ISSN 1055- 1425
November 2008
This work was performed as part of the California PATH Program of the
University of California, in cooperation with the State of California Business,
Transportation, and Housing Agency, Department of Transportation, and the
United States Department of Transportation, Federal Highway Administration.
The contents of this report reflect the views of the authors who are responsible
for the facts and the accuracy of the data presented herein. The contents do not
necessarily reflect the official views or policies of the State of California. This
report does not constitute a standard, specification, or regulation.
Final Report for Task Order 5306
CALIFORNIA PATH PROGRAM
INSTITUTE OF TRANSPORTATION STUDIES
UNIVERSITY OF CALIFORNIA, BERKELEY
Causes of Freeway Productivity Decline and
the Opportunities for Gain: A Quantitative
Study
UCB- ITS- PRR- 2008- 31
California PATH Research Report
Pravin Varaiya
CALIFORNIA PARTNERS FOR ADVANCED TRANSIT AND HIGHWAYS
C a u s e s o f f r e e w a y p r o d u c t i v i t y d e c l i n e a n d t h e o p p o r t u n i t i e s
f o r g a i n : A q u a n t i t a t i v e s t u d y
F i n a l R e p o r t f o r P A T H T a s k O r d e r 5 3 0 6
P r a v i n V a r a i y a
U n i v e r s i t y o f C a l i f o r n i a , B e r k e l e y , C A 9 4 7 2 0 - 1 7 7 0
T e l : ( 5 1 0 ) 6 4 2 - 5 2 7 0 , F a x : ( 5 1 0 ) 6 4 2 - 7 8 1 5
v a r a i y a @ e e c s . b e r k e l e y . e d u
A b s t r a c t
W o r k d o n e u n d e r T O 5 3 0 6 l e d t o t h r e e a c c o m p l i s h m e n t s . F i r s t , a m e a s u r e o f f r e e w a y
p r o d u c t i v i t y w a s p r o p o s e d . S e c o n d , t h e c a u s e s o f p r o d u c t i v i t y d e c l i n e l e d t o t h e n o t i o n
o f  c o n g e s t i o n p i e .  B o t h p r o d u c t i v i t y l o s s a n d c o n g e s t i o n p i e a r e a v a i l a b l e a s P e M S
a p p l i c a t i o n s . T h i r d , t h e s t u d y e n t i t l e d  A n E m p i r i c a l A s s e s s m e n t O f T r a  c O p e r a t i o n s 
[ 1 ] p r o v i d e s a d e t a i l e d e m p i r i c a l a c c o u n t o f c o n g e s t i o n .
K e y w o r d s : f r e e w a y p r o d u c t i v i t y ; p r o d u c t i v i t y l o s s ; c o n g e s t i o n p i e
E X E C U T I V E S U M M A R Y
W h e n a s e c t i o n o f a f r e e w a y g e t s c o n g e s t e d , b o t h s p e e d a n d  o w a r e r e d u c e d . W e p r o p o s e
t o m e a s u r e t h i s r e d u c t i o n a s l o s t p r o d u c t i v i t y . T h i s i s t h e n u m b e r o f l a n e - m i l e - h o u r s t h a t
a r e l o s t d u e t o t h e f r e e w a y o p e r a t i n g u n d e r c o n g e s t e d c o n d i t i o n s . W h e n t h e f r e e w a y s e c t i o n
i s c o n g e s t e d  t h e s p e e d d r o p s b e l o w a c e r t a i n , u s e r - d e  n e d t h r e s h o l d , e . g . 3 5 o r 6 0 m p h 
o n e  n d s t h e r a t i o r b e t w e e n t h e m e a s u r e d  o w a n d t h e c a p a c i t y f o r t h i s l o c a t i o n . T h e
p r o d u c t i v i t y l o s s i s t h e p r o d u c t o f ( 1 􀀀 r ) , t h e l e n g t h o f t h e s e g m e n t , a n d t h e c o n g e s t i o n
d u r a t i o n , e x p r e s s e d a s t h e n u m b e r o f e q u i v a l e n t l a n e - m i l e s - h o u r s o f f r e e w a y . ( I f t h e f r e e w a y
i s u n c o n g e s t e d , t h e p r o d u c t i v i t y l o s s i s z e r o . ) T h e c a l c u l a t i o n c a n b e c a r r i e d o u t a t a n y
s c a l e : f r e e w a y s e g m e n t , d i s t r i c t , s t a t e . F i g u r e 1 d i s p l a y s t h e p r o d u c t i v i t y l o s s f o r D i s t r i c t 4
d u r i n g S e p t e m b e r 9 , 2 0 0 8 - O c t o b e r 5 , 2 0 0 8 .
F i g u r e 1 : P r o d u c t i v i t y L o s s f o r D i s t r i c t 4 . S o u r c e : P e M S
C o n g e s t i o n ( h e n c e p r o d u c t i v i t y l o s s ) h a s m a n y c a u s e s w h o s e i m p a c t c a n b e s t a t i s t i c a l l y
e s t i m a t e d : t h e r e i s r e c u r r e n t a n d n o n - r e c u r r e n t c o n g e s t i o n t h a t c a n p o t e n t i a l l y b e r e d u c e d
b y i d e a l r a m p m e t e r i n g ; t h e r e i s e x c e s s d e m a n d t h a t c a n n o t b e m i t i g a t e d e v e n u n d e r i d e a l
r a m p m e t e r i n g ; a c c i d e n t s ; a n d , l a s t l y , t h e r e s i d u a l c o n g e s t i o n . T h e s e e s t i m a t e s c a n b e
d i s p l a y e d i n t h e f o r m o f a c o n g e s t i o n p i e a s i l l u s t r a t e d b y F i g u r e 2 . A d e t a i l e d s t u d y [ 2 ]
e x a m i n e s t h e c a u s e s i n m o r e d e t a i l f o r I - 8 8 0 a s i l l u s t r a t e d i n t h e c o n g e s t i o n p i e o f F i g u r e 3
D a t a f r o m P e M S p r o v i d e a n u n p a r a l l e l e d o p p o r t u n i t y t o a s s e s s f r e e w a y p e r f o r m a n c e a n d
s u g g e s t w a y s t o i m p r o v e f r e e w a y m a n a g e m e n t . T h e s t u d y [ 1 ] t a k e s u p t h i s o p p o r t u n i t y
u s i n g s i x s t u d i e s o f f r e e w a y c o n g e s t i o n , r a n g i n g f r o m b o t t l e n e c k i d e n t i  c a t i o n t o H O V l a n e
e  e c t i v e n e s s .
2
F i g u r e 2 : C o n g e s t i o n P i e f o r C a l i f o r n i a . S o u r c e : P e M S
F i g u r e 3 : C o n g e s t i o n p i e c h a r t f o r f o u r s c e n a r i o s o n I - 8 8 0 . S o u r c e : [ 2 ]
3
A C K N O W L E D G M E N T S
T h e w o r k s u m m a r i z e d i n t h i s r e p o r t w a s c a r r i e d o u t j o i n t l y w i t h J a i m y o u n g K w o n , M i c h a e l
M a u c h a n d C h a o C h e n . I t w a s s u p p o r t e d b y t h e C a l i f o r n i a D e p a r t m e n t o f T r a n s p o r t a t i o n
t h r o u g h t h e C a l i f o r n i a P A T H P r o g r a m . T h e c o n t e n t s o f t h i s r e p o r t r e  e c t t h e v i e w s o f t h e
a u t h o r w h o i s r e s p o n s i b l e f o r t h e f a c t s a n d t h e a c c u r a c y o f t h e d a t a p r e s e n t e d h e r e i n . T h e
c o n t e n t s d o n o t n e c e s s a r i l y r e  e c t t h e o  c i a l v i e w s o f o r p o l i c y o f t h e C a l i f o r n i a D e p a r t m e n t
o f T r a n s p o r t a t i o n . T h i s r e p o r t d o e s n o t c o n s t i t u t e a s t a n d a r d , s p e c i  c a t i o n o r r e g u l a t i o n .
R E F E R E N C E S
[ 1 ] C h e n , C . , J . K w o n , a n d P . V a r a i y a . A n e m p i r i c a l a s s e s s m e n t o f t r a  c o p e r a t i o n s . I n H . S .
M a h m a s s a n i , e d i t o r , P r o c e e d i n g s o f t h e 1 6 t h I n t e r n a t i o n a l S y m p o s i u m o n T r a n s p o r t a t i o n
a n d T r a  c T h e o r y , p a g e s 1 0 5  1 2 4 . E l s e v i e r , 2 0 0 5 .
[ 2 ] J . K w o n , M . M a u c h , a n d P . V a r a i y a . C o m p o n e n t s o f c o n g e s t i o n : D e l a y f r o m i n c i d e n t s ,
s p e c i a l e v e n t s , l a n e c l o s u r e s , w e a t h e r , p o t e n t i a l r a m p m e t e r i n g g a i n , a n d e x c e s s d e m a n d .
T r a n s p o r t a t i o n R e s e a r c h R e c o r d , 1 9 5 9 : 8 4  9 1 , 2 0 0 6 .
A P P E N D I X
T h e a p p e n d i x r e p r o d u c e s [ 1 ] a n d [ 2 ] .
4
Chen, Varaiya, Kwon: An Empirical Assessment Of Traffic Operations 1
1
AN EMPIRICAL ASSESSMENT OF
TRAFFIC OPERATIONS
Chao Chen and Pravin Varaiya,
University of California, Berkeley 94720- 1770
Jaimyoung Kwon,
Statistics Department, California State University, Hayward, CA 94542
ABSTRACT
The California Freeway Performance Measurement System stores real- time data from 26,000 loop
detectors. PeMS is accessed via an internet browser ( http:// pems. eecs. berkeley. edu/). It currently
has 3 TB of data, growing at 2 GB/ day. PeMS extracts useful information from these data and
displays it in graphical or tabular form. These data provide an unparalleled opportunity to assess
freeway performance and suggest ways to improve freeway management. The paper illustrates this
opportunity using six studies of freeway congestion, ranging from bottleneck identification to HOV
lane effectiveness. The paper is not a contribution to theory, but it may encourage theoreticians to
use a rich data set to formulate and address practical questions.
INTRODUCTION
Operational since 2001, PeMS receives real time data from 26,000 loops grouped into 8,040 Ve-hicle
Detector Stations ( VDS) covering 3,000 directional miles of freeways in major California
urban areas. PeMS also collects incident data from the Traffic Accident Surveillance and Analysis
System ( TASAS) and the California Highway Patrol.
The principal aim of this paper is to examine congestion as a performance measure and demonstrate
that data can be processed to reliably estimate the causes of congestion, and the gains from better
ramp metering, incident management, and traveler information. Each of the following six sections
addresses a different aspect of congestion. Some sections report previous research by the PeMS
Development Group.
2 ISTTT 2005
The section BPR CURVE suggests replacing the standard BPR curve by two curves: one for the
free flow regime, the other for the congestion regime. For Los Angeles the two regimes separate at
50 mph. Drivers in Los Angeles spend 30% of their time in the congestion regime, so congestion
delay can be reduced if this regime can be avoided. IDEAL METERING presents an empirical
procedure to rapidly obtain a rough estimate of this reduction by preventing the onset of the con-gested
regime at recurrent bottlenecks. For Los Angeles the procedure estimates an annual saving
of 50 million vehicle- hours.
Not all bottlenecks cause significant congestion. BOTTLENECKS summarizes an automated pro-cedure
to identify all bottlenecks and rank them by frequency of occurrence and severity of impact.
For San Diego County the procedure locates 160 bottlenecks, the ten most severe of which account
for 61 percent of the delay from all bottlenecks.
To estimate the delay from a collision, its effect must be separated from congestion caused by
bottlenecks. CONGESTION PIE reviews a technique that predicts what the congestion would
have been had the collision not occurred. Collisions and bottlenecks cause congestion, and delay
from bottlenecks can be reduced by ramp metering. Putting these considerations together yields
three congestion pie slices corresponding to collisions; congestion that can be eliminated by ramp
metering; and ‘ residual’ congestion due to all other causes, the largest being ‘ excess’ demand.
Congestion delay measures system performance. Travelers experience congestion as large varia-tions
in travel time. Because the travel time stochastic process exhibits a large temporal autocor-relation,
real time data can be processed to reliably predict travel time, as shown in PREDICTING
TRAVEL TIME. Travel time prediction increases welfare: It can suggest a shorter alternative route
if one is available; and it can reduce the uncertainty in travel time, even when that time itself cannot
be reduced.
The Bay Area provides a unique opportunity to study the impact of HOV lanes on non- HOV
traffic because the HOV lanes are time- actuated. HOV LANE EFFECTIVENESS presents limited
evidence suggesting that HOV actuation increases overall congestion, by imposing a congestion
penalty on non- HOV traffic ( which loses one lane) and a capacity penalty on the HOV lane ( which
acts as a one- lane highway with much lower speed).
BPR CURVE
Figure 1( a) is a scatter plot of speed vs. flow across all four lanes of I- 10W in Los Angeles at
vehicle detector station ( VDS) 717162. Each point represents a one- hour average for the 30- day
period 13 June- 13 July, 2004. Also displayed are two curves fitted to the BPR ( Bureau of Public
Roads) equation
v =
v f
1 +  ( q = C )  ;
Chen, Varaiya, Kwon: An Empirical Assessment Of Traffic Operations 3
in which v is speed, v f is free flow speed, q is flow, and C is capacity. Data with average hourly
speed below 30 mph are discarded. The capacity C is estimated to be the maximum hourly flow
observed during the 30- day period, and the free flow speed is the median speed when occupancy
is below 10%. The parameters  ;  are either user- specified or obtained using a nonlinear least-squares,
Marquardt- Levenberg algorithm ( Martin, W., 1998).
( a) BPR
0400
0500
0600
0700
0800
1100
1500
1600
1700
r cr
( b) Speed vs. flow
FIGURE 1 ( a) Scatter plot of 1- hour average speed vs. flow and ( b) trajectory of 5- min aver-age
speed vs. flow. Two BPR curves are fitted to the scatter plot in ( a). The shaded region,
 c r , in ( b) is the critical density separating free flow from congestion.
Figure 1( b) plots the temporal evolution of speed vs. flow at the same location as in figure 1
during 0400- 1700 ( 4: 00 AM- 5: 00 PM) on 13 July, 2004. Each point now represents a five- minute
average. The figure suggests a modified BPR procedure that divides traveler experience into two
distinct ‘ metastable’ regimes: the free flow regime implicit in the BPR curve, and a low- speed
congestion regime, separated by a ‘ critical density’ band,  c r . The likelihood of the two regimes
can be empirically computed for any location, freeway, or an entire region.
Figure 2( a) gives the frequency distribution of VMT ( veh- miles traveled) and VHT ( veh- hours
traveled) on I- 10E during 0500- 1900, 14 July, 2004. Drivers spent 35% of their time at an average
speed of 30 mph and 65% at an average speed of 60 mph, suggesting the two- regime BPR model
of Figure 2( b), separated at 50 mph. The free- flow BPR curve is as before. Two linear regressions
are fitted to data in the congestion regime,
v
v f
=  + 
q
C
:
The solid line is obtained by least- squares; the dotted line is the least quantile regression, which
is less sensitive to outliers. The likelihood of each regime, determined by frequency counting, is
P ( v > 5 0 mph ) = 0 : 7 9 , P ( v < 5 0 mph ) = 0 : 2 1 .
4 ISTTT 2005
( a) VMT, VHT on I- 10E ( b) Two- regime BPR model
FIGURE 2 ( a) Distributions of VMT and VHT vs. speed for I- 10E and ( b) A two- regime BPR
model.
IDEAL METERING
Figure 1( b) suggests that holding back volume surges by metering on- ramps may prevent the oc-currence
of the congestion regime at some bottlenecks, and figure 2( a) implies a large reduction
in delay if this can be done. Designing a ramp metering algorithm for a specific freeway sec-tion
is arduous. Many set points and feedback gains must be selected ( Papageorgiou, M., 1983;
Papageorgiou, M. et al., 1991), based on a calibrated simulation model. But there is
a simple procedure to roughly estimate the benefits from ramp metering without detailed simu-lations,
based on the hypothesis that the congestion regime can be avoided by controlling flow
according to the Ideal Metering Principle ( IMP) ( Jia, Z. et al., 2000):
If volume surges at on- ramps are held back by a metering policy that always keeps
flow below its capacity in every link, freeway speed will be maintained at 60 mph and
congestion will not appear. As a consequence of metering vehicles may be stopped at
the ramps for some time.
The IMP hypothesis has two parts. One part is that if flow is always maintained below capacity, or
equivalently, if density is always less than critical (  c r ) , traffic will be kept in the free flow regime.
Data like in figure 1( b) provide indirect support: If the traffic density is never allowed to enter
the critical region, traffic will always stay in the free flow regime. The definition of ‘ capacity’ is
Chen, Varaiya, Kwon: An Empirical Assessment Of Traffic Operations 5
empirical: It is taken to be ( say) 95% of the maximum sustained observed flow. The second part
of the hypothesis is that maximum flow occurs at free flow speeds, nominally 60 mph, as in Los
Angeles ( Jia, Z. et al., 2001) and Orange County ( Chen, C. and P. Varaiya, 2001).
Of course not all congestion is due to volume surges at on- ramps and practical considerations,
such as ramps of insufficient length, may prevent implementation of a proper metering policy. The
planner should ask: “ What will be the impact of implementing IMP- conforming ramp metering if
the IMP hypothesis is true?”
A procedure to answer this question is illustrated in ( Jia, Z. et al., 2000), using data for a 7- mile
section ( postmiles 0- 7) of I- 405N in Orange County, during 0500- 1000 for 10 weekdays in June
1998. The section is divided into 13 links, each corresponding to one VDS; eight links have one
on- and off- ramp each. A virtual on- ramp is created at the beginning of the most upstream link in
order to account for metering of on- ramps upstream of the study section.
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
0
200
400
600
800
1000
1200
1400
1600
Vehicle Hour Traveled, I405 N, postmile 0.936.21, June 1, 1998
time ( hour)
VHT / hour
FIGURE 3 The top graph is the time in VHT actually spent on the freeway section, every 5
minutes. Units are normalized to VHT per hour, so the total VHT on this section, between
0500 and 1000 is the area under the top graph. The middle graph is the VHT per hour under
IMP metering, including time in ramp queues. The bottom graph excludes time spent on the
ramps, so it is the VHT per hour that would be spent traveling at 60 mph. The area between
the top and middle graphs is the time saved by metering. The area between the middle and
bottom graphs is the time spent at the ramps. Source: ( Jia, Z. et al., 2000).
The capacity of each link is calculated as the maximum sustainable aggregate flow. Inflows at on-ramps
and exit flows at off- ramps are assumed to remain unchanged despite the metering, whose
impact is estimated as follows:
1. At each on- ramp, inflow is metered so that the link flow remains 5% below the link capacity;
6 ISTTT 2005
2. Traffic on each link after metering is assumed to move at 60 mph;
3. The queue at each on- ramp is calculated by accumulating the net inflow.
On average, two- thirds of the total delay ( defined as additional vehicle- hours traveled ( VHT) driv-ing
below 60 mph) is eliminated by ramp metering. More insight is gained from figure 3, which
shows how metering holds back large surges in demand.
This procedure was repeated in ( Chen, C. et al., 2001) for five freeways ( I- 5, I- 10, US 101, I-
110 and I- 405) in Los Angeles during 0000- 1200, 3- 9 October, 2000. That exercise found that
IMP- metering reduces delay by 70%. PeMS calculates the total congestion delay ( from driving
below 60 mph) for Los Angeles for 2003 to be 83 million vehicle- hours. The procedure suggests
that ramp- metering may eliminate 57 million vehicle- hours of delay, which at $ 20/ veh- hr is in
excess of 1 billion dollars. Even if only one- half of the delay savings from IMP- metering can
be practically realized, this represents an enormous productivity gain that good management can
achieve.
BOTTLENECKS
Bottlenecks can cause congestion, which may be reduced by ramp metering. A bottleneck may
be associated with physical features such as ramps, lane drops, grade changes, curvature, lane
closures, and accidents; but traffic jams and congestion may ‘ spontaneously’ arise in locations
with none of these features. In the absence of a guide to locating bottlenecks and estimating their
severity, we need an algorithm to automatically ( 1) identify all bottlenecks, and ( 2) calculate the
delay each one causes.
Such an algorithm is reported in ( Chen, C. et al., 2004b), and applied using flow and speed data
from 263 VDSs on 270 miles of seven freeways in San Diego. The algorithm uses a sustained speed
gradient between a pair of upstream- downstream detectors to identify bottlenecks. We describe the
algorithm. Consider a freeway with n detectors indexed i = 1 ;    ; n , each giving speed and flow
measurements, averaged over 5- minute intervals indexed t = 1 ; 2 ;    . Detector i is located at
postmile x i ; v i ( t ) = v ( x i ; t ) is its speed ( miles per hour, mph) and q i ( t ) = q ( x i ; t ) is its flow
( vehicles per hour, vph) at time t . If x i < x j , it is understood that x i is upstream of x j .
The algorithm has four steps. First, it declares an active bottleneck at certain locations and times if
the data meet criteria ( 1)–( 4) below. Second, it includes additional time periods as part of the same
bottleneck activation, provided nearby time intervals are selected in the first step. The criterion
for this is ( 5). Third, it calculates the delay caused by a bottleneck, using ( 9). Lastly, identified
bottlenecks are ranked in terms of frequency of occurrence and severity to isolate recurrent from
transitory bottlenecks and to help prioritize mitigation efforts.
Chen, Varaiya, Kwon: An Empirical Assessment Of Traffic Operations 7
Step 1 Declare an active bottleneck between locations x i < x j during t if all four inequalities hold:
x j 􀀀 x i < 2 m i l e s ; ( 1)
v ( x k ; t ) 􀀀 v ( x l ; t ) > 0 i f x i  x k < x l < x j ; ( 2)
v ( x j ; t ) 􀀀 v ( x i ; t ) > 2 0 m p h ; ( 3)
v ( x i ; t ) < 4 0 m p h : ( 4)
Thresholds in ( 1)–( 4) are selected on the basis of experience. In Los Angeles free flow speed is 60
mph and, when a bottleneck is activated, speed drops rapidly to below 40 mph ( e. g. figure 1( b)).
Hence the 20 mph minimum speed differential ( 3) and 40 mph congestion speed ( 4) thresholds.
The maximum separation of 2 miles in ( 1) is designed to include locations where speed continues
to drop as we go downstream, but the difference between each neighboring pair is small. Location
x i is upstream of x j , but there may be other detectors at x k ; x l between these locations. The
constraint ( 2) that speed should drop continuously is the algorithm’s characterization of an active
bottleneck.
Step 2 Sustained bottlenecks last longer than five minutes. Let A i ( t ) = 1 if there is an active
bottleneck at location i and time period t ; otherwise A i ( t ) = 0 . A bottleneck is sustained between
times t 1 and t 2 if
t + N 􀀀 1 X  = t
A i (  )  q N ; 8 t 1  t  t 2 􀀀 N + 1 ; ( 5)
with N = 7 and q = 5 = 7 . That is, a sustained bottleneck has at least five active bottleneck periods
( 25 min) within every seven consecutive periods ( 35 min). This ad hoc definition accounts for situ-ations
like in figure 4( a), in which at postmile 26 the bottleneck is continuously sustained between
0700 and 0800 except for several five- minute periods. The notion of sustained bottleneck allows
treating this as a single bottleneck rather than two or three bottlenecks. The most downstream
location of a sustained bottleneck is the location of an active bottleneck.
Figure 4( a) shows the result of applying the algorithm to data from I- 15S. The locations and times
of detected bottlenecks are the squares superimposed on the speed contours. The contours visually
suggest one sustained bottleneck between 0545 and 0945 at postmile 26, and another between 0645
and 0830 at postmile 15, and indeed both bottlenecks are identified by the algorithm.
Step 3 To calculate the delay, the algorithm first delineates the space- time congested region of each
bottleneck and then the delay in vehicle- hours associated with the region. As an example, the
speed contour in figure 4( a) shows regions of congestion upstream of two bottleneck locations.
The n detectors divide the freeway into n segments. A segment is declared congested at time t if its
speed is below 40 mph. The congested region associated with a bottleneck is the contiguous group
of congested segments immediately upstream of the bottleneck location. For an active bottleneck
just downstream of segment j at time t , the congested region is the set of segments B j ( t ) ,
B j ( t ) = f i : v k ( t ) < 4 0 m p h ; for all i  k  j g : ( 6)
8 ISTTT 2005
( a) Bottlenck location ( b) Delay distribution
FIGURE 4 ( a) Bottleneck detection on I- 15 SB on 5/ 1/ 2003. Traffic flows in order of decreas-ing
postmile. ( b) Distribution of daily delay among 160 bottleneck locations; the 10 ‘ outliers’
account for 61% of the delay. Source: ( Chen, C. et al., 2004b).
The delay D j ( t ) associated with the bottleneck during this period is the sum of the delays in B j ( t ) ,
D j ( t ) = X i 2 B j ( t )
d i ( t ) ; ( 7)
in which d i ( t ) is the delay in segment i at time t . Segment delay is the additional vehicle- hours
traveled driving below the free flow speed, 60 mph,
d i ( t ) = l i  q i ( t )   1
v i ( t ) 􀀀
1
v f  ; v f = 6 0 m p h : ( 8)
Here l i ; q i ( t ) , and v i ( t ) are the segment length, volume, and average speed on the segment at t . The
total delay attributed to a bottleneck at segment j that is active between times t 1 and t 2 is
D j ( t 1 ; t 2 ) =
t 2 X t = t 1
D j ( t ) : ( 9)
Step 4 The steps above found 1733 sustained bottlenecks distributed over 160 distinct locations on
64 workdays. These bottlenecks represent all locations and times that satisfy equations ( 1) - ( 5).
Their causes are unknown, and may include incidents or recurring conditions. The delay associated
with each detected bottleneck is computed using ( 9). The total delay associated with bottlenecks
during the test period is 1.2 million vehicle- hours, which is 64% of the total delay measured on
these freeways during this period. Of the delay caused by bottlenecks, 61% is attributed to the top
ten locations alone. These are the outliers in figure 4( b).
Chen, Varaiya, Kwon: An Empirical Assessment Of Traffic Operations 9
THE PIE OF CONGESTION
Bottlenecks cause congestion, some of which can potentially be removed by ramp metering. Col-lisions
also cause congestion. These considerations lead to the ‘ congestion account’ ( 10)-( 13), for
a contiguous section of freeway with n detectors indexed i = 1 ;    ; n . Using the earlier notation,
d i ( t ) = l i  q i ( t )   1
v i ( t ) 􀀀
1
v f  vehicle- hours ; ( 10)
D t o t =
n X i = 1
T X t = 1
d i ( t ) ; ( 11)
D r e c = D t o t 􀀀 D c o l ; ( 12)
D t o t = D c o l + D p o t + D r e m : ( 13)
Here v f is the reference speed, 60 mph. So d i ( t ) is the delay in segment i in interval t , and D t o t is
the total delay in the section. Both d i ( t ) and D t o t ( t ) are directly obtained from PeMS.
D c o l is the delay caused by collisions, which has to be estimated. D r e c , as defined in ( 12), is
often called the ‘ recurrent’ congestion, much of which occurs at bottlenecks. A significant amount
of D r e c can be potentially eliminated by ramp metering. We call this amount D p o t , which also
needs to be estimated. Putting all these definitions together gives the summary ( 13) in which
D r e m is the ‘ residual’ congestion. D r e m is largely due to ‘ excess demand’ whose impact cannot be
eliminated by ramp metering, and shows up as delay at ramps. D r e m also includes the contribution
to congestion of all other causes, such as adverse weather and special events.
The study in ( Kwon, J. and P. Varaiya, 2005) proposes an automated procedure to estimate all three
components in ( 13), using PeMS loop data and collision data from Traffic Accident Surveillance
and Analysis System ( TASAS) maintained by Caltrans. The procedure is applied to a 22.5 mile
( postmile 4.5 to 27) section of I- 15N in San Diego County. The time period is from 0500 to 2200,
for 44 weekdays ( 2 September- 31 October, 2002).
Figure 5 summarizes the study’s conclusions. The total average daily congestion pie is divided
into three slices. If D p o t and D r e m are reported together as D r e c , recurrent congestion would
amount to 70%. As Hallenbach et al. ( Hallenbach, M. E. et al., 2003, p. 11) observe, this large
‘ recurrent’ congestion may in part be caused by “ unusual volume surges at ramps . . . that are not
being effectively handled by the ramp metering program.” Figure 5( a) indicates that 30% of the
total congestion ( or 60% of recurrent congestion) can be removed by IMP- metering that effectively
handles these volume surges. Figure 5( b) summarizes traveler exposure to congestion in the study
section. Travelers spend 89% of their time in the free- flow regime, and 11% in the congestion
regime. The pies in figure 5 are for the study section. We are in the process of constructing
congestion portraits for all freeways in California for which PeMS and TASAS data are available.
We now discuss the four- step procedure in ( Kwon, J. and P. Varaiya, 2005). The first step delineates
10 ISTTT 2005
Collision ( 30%)
Potential
Reduciton ( 46%)
Excess
Demand ( 23%)
Delay Pie Chart
Free flow ( 89.2%)
Collision
( 3.3%)
Potential
Reduction ( 5.0%)
Excess
Demand ( 2.5%)
VHT Pie Chart
( a) Congestion pie
Collision ( 30%)
Potential
Reduciton ( 46%)
Excess
Demand ( 23%)
Delay Pie Chart
Free flow ( 89.2%)
Collision
( 3.3%)
Potential
Reduction ( 5.0%)
Excess
Demand ( 2.5%)
VHT Pie Chart
( b) Exposure pie
FIGURE 5 The congestion pie ( a) and the exposure pie ( b) automatically constructed for the
I- 15N study section. Source: ( Kwon, J. and P. Varaiya, 2005).
for each collision its time- space region of impact. The second step predicts how much delay this
region would have experienced had that collision not occurred; this is the recurrent congestion. The
third step calculates how much of this recurrent congestion can be eliminated by IMP- metering.
The fourth step puts the estimates together in the congestion pie.
Step 1 Following a collision, congestion propagates upstream up to some maximum spatial extent.
The congestion lasts a certain amount of time, called its duration. Empirically, freeway segment
i is declared congested during a 5- minute interval t if the speed v i ( t ) < 5 0 mph. ( This is slightly
different from the 40 mph criterion in ( 3).) Formula ( 10) is then used to calculate the total delay in
this duration- extent ‘ rectangle’. The precise algorithm is similar to that of ( 6)-( 7). The step leads
to the estimate D t o t ; a ( t ) of the total delay at time t in the impact region of each collision a . ( The
same procedure can be used to delineate the impact of non- collision incidents.)
Step 2 This step predicts D r e c ; a ( t ) , the recurrent congestion at time t that would have occurred in
the absence of collision a . This is the K - nearest neighbor prediction of the recurrent delay, based
on historical data of the delay D a ( t ; d ) during the same time t and over the same spatial extent, for
several other days d = 1 ;    ; T . More precisely, the estimate is the median value
D r e c ; a ( t ) = median f D a ( t ; d 0 k ) j k = 1 ;    ; K g ;
in which d 0 k ; k = 1 ;    ; K are K days with smallest values of j D a ( t a ; d ) 􀀀 D t o t ; a ( t a ) j for d =
1 ;    ; D . ( In the empirical study of figure 5, K = 3 .) Here t a is the time just before collision
a occurred. The recurrent congestion that would have occurred in the absence of collision a is
Chen, Varaiya, Kwon: An Empirical Assessment Of Traffic Operations 11
predicted to be
D r e c ; a = X t
D r e c ; a ( t ) ;
in which the sum is over the duration of impact. Finally,
D c o l ; a = X t
m a x ( D t o t ; a ( t ) 􀀀 D r e c ; a ( t ) ; 0 ) ; ( 14)
is the contribution to congestion of collision a .
Step 3 This step estimates the potential reduction in delay at recurrent bottlenecks by IMP- metering
discussed in IDEAL METERING. The procedure first identifies all bottlenecks following the al-gorithm
in BOTTLENECKS, and restricts attention to those that occur for more than 20% of the
days. Next, if the bottleneck time- space region overlaps with the impact region of a collision,
that day is excluded. An estimate of the reduction in delay is then computed using the procedure
in IDEAL METERING. This gives an estimate of D p o t in ( 13). Details are in ( Kwon, J. and P.
Varaiya, 2005).
Step 4 The three delays estimated above, together with overall VHT from PeMS are displayed in
the pies of figure 5.
An important side- effect of the procedure is an estimate of the delay caused by each collision,
D c o l ; a ( 14). Of 74 collisions during the study period, two- thirds cause no additional delay. These
occur either when recurrent congestion is very low or very high. Eight ‘ outliers’ ( 10% of collisions)
account for 90% of total collision delay. Incident management could be made more effective if the
high delay- causing accidents could be quickly diagnosed once they occur.
TASAS provides crash information including type of collision, number of vehicles involved, weather.
From this information, we find the strongest predictor of high delay- causing accidents is the num-ber
of vehicles involved; adverse weather is a moderately strong predictor; all others, including
injury and trucks, are weak predictors. Note, however, that the data set in the study contains only
74 collisions.
PREDICTING TRAVEL TIME
The delay on a freeway on the same day of week varies much more than the total demand. Trav-elers
experience this variation as large uncertainty in their travel time. Let T ( t ) be the travel time
of a trip over a fixed route starting at time t . T ( t ) is a stochastic process with trends that can be
calculated from historical data, and a large variance due to congestion. Let  2 ( t ) be the ( uncondi-tional)
variance of T ( t ) , and let  2 ( t ; s ) be the variance of the predictor ^ T ( t ; s ) of this travel time
conditioned on knowledge of traffic conditions up to time s  t . Because the travel time process
12 ISTTT 2005
has a large autocorrelation,  2 ( t ; s ) is much smaller than  2 ( t ) . We summarize a study ( Chen, C.
et al., 2004a) which estimates the benefits of prediction.
The study compares travel time along two alternate routes between the I- 5/ I- 805 interchange and
the I- 5/ I- 163 interchange in San Diego. Route 1 is entirely along I- 5S, Route 2 has its first segment
on I- 805 and the second segment on I- 163S. Travel times T 1 ( t ) and T 2 ( t ) along the two routes are
computed for departure times t between 0500 and 2200 during the 22 weekdays between 1 and 31
August, 2002. There are 1320 departure times over the study period at every 17 minutes.
Each point in the scatter plot of figure 6( a) represents ( T 1 ( t ) ; T 2 ( t ) ) with the same departure time t .
There are 1320 points. Two features of the scatter plot are clear. First, the travel time distributions
on the two routes are similar. Second, there is a large uncertainty: 90% of the distribution lies
between 12 and 35 minutes, with a median below 20 min.
( a) Travel times ( b) Prediction vs. historical ( c) Prediction vs. optimum
FIGURE 6 Scatter plot of travel times along the two routes ( a). Comparison of minimum
predicted travel time vs. historical ( b) and vs. true minimum travel time ( c). Source: ( Chen,
C. et al., 2004a).
A PeMS application predicts travel time ^ T ( t ; t ) for a trip starting at any time t , based on historical
data and real time data available up to time t ( van Zwet, E. and J. Rice, 2001). We now estimate the
travel time savings using the PeMS prediction. Figure 6( b) compares the travel time that would be
experienced by a traveler who selects the route with the shorter predicted travel time m i n i ^ T i ( t ; t ) ,
with that of a traveler who selects the route with the shorter expected travel time m i n i E T i ( t ) ,
which can be estimated from historical data alone. Most of the points lie on or below the 45 degree
line, indicating that reliance on PeMS prediction is much better than historical experience. The
travel time saving is the horizontal distance to the 45 degree line.
Figure 6( c) compares the travel time based on PeMS prediction with that of a clairvoyant traveler
who unerringly chooses the route with the shorter travel time, m i n i T i ( t ) . Naturally, all points
lie below the 45 degree line, but the significant feature is how frequently the points lie on the 45
Chen, Varaiya, Kwon: An Empirical Assessment Of Traffic Operations 13
degree line, indicating that prediction correctly selects the ex post shorter route.
When there are alternative routes as is the case here, accurate travel time prediction reduces both
the average travel time and the uncertainty. Even when alternative routes are not available, the
reduction in uncertainty increases traveler welfare. Estimates in ( Chen, C. et al., 2004a) suggest
that the benefits are significant for the example presented here.
As a final remark we note that the travel time estimate in ( van Zwet, E. and J. Rice, 2001) involves
predicting the traffic conditions that the traveler will encounter along the route. Such a predictor
performs much better than the commonly used predictor which simply adds up the most recently
reported travel times on the segments along the route.
EVALUATION OF HOV LANE EFFECTIVENESS
Several studies reach the obvious conclusion that HOV travelers benefit from lower travel times,
see e. g. ( DKS Associates, 2003; The PB Study Team, 2002). But these studies do not evaluate the
impact of HOV lanes on overall congestion, including the congestion on mixed- flow lanes. San
Francisco Bay Area data are especially helpful in evaluating this impact, because its HOV lanes
are time- actuated. To facilitate comparison, the evidence below is for freeways with heavier PM
peak traffic. In all cases, lane 1 ( the fast lane) is HOV actuated on weekdays between 0500- 0900
( 5: 00- 9: 00 AM) in the morning and 1500- 1900 ( 3: 00- 7: 00 PM) in the evening; at all other times
HOV is deactuated. We argue that in the Bay Area, HOV lanes increase overall congestion.
FIGURE 7 Speed and flow in lanes 1( HOV), 2 and 3 on 18 August 2004 at VDS 400104 on
SR- 237E.
Figure 7 shows speed and flow on all three lanes, 1( HOV), 2 and 3, of SR- 237E at a particular
14 ISTTT 2005
location on 18 August 2004. During the 0500- 0900 HOV actuation period, the HOV lane is under-utilized,
but since overall traffic is low, all lanes are in the free flow regime. ( Most HOV lanes in
the off- peak direction are underused ( DKS Associates, 2003, Table 3, p. 7).)
Immediately after deactuation at 0900, speed and flow are ( nearly) equalized on all lanes, and
they remain in the free flow regime until HOV re- actuation at 1500. At 1500 HOV flow drops
dramatically, compensated by increased flows in lanes 2 and 3. But until 1700, all three lanes
remain in the free flow regime, and flows in lanes 2 and 3 reach a maximum. From 1700 until
1900, HOV flow increases and speed decreases, and the HOV lane remains in free flow. However,
lanes 2 and 3 enter the congestion regime. They suffer a large reduction in both speed and flow.
The decline in flow is severe enough to reach the level of the HOV lane at 1900.
The impact of HOV actuation on overall congestion can be seen by comparing the behavior before
and after HOV deactuation at 1900 in figure 7. HOV activation during 1700- 1900 reduces capacity
for non- HOV traffic ( which loses one lane), pushes non- HOV lanes into the congestion regime,
and reduces total non- HOV flow. Thus traffic suffers a non- HOV congestion penalty. Shortly after
deactuation at 1900, all lanes enter the free flow regime, and total flow reaches a maximum over
the entire day. More surprisingly, even HOV lane performance improves after deactuation: both
speed and flow increase. Put inversely, both speed and flow in the HOV lane decline during HOV
actuation, even though it is in free flow. We call this the HOV capacity penalty. In summary: HOV
actuation imposes a congestion penalty on non- HOV lanes and a capacity penalty on the HOV
lane.
The HOV capacity penalty— increased HOV speed and flow after deactuation— is seen in the six
freeway locations we examined. Figure 8 shows speeds in six different freeways during 1400-
2000, starting one hour before the afternoon HOV actuation at 1500 and ending one hour after
HOV deactuation at 1900. ( Flows are not shown as they have the expected behavior, similar to that
in figure 7.) In all cases, speeds in all lanes, including lane 1( HOV), increase after deactuation;
moreover, flow in lane 1( HOV) increases, and flows in the other lanes decrease.
The lane 1( HOV) capacity penalty is explained as follows. The flow increases after deactuation
because drivers in lane 2 move into the lower density lane 1. The speed decreases during HOV
actuation because the HOV lane becomes a one- lane highway whose speed is governed by the low
speed vehicles– the ‘ snails’. As the non- HOV congested lanes are even slower, a faster HOV driver
cannot pass the slower snail in front of it. However, as soon as HOV is deactuated, slower drivers
move to the outer lanes and the fastest drivers move to ( what was) the HOV lane. Speed in all lanes
increase— usually dramatically as in figure 8.
The hypothesis that during HOV actuation speed is controlled by snails is confirmed in the scatter
plots of figure 9. Each point is a 5- minute average of flow and speed. Plot ( a), during HOV
actuation, shows a sharp decrease in speed as flow ( and hence the number of snails) increases,
even though the lane is in free flow. Plot ( b) shows no decrease in speed, as only the fast drivers
Chen, Varaiya, Kwon: An Empirical Assessment Of Traffic Operations 15
FIGURE 8 Speeds in all lanes at locations on six different Bay Area freeways, 1400- 2000, be-ginning
one hour before HOV activation ( at 1500) and ending one hour after HOV activation
( at 1900). In all cases, speed is highest in lane 1 ( HOV), followed by lane 2, lane 3, etc. The
notation 80E- 400808- 080804 means VDS 400808 on I- 80E on August 8, 2004.
are in lane 1. The difference between plots ( a) and ( b) is typical of a one- lane vs. a multi- lane
highway in free flow.
Three different ( non- exclusive) causes may account for snails. A proportion of HOV drivers may
be intrinsically slow, so their number grows as HOV flow increases. Second, the slowdown may be
caused by lane changes by HOV drivers ( and SOV violators) from the slower lane 2 into the HOV
lane. The lane changes increase in proportion with HOV lane flow, further reducing HOV lane
speed. Third, as the speed differential between the HOV and the adjacent non- HOV lane increases,
drivers in the HOV lane may slow down due to the increased perceived risk of a collision should
someone from the non- HOV lane merge into the HOV lane. In the last two cases, an HOV lane
that is physically separated from lane 2 would not exhibit the slowdown seen in figure 9 ( a). In
either case, the slowdown would not be seen in freeways with two HOV lanes.
We finally arrive at the interesting question: “ Will the overall congestion in the six cases in figure
16 ISTTT 2005
( a) 1600- 1900, HOV actuated ( b) 1900- 2100, HOV de- actuated
30
40
50
60
70
80
90
40 60 80 100 120 140 160 180
30
40
50
60
70
80
90
40 60 80 100 120 140 160 180
Flow ( veh/ 5- min) Flow ( veh/ 5- min)
Speed ( mph)
Speed ( mph)
FIGURE 9 Speed vs. flow ( 5- min averages) in lane 1, ( a) 1600- 1900, HOV actuated, and ( b)
1900- 2100, HOV de- actuated, for five weekdays in August, 2004, at VDS 400352 on I- 880S.
8 be reduced by eliminating the HOV lane?” The answer would be unreservedly ‘ yes’, but for
two qualifications: one having to do with freeway management, the other with mode choice. It
is obvious that a management strategy with no HOV lane and no metering will lead to greater
congestion than a strategy with one HOV lane and no metering, because HOV actuation serves as
a ( one- lane) metering mechanism. So to fairly compare an HOV vs. a non- HOV regime, we must
assume that proper ramp metering is in place to guarantee vehicle flow in non- HOV lanes that is
close to maximum observed vehicle flow.
The second qualification is more interesting. It is based on either of two claims: ( 1) HOV lanes
move significantly more people overall ( even if they don’t move more vehicles), ( 2) HOV lanes
induce enough drivers to switch from SOV to HOV to compensate for both the congestion penalty
imposed on non- HOV lanes and the capacity penalty imposed on the HOV lane by HOV actuation.
We cannot address the second claim because there are no empirical estimates of the SOV- HOV
mode shift for the Bay Area. We evaluate the first claim that HOV actuation increases flow of
persons/ hour.
We calculate flow of persons per hour ( PPH) by multiplying vehicle flow ( from PeMS) and AVO
( average vehicle occupancy). Since the accuracy of vehicle counts exceeds 90- 95%, the single
most important empirical quantity in any study of HOV effectiveness is the AVO. Unfortunately,
AVO estimates are very unreliable for many reasons ( Levine, N. and M. Wachs, 1994), so we will
use a range of estimates.
According to ( California Department of Transportation, District 4, Office of Highway Operations,
2002, p. 66) on the section of I- 880S that includes VDS 400486 in figure 8, during the afternoon
peak hour, the HOV lane AVO is 2.1, and the AVO on the three non- HOV lanes is 1.1. We use
Chen, Varaiya, Kwon: An Empirical Assessment Of Traffic Operations 17
these estimates for the HOV actuation period. ( The HOV AVO rate should be reduced by a highly
variable HOV violation rate measured at 5.8% on 5 July, 2002.)
AVO estimates during HOV deactuation are not available, and we have several alternatives: the
State Household Travel Survey gives an AVO of 1.5 for all trips and 1.1 for home to work trips;
the Metropolitan Transportation Commission for the Bay Area gives an AVO of 1.4 for all trips
and 1.1 for home to work trips; lastly, the California Life- Cycle Benefit/ Cost Analysis Model
uses a default of 1.38 for peak period AVO. We will use 1.25, 1.3 and 1.4 for AVO during HOV
deactuation. Figure 10 ( a) plots the flow in persons per 5- minutes, aggregated over all lanes, with
HOV AVO = 2.1 and non- HOV AVO = 1.1 during HOV actuation, and AVO = 1.25, 1.3 or 1.4
during HOV deactuation.
500
550
600
650
700
750
800
14: 00 14: 30 15: 00 15: 30 16: 00 16: 30 17: 00 17: 30 18: 00 18: 30 19: 00 19: 30
5
10
15
20
25
30
14: 00 14: 30 15: 00 15: 30 16: 00 16: 30 17: 00 17: 30 18: 00 18: 30 19: 00 19: 30
Cost/ person Index
Cost/ vehicle Index
HOV HOV
AVO = 1.4
AVO = 1.3
AVO = 1.25 AVO1= 2.1 AVO2- 4= 1.1
FIGURE 10 ( a) Flow in persons per 5- min using the indicated AVO values, and ( b) cost index
per person- mile and per vehicle- mile, 1400- 2000, 18 August 2004, at VDS 400486, I- 880S.
With the two higher AVO estimates, HOV actuation causes a reduction in the flow of persons per
hour compared with the period 1400- 1500 before actuation. With the lowest AVO estimate, HOV
actuation causes a small increase in PPH compared with the period 1400- 1500. So the data do not
support the claim that HOV actuation significantly increases ( say by 10%) the flow in persons per
hour.
In comparing the HOV vs. non- HOV regime, we should not ignore the travel time cost imposed by
HOV actuation. Knowing the speed and the flow in persons/ 5- min and vehicles/ 5- min in each lane,
we can calculate the amount of time that each person and vehicle takes to travel a fixed distance.
This gives us a ‘ cost index’, which will vary over time, as the flow and speed vary. Figure 10 ( b)
displays the two cost indices ( AVO = 1.25 is used for these plots). Evidently, the average person
( on all lanes) pays a travel time cost during HOV actuation ( 1700- 1900) that is two- and- a- half
times higher. Of course, a significant part of this higher cost is due to inadequate ramp metering.
If we think of the freeway as a ‘ people- mover’ and the cost of its operation to be travel time, we
must conclude that the cost is increased during HOV actuation. This is a much better indicator
of productivity loss than the productivity gain measured as the ratio between HOV AVO and non-
18 ISTTT 2005
HOV AVO in ( DKS Associates, 2003, p. 6,8). The latter producitivity gain merely reflects the fact
that HOV actuation causes carpools to move into the HOV lane.
We close this section with some remarks. First, the analysis above leads to conclusions that run
counter to those reached by most studies of HOV effectiveness. Because the evidence presented
here is fragmentary, the analysis must be repeated with a more complete data set before the con-clusions
can be trusted.
Second, it is possible from Bay Area data to estimate the SOV- HOV mode shift, based on the
hypothesis that the shift will be more pronounced the larger is the travel time differential between
HOV and non- HOV lanes. Also, people may find the SOV- HOV shift to be less inconvenient on
some routes than on others.
Third, when a 2+ ( i. e. two or more persons) HOV lane becomes congested, it is sometimes con-verted
to a 3+ lane. The SOV- 3+ HOV shift will certainly be lower than the SOV- 2+ HOV shift. So
the conversion from 2+ to 3+ HOV lane may increase overall congestion.
Lastly, because HOV lanes in the Bay Area are time- actuated, it is straightforward to estimate both
the non- HOV congestion penalty and the HOV capacity penalty. This distinction is less obvious in
a 24- hour HOV facility, although it, too, imposes both penalties.
There is interest in increasing the utilization of underused HOV lanes by converting them into HOT
( HOV/ Toll) lanes. The snail phenomenon implies, however, that even modest increases in volume
following conversion will bring down HOT speed to that of non- HOT lanes ( which, moreover, will
have higher speed because they carry less traffic). That is, the HOV capacity penalty does not leave
much room for additional traffic, so that even the cautious estimates for revenue enhancement in
the Bay Area may be overly optimistic ( DKS Associates, 2003, p. 22). A recent proposal to permit
hybrid vehicles into HOV lanes will certainly increase congestion.
From a purely technical viewpoint, this discussion suggests that a better way to manage freeways
is to eliminate HOV lanes, institute ramp metering, and permit HOV/ HOT bypass at ramps. This
will eliminate the HOV penalties, while encouraging mode shift from SOV to HOV. On the other
hand, by having weak or no ramp metering, the HOV regime can always be made to look better.
For policy considerations this technical viewpoint has to be weighed with many other factors.
CONCLUSIONS
In its draft Transportation Management Systems ( TMS) Master Plan ( System Metrics Group, Inc.,
2003), Caltrans proposes an action plan to improve incident management, traffic control, and trav-eler
information. Central to the plan is its reliance on specific performance indicators to serve “ as
monitoring and evaluation tools, and establish an accountability framework for the implementation
Chen, Varaiya, Kwon: An Empirical Assessment Of Traffic Operations 19
of planned TMS improvements.” Caltrans has invested significant resources to develop a perfor-mance
measurement system ( PeMS). This paper illustrates why PeMS became a major source of
‘ performance indicators’ and suggestions for performance targets.
The paper uses PeMS data to study freeway congestion from six different perspectives, ranging
from identification of bottlenecks to evaluating the benefits of ramp metering and the effectiveness
of HOV lanes. In each study, the aim is to measure the severity of congestion and reveal the
opportunity for improvement. The approach is to argue on the basis of statistical models that the
data are used to estimate. Qualitatively of course the models are inspired by prior theory, but the
emphasis is always on quantitative conclusions.
Partly motivated by the success of PeMS, some universities and DoTs are developing small- scale
protoypes of PeMS- like systems. These efforts will have a small impact until state DoTs invest in
data collection infrastructure. The availability of these data will shift DoT focus from construc-tion
to operations improvements. Academic research, too, will change as it exploits opportunities
opened up by access to large- scale data sets and pays more attention to questions that address the
opportunities for operations improvements and conducting experiments that demonstrate improve-ments.
ACKNOWLEDGEMENT
We are grateful for comments and criticsm from Professor MartinWachs of U. C. Berkeley; Robert
Copp, Fred Dial and David Seriani of Caltrans; and Tarek Hatata of the System Metrics Group.
This study is partly based on research that was supported by grants from Caltrans to the California
PATH Program.
The contents of this paper reflect the views of the authors who are responsible for the facts and the
accuracy of the data presented herein. The contents do not necessarily reflect the official views of
or policy of the California Department of Transportation. This paper does not constitute a standard,
specification or regulation.
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Papageorgiou, M. Applications of Automatic Control Concepts to Traffic Flow Modeling and
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Papageorgiou, M., H. Hadj- Salem, and J. Blosseville. ALINEA: a local feedback control law for
on- ramp metering. Transportation Research Record, 1320, 1991.
System Metrics Group, Inc. Transportation Management Systems Plan, 2003.
The PB Study Team. HOV Performance Program Evaluation Report. Los Angeles County
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van Zwet, E. and J. Rice. A simple and effective method for predicting travel times on freeways.
In 2001 IEEE Intelligent Transportation Systems Proceedings, pages 227– 232, Oakland, CA,
2001.
The Components of Congestion: Delay from Incidents, Special Events, Lane
Closures, Weather, Potential Ramp Metering Gain, and Excess Demand
Jaimyoung Kwon*
Department of Statistics
California State University, East Bay
Hayward, CA 94542
Tel: ( 510) 885- 3447, Fax: ( 510) 885- 4714
jaimyoung. kwon@ csueastbay. edu
Michael Mauch
DKS Associates
8950 Cal Center Drive, Suite 340
Sacramento, CA 95826- 3225
Tel: ( 916) 368- 2000, Fax: ( 916) 368- 1020
mvm@ dksassociates. com
Pravin Varaiya
Department of Electrical Engineering and Computer Science
University of California, Berkeley CA 94720
Tel: ( 510) 642- 5270, Fax: ( 510) 642- 7815
varaiya@ eecs. berkeley. edu
For Presentation and Publication
85th Annual Meeting
Transportation Research Board
January 2006
Washington, D. C.
July 30, 2005
# Words: 4,279 ( excluding Figure and Table captions)
Plus 2 Table and 3 Figures ( 1,250)
TOTAL: 5,529
* Corresponding Author
Kwon/ Mauch/ Varaiya 1
ABSTRACT
A method is presented to divide the total congestion delay in a freeway section into six
components: the delay caused by incidents, special events, lane closures, and adverse weather;
the potential reduction in delay at bottlenecks that ideal ramp metering can achieve; and the
remaining delay, due mainly to excess demand. The fully automated method involves two steps.
First, the components of non- recurrent congestion are estimated by statistical regression. Second,
the method locates all bottlenecks and estimates the potential reduction in delay that ideal ramp
metering can achieve. The method can be applied to any site with minimum calibration. It
requires data about traffic volume and speed; the time and location of incidents, special events
and lane closures; and adverse weather. Applied to a 45- mile section of I- 880 in the San
Francisco Bay Area, the method reveals that incidents, special events, rain, potential reduction
by ideal ramp metering, and excess demand respectively account for 13.3%, 4.5%, 1.6% 33.2%
and 47.4% of the total daily delay. The delay distribution of the various components is different
between the AM and PM peak periods and between the two freeway directions. Quantifying the
components of congestion at individual freeway sites is essential in developing effective
congestion mitigation strategies.
Keywords: freeway congestion; incidents; weather; ramp metering; loop detectors
Kwon/ Mauch/ Varaiya 2
1. INTRODUCTION
Congestion is caused by incidents, special events, lane closures, weather, inefficient operations,
and excess demand. Their impact can be summarized in the division of the congestion ‘ pie’ into
its component as in Figure 1. Knowledge of the congestion pie is essential to the selection of
effective congestion mitigation strategies ( 1).
The paper presents a method to divide the total congestion Dtotal into six components: ( 1) Dcol,
the congestion caused by incidents, which could be reduced by quicker response; ( 2) Devent, the
congestion caused by special events, which could be reduced by public information and
coordination with transit; ( 3) Dlane, the congestion caused by lane closures, which could be
reduced by better scheduling of lane closures; ( 4) Dweather, the congestion caused by adverse
weather, which could be reduced by demand management and a better weather response system;
( 5) Dpot, the congestion that can be eliminated by ideal ramp metering; and ( 6) the residual delay,
Dexcess, largely caused by demand that exceeds the maximum sustainable flow. The method is
applied to a 45- mile section of I- 880 in the San Francisco Bay Area, using data for January- June,
2004.
The method refines previous studies ( 2,3,4) that group Dpot and Dexcess together as ‘ recurrent’
congestion. It also refines our recent work ( 15), which considers only three components ( Dcol,
Dpot and Dexcess). Transportation agencies measure recurrent congestion in various ways, and find
it accounts for 40%- 70% of total congestion ( 5). The availability of more comprehensive data
has prompted attempts to separately estimate the contribution of different causes of congestion.
There are studies that divide total congestion into ‘ recurrent’ and ‘ non- recurrent’ congestion; and
studies that divide the non- recurrent congestion into accident- induced congestion and other
incident- induced congestion. There also are estimates of the congestion caused by adverse
weather. These studies are reviewed in the next section.
These studies leave a large fraction ( between 40 and 70 percent) of the total congestion
unexplained. This unexplained residual is often called ‘ recurrent’ congestion. As Hallenbeck et
al. observe, “ Many large delays still occur for which incidents are not responsible, and for which
no ‘ cause’ is present in the [ data].” They suggest that one cause of these delays may be “ unusual
volume surges at ramps ... that are not being effectively handled by the ramp metering program”
( 2, p. 11). The proposed method estimates this potential reduction in delay, Dpot.
The paper is organized as follows. Previous studies are reviewed in Section 2. The proposed
method is described in Section 3. The congestion components of I- 880 are determined in Section
4. Section 5 concludes the paper.
2. PREVIOUS STUDIES
Transportation agencies until recently only reported recurrent congestion. ( For an example see
( 7); for an extensive survey of the practice see ( 5).) The availability of more comprehensive data
has inspired studies to quantify the relative impact of different causes of congestion.
Kwon/ Mauch/ Varaiya 3
Several studies estimate the impact of incidents. The earliest studies relied on correlating
specially- collected incident data using ‘ floating cars’ with loop- detector data ( 8). These data
provide a great deal of information about the nature of incidents, but the data collection efforts
are too expensive to replicate on a large scale or on a continuing basis.
Date from California Highway Patrol computer aided dispatch ( CAD) and Freeway Service
Patrol ( FSP) logs were used to evaluate FSP effectiveness in Los Angeles freeways ( 9) and in
Oregon ( 10). These studies need much human effort, data analysis skill, and subjective judgment
in determining the spatial and temporal region of the congestion impact of an incident. Our
previous work ( 15) developed an automated method to delineate an incident’s impact region. But
that approach requires accurate time and location of incidents, which may not be available.
Determining every individual incident’s impact region can be avoided if one is willing to average
out the impact of individual incidents as in ( 2, 3). Both studies separate ‘ non- recurrent’ and
‘ recurrent’ congestion, but they differ in definition and method.
Skabardonis et al. ( 3) consider a freeway section during a peak period. The total congestion on
each of several days is calculated as the additional vehicle- hours spent driving below 60 mph
( see equation ( 1) below). Each day is classified as ‘ incident- free’ or ‘ incident- present’. The
average congestion in ‘ incident- free’ days is defined to be the recurrent delay. Total congestion
in incident- present days is considered to be the sum of recurrent and incident- induced
congestion. Subtracting average recurrent congestion from this gives an estimate of the average
non- recurrent or incident- induced congestion. On the other hand, Hallenbeck et al. ( 2) take the
median traffic conditions on days when a freeway section does not experience lane- blocking
incidents as the “ expected, recurring condition.”
A less data- intensive approach is taken by Bremmer et al. ( 4). In the absence of incident data,
they simply assume that an incident has occurred if a trip “ takes twice as long as a free- flow trip
for that route.” The aim of this study is to forecast travel times, measure travel time reliability,
and conduct cost- benefit analysis of operational improvements, rather than to measure the
congestion contribution of different causes.
Lastly, the impact of inclement weather on freeway congestion is studied in ( 11, Chapter 22) and
( 12), which find that light rain or snow, heavy rain, and heavy snow reduces traffic speed by 10,
16, and 40 percent, respectively.
3. PROPOSED METHOD
The method applies to a contiguous section of freeway with n detectors indexed i = 1,…, n,
whose flow ( volume) and speed measurements are averaged over 5- minute intervals indexed t =
1,…, T. Days in the study period are denoted by d = 1,2,…, N. Detector i is located at postmile xi;
vi( d, t) = v( xi, d, t) is its speed ( miles per hour, mph) and qi( d, t) = q( xi, d, t) is its flow ( vehicles
per hour, vph) at time t of day d.
The n detectors divide the freeway into n segments. Each segment’s ( congestion) delay is
defined as the additional vehicle- hours traveled driving below free flow speed vref, taken to be 60
mph. So the delay in segment i in time t is
Kwon/ Mauch/ Varaiya 4
Di( d, t) = li × qi( d, t) × max{ 1/ vi( d, t) − 1/ vref, 0} vehicle- hours, ( 1)
in which li is the segment length in miles. The total delay in the freeway section on day d is the
delay over all segments and times,
Dtotal( d)= ΣΣ
= =
n
i
T
t
Di d t
1 1
( , ). ( 2)
The average daily total delay is simply
Dtotal = Σ=
N
d
total D d
N 1
1 ( ) . ( 3)
In the application below we separately consider the daily delay over two peak periods, 5- 10 AM
for the morning peak and 3- 8 PM for the afternoon peak.
Incidents are indexed a = 1, 2, … . The time τ a
when incident a occurs and its location σ a
are
approximately known. The incident clearance time and the spatial and temporal region of the
incident’s impact are not known.
Decomposition of Delay
The method divides the average daily total delay ( 3) into six components,
. total col event lane weather pot excess D = D + D + D + D + D + D ( 4)
It will be useful to define
, non rec col event lane weather D = D + D + D + D − ( 5)
. rec tot non rec pot excess D = D − D = D + D − ( 6)
Above,
Dcol is the daily delay caused by incidents,
Devent is the daily delay caused by special events,
Dlane is the daily delay caused by lane closure,
Dweather is the daily delay caused by adverse weather condition,
Dpot is the potential reduction of Drec by ramp metering,
Dexcess is the residual delay, attributed mostly to excess demand,
Drec is the daily ‘ recurrent’ delay, and
Dnon- rec is the daily ‘ recurrent’ delay.
Dtotal, calculated from flow and speed data, is the average daily total delay. Dcol, Devent, Dlane and
Dweather are components of so- called ‘ non- recurrent’ congestion. The difference between their
Kwon/ Mauch/ Varaiya 5
sum and Dtotal is the ‘ recurrent’ congestion ( 2, 3). A portion of recurrent congestion due to
frequently occurring bottlenecks could, in principle, be reduced by ramp metering. That potential
reduction is estimated as Dpot. The remaining delay, Dexcess, is due to all other causes, most of
which is likely due to demand in excess of the maximum sustainable flow. The delay due to
excess demand can only be reduced by changing trip patterns. We now describe how each
component of ( 4) is estimated.
Non- Recurrent Delays
The components of non- recurrent delay are identified using the following model,
Dtotal( d) = β0 + βcol Xcol( d) + βevent Xevent( d) + βlane Xlane( d) + βweather Xweather( d) + ε( d), ( 7)
Where
ε( d) is the error term with mean zero,
Xcol( d) is the number of incidents on day d,
Xevent( d) is the number of congestion- inducing special events such as sport games on day
d,
Xlane( d) is the number of lane- closures on day d, and
Xweather( d) is the 0- 1 indicator of adverse weather condition on day d.
The explanatory variables listed above are used in our application, but the list could be
augmented if additional data are available. For example, Xevent( d) could be the attendance at
special events instead of the number of special events; Xlane( d) could be the duration instead of
the number of lane closures; and Xweather( d) could be the precipitation ( as in our application).
The model assumes that each incident, special event, lane- closure, and adverse weather condition
contributes linearly to the delay. Figure 2 illustrates that such model is reasonable for our study
site. More complicated causality between explanatory variables, such as between the bad weather
and the number of accidents, is not considered to keep the number of parameters in the model
small. But if one has enough data and the interaction is strong enough, such interaction terms
could be included. ( For the San Francisco Bay Area data considered below, the correlation
coefficient between precipitation and number of accidents is only 0.032.)
Fitting the model to the data via linear least squares gives the parameter estimates, again denoted
β0, βcol, βevent , βlane and βweather. The components of the total delay then are
Dcol = βcol × avg{ Xcol( d)}, ( 8)
Devent = βevent × avg{ Xevent( d)}, ( 9)
Dlane = βlane × avg{ Xlane( d)}, and ( 10)
Dweather = βweather × avg{ Xweather( d)}, ( 11)
in which the average is taken over days, d = 1,…, N.
Kwon/ Mauch/ Varaiya 6
The intercept β0 in ( 7) is the delay when there are no incidents, special events, lane- closures, or
adverse weather. Thus, consistent with convention, it may be identified with recurrent
congestion, since it equals total delay minus the non- recurrent delay Dnon- rec defined above,
β0 = Drec = Dtotal – Dnon- rec. ( 12)
Recurrent Delay Algorithm: Separating Recurrent and Non- recurrent Congestion
The next step is to divide the recurrent delay into the delay that can be eliminated by ramp
metering and the delay due to excess demand. For this, the method identifies recurrent
bottlenecks on the freeway section using the automatic bottleneck identification algorithm
proposed in ( 13). Then the ideal ramp metering ( IRM) is run on those recurrent bottlenecks that
are activated on more than 20% of the weekdays considered ( 14, 15).
Here is a brief description of the IRM algorithm. For a specific recurrent bottleneck, let segment
i and j be the upstream and downstream boundaries of the bottleneck, respectively. For the
upstream boundary j, we use the median queue length of the bottleneck. Then we compute the
total peak period volume at the two locations. The difference between the two would be the
difference between the total number of cars incoming or exiting the freeway between the two
segments. We assume that all those cars contributing to the difference are arriving ( or leaving) at
a virtual on- ramp ( off- ramp) at the upstream segment i. Also, the time- series profile of that extra
traffic is assumed identical to the average of those at segment i and j. That enables us to compute
the modified total input volume profile at the segment i. The capacity of the whole section is the
maximum sustainable ( over 15- minute) throughput at location j and we compute this from the
empirical data. We meter the virtual input volume at segment i at 90% of Cj to prevent the
breakdown of the system, assuming:
( 1) The metered traffic will be free flow ( 60 mph) throughout the freeway section, and
( 2) The upstream meter has infinite capacity.
Thus, under IRM, the delay occurs only at the meters. The potential savings from IRM at these
bottlenecks for each day d is then computed as,
Dpot( d) = DBN, before IRM( d) - DBN, after IRM( d). ( 13)
Here DBN, before IRM( d) and DBN, after IRM( d) is the delay at the bottlenecks before and after IRM is
run. The average daily potential saving is
Dpot = min { median( Dpot( d), d = 1, …), Drec}. ( 14)
In ( 14) the median instead of the mean is used to ensure that the influence of incidents and
special events etc. is minimized in the computation. Also, the potential saving can’t be larger
than the total recurrent delay Drec.
Due to the ‘ ideal’ nature of IRM, Dpot need to be interpreted with caution. Especially, the
assumption of a very large, though not infinite, capacity at the meter is not realistic for many
Kwon/ Mauch/ Varaiya 7
urban freeways and metering at certain locations can lead to breakdown of arterial traffics nearby.
Thus, it is recommended that Dpot be viewed as the maximum possible saving in the recurrent
delay by metering.
Congestion Pie
The method described above divides the average daily total delay Dtotal into six components,
summarized in easily understood pie charts like those in Figure 1.
4. CASE STUDY
The method is applied to a 45.33 mile ( postmile .39 to 45.72) section of southbound ( SB) and
northbound ( NB) I- 880 in the San Francisco Bay Area. Two time periods are considered: AM
peak, 5- 10 AM; and PM peak, 3- 8 PM. Data cover 110 weekdays during January 5– June 30,
2004. There are four scenarios, distinguished by peak period and freeway direction: SB AM, SB
PM, NB AM and NB PM.
Data Sources
Traffic Speed and Volume Data
The 90 ( NB) and 94 ( SB) loop detector stations in the section provide 5- minute lane- aggregated
volume and speed data, available at the PeMS website ( 16).
Freeway Service Patrol ( FSP) Incidents
Incident data are for Freeway Service Patrol ( FSP) assisted incidents. On an average non- holiday
weekday the FSP assists upwards of 80 motorists on I- 880 during 6: 00- 10: 00 AM and 3: 00- 7: 00
PM. FSP peak hours are an hour shorter than peak hours used for computing total delay ( 5- 10
AM and 3- 8 PM) but we don’t expect the effect would be substantial. On weekends and
holidays, FSP assistance is not provided. FSP drivers record the date and time, duration, freeway
name and direction, incident description ( e. g. traffic accident, flat tire, out- of- gas), and location
( e. g. on- or off- ramp, left shoulder, right shoulder, in- lane). We only consider in- lane incidents
( as opposed to those on the left or right shoulder or on a ramp) during peak hours. There were
829 such incidents during the study period.
Special Events
On 45 out of 110 weekdays, there were special events in the Oakland Coliseum, near postmile 36
of I- 880, including baseball ( the Oakland A’s) and basketball ( the Golden State Warriors) games
and show performances, mostly starting at 7 PM. Data were provided by Networks Associates
Coliseum & The Arena in Oakland.
Kwon/ Mauch/ Varaiya 8
Weather
Weather data were collected from California Department of Water Resource ( DWR) for
“ Oakland north” ( station ID “ ONO”) station ( 17). The station reports daily precipitation,
temperature, wind speed and direction, etc; only precipitation was considered in the analysis.
Lane closure
Lane closure data were obtained from the Lane Closure System ( LCS) managed by California
Department of Transportation ( 18). LCS records include, for each lane closure:
Location: freeway, direction, county, and postmile,
Begin/ End date and time,
Facility/ Lanes: on/ off- ramp, # lanes, which lanes, and
Type of work: sweeping, construction, etc.
For the first half of 2004, for NB I- 880, there were 224 lane closures, 126 of them in the traffic
lanes. It turns out that all day time closures were ‘ sweeping’ or ‘ call box remove/ repair’, which
involve a moving closure of at most one lane and have negligible impact on congestion. All
congestion- inducing lane closures ( repair, striping, and paving) occurred at night ( after 10 PM
and before 5 AM) or on weekends outside the AM and PM peaks. This was also the case for SB
880. Thus we assign Dlane = 0 for all scenarios.
Results
Table 1 summarizes the regression results for non- recurrent congestion. The last column shows
the multiple R- squared values for each scenario, which is the ratio of the sum of squares of the
delay explained by the regression model and the total sum of squares around the mean. The F-statistic
for testing whether the fit of the model is valid is significant with practically zero P-value
for all four scenarios, suggesting the linear regression model successfully explains the
delay variation. We also observe:
1. βevent is statistically significant ( P- value < .10) only for PM shifts. This is to be expected
since most special events occur in the afternoon or evening. Each special event, on the
average, contributes a delay of 1,084 and 705.5 veh- hrs for NB and SB respectively.
2. βcol is statistically significant ( P- value < .001) only for PM shifts. This suggests that
congestion in the morning peak hours is more recurrent in nature than in the
afternoon/ evening. In PM shifts, each incident contributes a delay of 486.13 ( NB) and
383.75 ( SB) veh- hrs on the average.
3. βweather is statistically significant ( P- value < .001) only during AM shifts. On average, one
inch of rain adds 1305.7 ( NB) and 2125.6 ( SB) veh- hrs of delay. Note that it rained on 29
out of 110 weekdays; the median precipitation was .13 inches, and the maximum was
2.44 inches.
Figure 2 shows the relationship between Dtotal and some of the explanatory variables illustrating
the correlation between the total delay and those variables.
Kwon/ Mauch/ Varaiya 9
Next, formulas ( 8)-( 11) are used to compute the delay components shown in Table 2. Before
applying the formula, we set to zero those regression coefficients that are not statistically
significant at significance level 0.1.
The automatic bottleneck detection algorithm is applied to speed data of the kind whose contour
plot is shown in Figure 3. Clearly visible in the figure are an AM bottleneck near postmile 10
and a larger PM bottleneck near postmile 27. Dpot and Dexcess are computed from the IRM
algorithm and shown in the right columns of Table 2. About 44% of recurrent delay can
potentially be eliminated by ideal ramp metering: ( Dpot and Dexcess are extrapolated from district
wide quantities; freeway- specific computation is underway in PeMS v. 6.0.)
From the charts in Figure 1 one can conclude:
1. One- third of the congestion delay occurs at recurrent bottlenecks and can be potentially
eliminated by ideal ramp metering.
2. One- half of the delay is due to excess demand in both directions, and can be reduced only
by changing trip patterns.
3. Incidents and special events contribute 18% of the delay. The former can be reduced by
more rapid detection and response; impact of special events may be reduced by
information on changeable message signs.
The 486.13 ( NB) and 383.75 ( SB) vehicle- hours of delay per incident for the PM shift is in
rough agreement with other estimates. A regression of total daily delay vs. number of accidents
for all of Los Angeles yields a slope of 560 vehicle- hours per accident ( 6, p. 20). For southbound
I- 5 in Seattle, Hallenbeck et al. find that a lane- blocking incident causes between 318
( conservative estimate) and 591 ( liberal estimate) vehicle- hours of delay ( 2, p. 15).
The average daily delay caused by incidents, Dcol, is 986 and 837 vehicle- hours, which is 20.3%
and 18.8% of total PM delay for NB and SB, respectively. By way of comparison, Hallenbeck et
al. find that “ for the urban freeways examined [ in the Central Puget Sound region of Washington
State] lane- blocking incidents are responsible for between 2 and 20 percent of total daily delay”
( 2, p. 8). These average numbers must be used with caution because the delay impact of incidents
varies considerably from freeway to freeway and over different times of day. For example, in our
study, during the AM peak ( 5- 10 AM), the average incident- induced delay is 0 ( because βcol is
not significantly different from 0) for NB and 9.9% of the total peak hour delay for SB.
Aggregating over both peaks and both directions, the delay components are 13.3%, 4.5%, 1.6%,
33.2%, and 47.4% for incidents, special events, rain, potential reduction and excess demand.
5. CONCLUSION
Between 1980 and 1999, highway route- miles increased 1.5 percent while vehicle miles of travel
increased 76 percent ( 1). In 2000, the 75 largest metropolitan areas experienced 3.6 billion hours
of delay, resulting in $ 67.5 billion in lost productivity, according to the Texas Transportation
Institute. Mitigating congestion through more efficient operations is a priority of transportation
agencies. The first step in designing an effective mitigation strategy is to know how much each
cause contributes to congestion. One can then design a set of action plans, each aimed at
Kwon/ Mauch/ Varaiya 10
reducing the contribution of a particular cause. The more detailed the set of causes that are
considered, the more effective the strategy that can be devised.
The paper proposes a fully automated method that calculates six components of congestion:
delay attributed to incidents, special events, lane closures, and weather; delay that can be
eliminated by ramp metering; and the remaining delay, mostly due to excess demand.
The method is applied to a 45- mile section of I- 880 in the San Francisco Bay Area for AM and
PM peaks and for both directions. Incidents and special events together account for 17.8% of
total delay. Lane closures caused no delay because delay- causing closures were not scheduled
during peak hours. Rain caused 1.6% of total delay. A surprisingly large 33% of all delay could
be eliminated by ideal ramp metering. Lastly, 47% of the delay is due to excess demand.
Certainly, as discussed in the text, the 33% potential reduction due to metering needs to be
interpreted with caution, as the maximum possible reduction. Even with such precaution, if these
estimates are supported in more detailed studies, it is likely that most congestion mitigation
strategies would harvest large potential gains from ramp metering.
ACKNOWLEDGEMENT
We are grateful for comments and criticism from John Wolf, Fred Dial, Jose D. Perez and Lisa
Davies of Caltrans; Tarek Hatata of the System Metrics Group; and Alex Skabardonis and Karl
Petty of the PeMS Development Group. This study is supported by grants from Caltrans to the
California PATH Program.
The contents of this paper reflect the views of the authors who are responsible for the facts and
the accuracy of the data presented herein. The contents do not necessarily reflect the official
views of or policy of the California Department of Transportation. This paper does not constitute
a standard, specification or regulation.
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Kwon/ Mauch/ Varaiya 11
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Kwon/ Mauch/ Varaiya 12
LIST OF TABLES
TABLE 1 Regression Result for Non- Recurrent Delay ............................................................... 13
TABLE 2 Delay Contributions from Each Cause and Congestion Pie1 ....................................... 14
LIST OF FIGURES
FIGURE 1 Congestion pie chart for four scenarios on I- 880. ...................................................... 15
FIGURE 2 Relationship between delay and selected factors. The distribution of the average daily
total delay Dtotal( d), summarized as the box- and- whisker plot, is shown for each level of the
number of incidents ( upper left), special event occurrence ( upper right), or adverse weather
condition ( bottom plots)........................................................................................................ 16
FIGURE 3 Lane- aggregated speed by postmile and time of day for I- 880 S on April 2, 2004. .. 17
Kwon/ Mauch/ Varaiya 13
TABLE 1 Regression Result for Non- Recurrent Delay
Scenario Factor Estimate Std. Error t value
Multiple R-squared
NB AM ( Intercept) 3,301.1 191.1 17.28 0.000 *** 0.12
Event - 221.5 216.2 - 1.03 0.308
Incident 115.8 74.2 1.56 0.122
Weather 1,305.7 384.4 3.40 0.001 ***
NB PM ( Intercept) 3,419.7 408.1 8.38 0.000 *** 0.14
Event 1,084.6 416.0 2.61 0.010 *
Incident 486.1 133.9 3.63 0.000 ***
Weather 75.4 732.7 0.10 0.918
SB AM ( Intercept) 3,402.6 339.6 10.02 0.000 *** 0.17
Event - 482.0 342.2 - 1.41 0.162
Incident 221.1 127.6 1.73 0.086 .
Weather 2,125.6 598.5 3.55 0.001 ***
SB PM ( Intercept) 3,311.1 374.8 8.83 0.000 *** 0.12
Event 705.5 419.9 1.68 0.096 .
Incident 383.8 116.9 3.28 0.001 **
Weather 28.7 751.3 0.04 0.970
Pr(>| t|) 1
1. Significance codes “***”, “**”, “*” and “.” mean the P- value is between 0 and .001, between
.001 and .01, between .01 and .05, and between .05 and .1, respectively.
Kwon/ Mauch/ Varaiya 14
TABLE 2 Delay Contributions from Each Cause and Congestion Pie1
Scenario Factor β
Mean
Weakday
Occurrences
Delay
Contributions
( veh- hrs)
Factor,
after
Bottleneck
Analysis
Delay
Contributions
( veh- hrs)
Percent
of
Total
Delay
NB AM Recurrent 3,301 NA 3,301 Pot 1,307 38.4%
NA NA NA Excess 1,994 58.6%
Event 0 0.42 0 Event 0 0.0%
Incident 0 1.55 0 Incident 0 0.0%
Weather 1,306 0.08 102 Weather 102 3.0%
NB PM Recurrent 3,420 NA 3,420 Pot 1,336 27.5%
NA NA NA Excess 2,084 42.9%
Event 1,085 0.42 454 Event 454 9.3%
Incident 486 2.03 986 Incident 986 20.3%
Weather 0 0.08 0 Weather 0 0.0%
SB AM Recurrent 3,403 NA 3,403 Pot 1,327 33.5%
NA NA NA Excess 2,076 52.4%
Event 0 0.42 0 Event 0 0.0%
Incident 221 1.78 394 Incident 394 9.9%
Weather 2,126 0.08 166 Weather 166 4.2%
SB PM Recurrent 3,311 NA 3,311 Pot 1,565 35.2%
NA NA NA Excess 1,746 39.3%
Event 705 0.42 295 Event 295 6.6%
Incident 384 2.18 837 Incident 837 18.8%
Weather 0 0.08 0 Weather 0 0.0%
1. NA means the number is not needed.
Kwon/ Mauch/ Varaiya 15
Precip.
Potential
Reduction
Excess
Demand
NB AM
Events
Incidents
Potential
Reduction
Excess
Demand
NB PM
Incidents
Precip.
Potential
Reduction
Excess
Demand
SB AM
Events
Incidents
Potential
Reduction
Excess
Demand
SB PM
FIGURE 1 Congestion pie chart for four scenarios on I- 880.
Kwon/ Mauch/ Varaiya 16
0 1 2 3 4 5 6 7
2000 6000 10000 14000
NB PM
FSP Incidents
Delay ( veh- hrs)
FALSE TRUE
2000 6000 10000 14000
NB PM
PM Events
Delay ( veh- hrs)
FALSE TRUE
2000 4000 6000 8000
SB AM
Precipitation > 0.13 in.
Delay ( veh- hrs)
FALSE TRUE
2000 4000 6000
NB AM
Precipitation > 0.13 in.
Delay ( veh- hrs)
FIGURE 2 Relationship between delay and selected factors. The distribution of the average
daily total delay Dtotal( d), summarized as the box- and- whisker plot, is shown for each level
of the number of incidents ( upper left), special event occurrence ( upper right), or adverse
weather condition ( bottom plots).
Kwon/ Mauch/ Varaiya 17
FIGURE 3 Lane- aggregated speed by postmile and time of day for I- 880 S on April 2, 2004.