.5
1
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
Shifted time in seconds
Correlation
Figure 4.2( b) Estimating segment travel time using cross- correlation technique
( Gardiner Expressway, Toronto, Canada, March 5, 1997)
34
4.2. Algorithm Validation
Validation of the algorithm was conducted using data from the site shown in Figure 4.3, a
stretch of eastbound Interstate 80 in Berkeley, California. The vehicle counts used as
input to the algorithm were collected ( over 20- sec sampling intervals) on August 9, 2003
using the inductive loops shown in the figure. Validation data ( vehicle accumulations
and trip times between the detectors in series) were sampled from video taken from the
nearby over- crossing.
Ashby off- ramp
350m
Ashby on- ramp
L7 L8
N
Direction of Traffic
: location of detectors
Figure 4.3 Eastbound Interstate 80, Berkeley, California
The algorithm furnished estimates of R j and aj
* up to time t = 11: 57 ( The time series of
flow deviations were constructed at 1- sec intervals for 30- min periods.) Shortly after
11: 57, queues formed and persisted on the intervening freeway segment for nearly 5
hours, such that an aj
* was not obtained again until t = 16: 54. The correction factor, b,
35
was determined for this later time and used to adjust the estimates of accumulation made
during the ( entire) queued period.
0
100
200
300
400
16: 25
16: 30
16: 35
16: 40
16: 45
16: 50
Vehicle Accumulations ( vehicles)
Not corrected for bias
Corrected for bias
Count from video
Time
Figure 4.4 Comparison of estimated and actual vehicle accumulations between detectors
L7 and L8 ( I- 80, Berkeley, California, August 9, 2003)
The lightly drawn curve in Figure 4.4 presents these adjusted accumulations for the final
35- mins or so of queuing. The shaded circles are accumulations that were counted
directly from the frames of videotape. These circles were extracted at 1- min time steps,
except for those times when large trucks obscured from viewing the presence of cars
downstream, rendering accurate counts impossible. The ( self- corrected) estimates
differed on average from the field- measured values by only about 6 percent.
36
The value of the algorithm’s self- correcting feature is underscored using the dark curve in
Figure 4.4. This line shows the accumulations the algorithm would have furnished had
the bias factor, b, not been applied. The dark line deviates from the field- measured
circles by 200 vehicles or more, a finding that is not surprising given that the
( uncorrected) detector counts were allowed to drift for some 5 hours.
20
40
60
80
100
120
140
16: 25
16: 30
16: 35
16: 40
16: 45
16: 50
Travel Time ( second)
Time
estimated from video
Loop detector estimate
Algorithm estimate
Figure 4.5 Trip time comparison between detectors L7 and L8
( I- 80, Berkeley, California, August 9, 2003)
Finally, Figure 4.5 is provided here to validate R j estimated by the algorithm. The light
line in this figure displays the algorithm’s ( self- corrected) estimates at 1- sec time steps.
The shaded circles in Figure 4.5 are trip times sampled from the video; each is the
average of 4 vehicles observed in the freeway’s shoulder and median lanes. These
estimates agree with the field- measured values to within 7 percent.
37
In contrast, the dark line in Figure 4.5 displays trip times estimated by averaging the
harmonic mean vehicle speeds measured ( in all lanes) by the upstream detectors with
those measured by the downstream ones 8 . These latter estimates tend to differ
substantially from the values sampled from the video. The data displayed in Figure 4.5
show that more accurate estimates of the segment travel time can be obtained using the
algorithm for estimating vehicle accumulation.
8 According to Oh, Jayakrishnan and Recker ( 2002), this is a common approach to trip time estimation.
38
4.3. Applications of the Algorithm
This section describes how the algorithm can be applied as part of traffic control
schemes, for automatic incident detection and for delay estimation. These applications
are based on observations from a few days of data and are on- going research topics.
4.3.1. Real- time ramp metering strategy
Findings from this dissertation revealed that breakdowns only occurred after the vehicle
accumulations in the vicinity of the bottleneck exceeded some critical accumulation.
When vehicle accumulations remained below the critical value, high outflows were
sustained for the entire afternoon rush ( e. g. on May 11, 1997 at the Gardiner Expressway)
and breakdown did not occur. This finding suggests that by controlling inflows ( e. g.
metering rates) to the bottleneck area in response to measured vehicle accumulation,
breakdown can be entirely avoided.
In some circumstances, keeping the vehicle accumulation below the critical value during
the entire rush period is not possible due to the limited space available for storing queued
vehicles on a metered ramp, for example. Still, damping the rate at which the vehicle
accumulation increases can postpone breakdown and mitigate the delay. Maintaining the
higher ( pre- breakdown) capacity for a longer period reduces system- wide delay.
The algorithm’s estimates can also be the basis for implementing control after a capacity
drop has occurred. Although the algorithm cannot function in a self- correcting manner
once a queue arises on the freeway segment spanning the detectors in series, control
39
during periods of capacity drop can be deployed in a restrictive fashion. ( The severity of
this control would be limited by certain local conditions, such as the space available for
storing queued vehicles on a metered ramp.) Recoveries in outflows observed on
February 11, 1997 at the Gardiner Expressway and on August 21, 2002 at the SR- 24
suggest such a strategy is possible.
4.3.2. Incident detection
Incidents can be detected and differentiated from the activations of recurrent bottlenecks
by monitoring the vehicle accumulations. Both events cause vehicle accumulations to
increase. Depending on the causes ( i. e., incident or activation of recurrent bottleneck),
however, the rate at which accumulations increase can be notably different. Evidence is
shown in Figure 4.6.
The figure shows vehicle accumulations between detectors 60 and 70 at the Gardiner
Expressway on March 5, 1997 from 12: 30 to 18: 00. Marked increases in the vehicle
accumulations were observed twice during this period. The first sustained increase in the
vehicle accumulations ( at a rate of 227 vph) was observed at 13: 10, as indicated in the
figure. This increase was caused by an incident which is described as the presence of
“ maintenance crew” in the daily unscheduled traffic event report from Toronto’s Road
Emergency Services Communication Unit ( RESCU). The incident was recorded in the
RESCU report at13: 25; this was about 15 minutes after the marked increase in the vehicle
accumulation had been observed. The queue caused by the incident was cleared up by
14: 09 ( according to the RESCU report).
40
The second sustained increase in vehicle accumulation ( 112 vph) was observed from
15: 10 to 15: 52 ( Figure. 4.9). According to the RESCU report, formation of a queue was
detected between detectors 60 and 70 at approximately 15: 40. The cause of the queue
was described as “ high traffic volume” in the report; it was caused by the activation of
the recurrent bottleneck. The summary of the RESCU report describing these two events
is presented in Table 4.1, and the actual RESCU report is included in the appendix A.
Vehicle Accumulations ( vehicles)
0
20
40
60
80
100
120
140
12: 30
13: 00
13: 30
14: 00
14: 30
15: 00
15: 30
16: 00
16: 30
17: 00
17: 30
18: 00
Time
227 vph
112 vph
( 13: 10, 25)
( 15: 10, 35)
Direction of Traffic
60
70
( 15: 52, 95)
( 13: 25, 80)
( 14: 09, 65)
( 15: 40,67)
Figure 4.6 Vehicle accumulation between detectors 60 and 70 from 12: 30 to 18: 00
( Gardiner Expressway, Toronto, Canada, March 5, 1997)
The rate at which the vehicle accumulation increased due to an incident ( 227 vph) was
substantially higher than when it was caused by high traffic volume ( 112 vph) on March
41
5, 1997. The highest rate at which vehicle accumulations increased on four other days
due to high volume of traffic was 143 vph. Furthermore these rates were sustained for
prolonged periods of time; these periods ranged from 10 minutes to nearly 50 minutes.
These substantial differences ( i. e., the rate at which vehicle accumulations increase)
suggest that incidents can be detected and distinguished from the activations of recurrent
congestion.
Date March/ 5/ 1997 March/ 5/ 1997
Location Between detectors 60 and 70 Between detectors 60 and 70
Detection time 13: 25 15: 40
Event Cause Maintenance Crew High Traffic volume
Description Incident blocked one lane P. M. Peak Congestion
Queue Dissipated time 14: 09 19: 46
Table 4.1 Description of the two events
4.3.3. Delay estimation
Once vehicle accumulations for an entire day are estimated in an off- line fashion, the
delay caused by incidents and recurrent congestion can be computed separately. Figure
4.7 shows the segment travel time estimated by the algorithm between detectors 60 and
70 from 12: 30 to 18: 00 ( on March 5, 1997) and the validity of such estimation has been
presented in section 4.2. The area denoted as I, is the delay caused by the incident and R
is that of recurrent congestion. These areas can be multiplied with flows during the same
period to estimate total delay. These are very important statistics for evaluating
performance of freeways and for planning purposes.
42
0
20
40
60
80
100
120
140
12: 30
13: 00
13: 30
14: 00
14: 30
15: 00
15: 30
16: 00
16: 30
17: 00
17: 30
18: 00
Time
Travel Time ( seconds)
I
R
Direction of Traffic
60
70
Figure 4.7 Estimated travel times between detectors 60 and 70 under assumption of a
FIFO queue discipline ( Gardiner Expressway, Toronto, Canada, March 5, 1997)
43
5. Conclusions
Section 5.1 summarizes the findings from this dissertation and section 5.2 presents an
outline of areas for further research.
5.1. Summary of findings
The breakdown mechanism observed at the Gardiner Expressway was triggered by the
freeway on- ramp flow maneuvering into the median lane. The vehicles in the median
lane were slowed down due those maneuvering vehicles, and the breakdown mechanism
was completed when the speed of the vehicles in the median lane became slower than the
shoulder lane traffic. Findings showed that the vehicle accumulations in the vicinity of
the bottleneck are good proxies for this breakdown mechanism.
At the SR- 24, regrettably, the cameras’ vantage points did not offer views of traffic
flowing between the four measurement locations and no occupancy data were available.
These restrictions made uncovering details of the breakdown mechanism at the SR- 24
site impossible. The findings did, however, confirm that the accumulation is a good
proxy for this bottleneck’s unidentified breakdown mechanism.
Monitoring the vehicle accumulations near the bottleneck revealed many important
characteristics of breakdown. Breakdown only occurred after the vehicle accumulation
exceeded some threshold ( critical accumulation). The critical accumulation was site
specific and fairly reproducible. When the vehicle accumulation was reduced sufficiently
44
below the site’s critical accumulation, recovery in outflow was observed. Furthermore,
findings showed that breakdown can be entirely avoided by controlling the accumulation.
An algorithm for estimating vehicle accumulations has been developed in this
dissertation. The algorithm estimates vehicle accumulations that arise on the intervening
( freeway) segments between the detectors. These estimates can be obtained in real- time
at short intervals of a second or so. The systematic errors ( bias) that invariably arise in
detector counts are automatically corrected when traffic is freely flowing.
The validity of the algorithm has been tested by comparing its estimates with actual
accumulations counted from videotape. The algorithm’s estimates were on average only
6% different from the actual vehicle accumulations. The segment travel times were also
estimated using the algorithm under the assumption of a FIFO queue discipline, and the
estimated travel times were more accurate ( see Figure 4.5) that segment travel time
estimated using the speed obtained from loop detector data.
45
5.2. Areas of further research
The algorithm can estimate the vehicle accumulations in real- time at short intervals of
second or so. The algorithm is thus well suited for monitoring accumulations near a
bottleneck prior to capacity drops and the estimates it furnishes can, in turn, dictate
control actions ( e. g. metering rates) that prolong higher bottleneck outflows. One such
strategy that employs ramp metering has been qualitatively described in section 4.3.1.
This study, however, did not empirically demonstrated how such metering strategy ( in
section 4.3.1) can mitigate the delay. Cassidy and Rudjanakanoknad ( 2002) presented a
study of one such strategy, and their efforts to develop more systematic ways of
controlling freeway traffic using ramp metering is ongoing.
Section 4.3.2 presented an example of how incidents and the activations of recurrent
bottleneck can be detected and differentiated by monitoring the vehicle accumulation.
Incident reported in this dissertation caused the accumulation to increase at a rate
substantially higher than what was generated by a recurrent bottleneck activation. This
is, however, based on comparing the observations from only one incident with multiple
non- incident days. Additional days of incident data need to be analyzed to develop more
systematic ways of detecting incidents by monitoring the vehicle accumulations.
46
Reference
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4. Cassidy, M. J. & Bertini, R. L. ( 1999a), Some Traffic Features at Freeway
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48
Appendix- A
DAILY UNSCHEDULED TRAFFIC EVENT REPORT ( Gardiner
Expressway, March 5, 1997)
For 05- MAR- 1997 00: 00 To 06- MAR- 1997 00: 00
QUEUE EVENTS
Report Date: 97 3 6 01: 16: 02
Page: 11
Event ID : 5406 Event Type : QUEUE
Detected : 5- MAR- 1997 15: 39: 51 Confirmed : 1- JAN- 1900
00: 00: 00 Owner : MFREDERICKS
Queue Source : OPERATOR
Queue Cause : TRAFFIC VOLUME
Event State : OPERATOR DECLARED
Start Location: 99m downstream of STRACHAN, 1206m upstream of DUFFERIN
on the Westbound_ Gardiner
End Location : 448m downstream of REES, 0m upstream of SPADINA on the
Westbound_ Gardiner
Severity : not severe
Manual Q Track: disabled
System Q Track: enabled
Precipitation : not specified
Road Condition: not specified
Description :
Updated: 5- MAR- 1997 15: 39: 52
EVENT UPDATES:
--------------
Updated: 5- MAR- 1997 15: 39: 57 Manual Q Track: enabled
Updated: 5- MAR- 1997 15: 48: 19 Owner : NOT_ OWNED
Updated: 5- MAR- 1997 15: 48: 38 Owner : HPANESAR
Updated: 5- MAR- 1997 15: 51: 22 Event State : CONFIRMED
Updated: 5- MAR- 1997 15: 51: 51 Description : P. M. peak hour
congestion.
Updated: 5- MAR- 1997 16: 03: 15 Owner : NOT_ OWNED
Updated: 5- MAR- 1997 16: 03: 41 Owner : MFREDERICKS
Updated: 5- MAR- 1997 16: 13: 02 End Location : 297m downstream of BAY,
0m upstream of YORK on the Westbound_ Gardiner
Updated: 5- MAR- 1997 16: 13: 02 Manual Q Track: disabled
Updated: 5- MAR- 1997 16: 13: 16 Manual Q Track: enabled
Updated: 5- MAR- 1997 18: 04: 35 Start Location: 599m downstream of
DOWLING, 815m upstream of PARKSIDE on the Westbound_ Gardiner
Updated: 5- MAR- 1997 18: 04: 35 End Location : 388m downstream of REES,
60m upstream of SPADINA on the Westbound_ Gardiner
Updated: 5- MAR- 1997 18: 04: 35 Manual Q Track: disabled
Updated: 5- MAR- 1997 18: 04: 39 Manual Q Track: enabled
Updated: 5- MAR- 1997 18: 39: 05 Start Location: 299m downstream of
COLBORNE LODGE, 268m upstream of ELLIS on the Westbound_ Gardiner
Updated: 5- MAR- 1997 18: 39: 05 Manual Q Track: disabled
Updated: 5- MAR- 1997 18: 39: 28 Manual Q Track: enabled
49
Updated: 5- MAR- 1997 19: 18: 21 End Location : 645m downstream of
SPADINA, 10m upstream of BATHURST on the Westbound_ Gardiner
Updated: 5- MAR- 1997 19: 18: 21 Manual Q Track: disabled
Updated: 5- MAR- 1997 19: 18: 27 Manual Q Track: enabled
Updated: 5- MAR- 1997 19: 23: 51 Owner : NOT_ OWNED
Updated: 5- MAR- 1997 19: 24: 01 Owner : HPANESAR
Updated: 5- MAR- 1997 19: 31: 42 End Location : 1305m downstream of
STRACHAN, 0m upstream of DUFFERIN on the Westbound_ Gardiner
Updated: 5- MAR- 1997 19: 31: 42 Manual Q Track: disabled
Updated: 5- MAR- 1997 19: 32: 04 Manual Q Track: enabled
Updated: 5- MAR- 1997 19: 46: 03 Event State : CONFIRMED( SYSTEM CLEAR)
Updated: 5- MAR- 1997 19: 46: 19 Event State : FREE
Updated: 5- MAR- 1997 19: 46: 19 Manual Q Track: disabled
DAILY UNSCHEDULED TRAFFIC EVENT REPORT
For 05- MAR- 1997 00: 00 To 06- MAR- 1997 00: 00
INCIDENT EVENTS
Report Date: 97 3 6 01: 15: 57
Page: 23
Event ID : 5400 Event Type : INCIDENT
Detected : 5- MAR- 1997 13: 25: 22 Confirmed : 1- JAN- 1900
00: 00: 00 Owner : RHENDERSON
Event Source : OPERATOR
Event Cause : MAINTENANCE CREW
Event State : OPERATOR DECLARED
Severity : not severe
Station ID : dw0060dwg
Location : 399m downstream of STRACHAN, 906m upstream of DUFFERIN
on the Westbound_ Gardiner
Blocked Lanes : OOX
Left Shoulder :
Right Shoulder:
2nd Incident : not specified
Precipitation : not specified
Road Condition: not specified
Description :
Updated: 5- MAR- 1997 13: 25: 23
EVENT UPDATES:
--------------
Updated: 5- MAR- 1997 14: 05: 39 Owner : NOT_ OWNED
Updated: 5- MAR- 1997 14: 05: 55 Owner : MFREDERICKS
Updated: 5- MAR- 1997 14: 09: 02 Event State : FREE
DAILY UNSCHEDULED TRAFFIC EVENT REPORT