Estimate link travel time using probe vehicle

Material Information

Estimate link travel time using probe vehicle
Li, Lu
Publication Date:
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vii, 48 leaves : illustrations ; 28 cm


Subjects / Keywords:
Traffic engineering -- Colorado ( lcsh )
Traffic flow -- Measurement -- Colorado ( lcsh )
Travel time (Traffic engineering) -- Measurement -- Colorado ( lcsh )
Global Positioning System ( lcsh )
Global Positioning System ( fast )
Traffic engineering ( fast )
Traffic flow -- Measurement ( fast )
Travel time (Traffic engineering) -- Measurement ( fast )
Colorado ( fast )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )


Includes bibliographical references (leaf 48).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Lu Li.

Record Information

Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
43923161 ( OCLC )
LD1190.E53 1999m .L5 ( lcc )

Full Text
Lu Li
B. S., Colorado State University, 1996
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering

This thesis for the Master of Science
degree by
Lu Li
has been approved

Li, Lu (M. S., Gvil Engineering)
Estimate Link Travel Timing Using Probe Data
Thesis directed by Professor Sarosh Khan
Advanced Traffic Management Systems (ATMS) typically rely on inductance loop
detectors installed in pavements for information on average traffic speed, flow and density
of a transportation network In recent years, research has focused on using vehicles
instrumented with global positioning systems (GPS) that serve as probes in the traffic
stream. Probe vehicles report their location or travel time and provide a means of
estimating average link travel time. This study examines the relationship between number
of probe reports and variance of average link travel-time under different flow conditions.
The study shows that as the number of probe vehicle increases, the marginal improvement
in the standard error of travel time estimate is generally greater under higher flow
conditions. However, this depends on specific link characteristics. Therefore, using flow-
specific of average covariance and average variance estimates, and link travel time
functions provide a better assessment of the accuracy of probe reports.
This abstract accurately represents the content of the candidates thesis. I recommend its

The author wishes to thank Colorado Department of Transportation, Dr. Sarosh Khan,
Chip Taylor, Brian Hoeschen, Kittichai Thanasupsin and Pawan Maini for their efforts in
this research project.

1. INTRODUCTION.............................................1
2. REVIEW OF THE LITERATURE.................................3
Number of Probes vs. Reliability.....................3
ADVANCE Experience from Chicago......................6
Quality of the Probe Reports....................8
Probe Data Fusion..............................11
Variance of Travel Time........................13
Review Summary......................................15
3. METHODOLOGY.............................................17
Study Approach......................................19
4. PROJECT DATA............................................21
Study Network.......................................21
Data Sources........................................23
Freeway Geometry Data...............................23
Freeway Traffic Volumes and Travel Time.............24
5. MICRO-SIMULATION MODEL..................................28
Probe Vehicle File Data.............................31
6. RESULTS.................................................36
Selection of Links..................................36
Flow Rates..........................................36
Link Travel Time-Flow Relationships.................40
Variance of Average Travel Time.....................41
Standard Error of Average Travel Time...............42
7. CONCLUSION OF STUDY.....................................46

1. Link travel time estimation................................................17
2. Travel time function.......................................................19
3. Study area is a section of rural interstate highway 1-70 located in mountainous
4. Network roadway grades.....................................................24
5. Video cameras on 1-70 near US 40 and Bakerville............................26
6. Collection of Traffic Data.................................................27
7. Basic CORSIM model process.................................................29
8. Schematic of study network in CORSIM Simulation Model......................30
9. CORSIM source code modification............................................32
10. Difference between GPS and CORSIM link speed...............................35
11. Speed-flow plot for link 431-552, 0% grade.................................38
12. Speed-Flow plot for link 557-558, 5% grade.................................38
13. Speed-flow plot for Link 534-552, 0% grade.................................39
14. Speed-flow plot for link 316-416 between US-6 on and off-ramp..............39
15. Travel time plot for I ink 431-532.........................................40
16. Travel time plot for link 557-558 (5% grade)...............................41
17. Standard error of estimate of average travel time for congested and uncongested
18. Interaction of supply and demand to assess probe estimate accuracy.........43
19. Standard error of travel time estimate for link 557-558 for congested and
uncongested conditions.....................................................44
20. Standard error of travel time estimates using probe data for uncongested and
congested flow conditions..................................................45

1. Individual vehicles trajectory data from CORSIM............................34
2. Model detector output flow rates............................................37
3. Average variance and average covariance estimates of probe travel time for four
links under congested and uncongested conditions............................41

Advanced Traffic Management Systems (ATMS) typically rely on inductance loop
detectors installed in pavements for information on average traffic speed, flow and density
of links or sections of a transportation network. In recent years, research has focused on
using vehicles instrumented with global positioning systems (GPS) that report their
location or travel time to estimate average link travel time. These instrumented vehicles are
often called probes.
In mountainous terrain at high altitude, loop detectors are difficult to maintain due to icy
road conditions, and snow removal practices. For these corridors, probe vehicles could
potentially serve as a source of traffic information. A research project is underway to
investigate the feasibility of using probe vehicles on the 1-70 Interstate highway corridor
from Denver International Airport to the Ski Areas Vail and Aspen, to provide reliable
travel time information. Regular buses and vanpools from the airport to the ski areas could
be instrumented to serve as probes. The objective of this study is to examine the
relationship between number of probe reports and variance of link travel time estimates,
under congested and uncongested conditions.
To estimate the variance and covariance of probe travel time under congested and
uncongested conditions, probe reports for a freeway section were simulated and analyzed.
Therefore, the specific objectives of this study were to:
1) Model a section of the 1-70 corridor westbound from SH-40 to US-6 using
CORSIM, a microscopic traffic simulation model

2) Develop the capability to simulate probe vehicles using CORSIM
3) Compare field and simulation link travel time data
4) Analyze the variance of probe travel time estimates under congested and
uncongested conditions
5) Use link travel time functions to identify the standard error of average link travel
In addition, this study also reports on some drawbacks and modeling issues of CORSIM.
This section defined the terminology used throughout this thesis.
Probe vehicle: vehicles equipped with global positioning systems reporting their location
at pre-specified intervals.
Link: sections of freeway or urban streets without major geometric property changes (lane
drop, change in grade, major traffic generator, etc.)
Link travel time: travel time for a vehicle from the upstream end of a link to its
downstream end
Flow: The number of vehicle crossing a given section of roadway over time.

Providing reliable travel time information is an important function of a traffic management
center. Sensors that provide an estimate of traffic flow, speed and density at a section of
roadway include fixed-location surveillance such as inductance loop detectors, radar
sensor, and video image processing. Probe vehicles offer an alternate source of
information as they traverse various links of a network, and transmit location, speed
and/or point-to-point travel time information to a traffic information center, in real-time.
This chapter reviews the literature on the use of probes to estimate link travel time.
Number of Probes vs. Reliability
An article by Srinivasan and Jovanis, in 1996 [Srinivasan and Jovanis, 1996], presented a
procedure to estimate the number of probe vehicles required based on the measure of
reliability and adequate network coverage.
In real-time traffic operation, probe vehicle data is collected to obtain and transmit point
to point travel time data to a traffic information center or a traffic operation center. In
order to minimize the cost of collecting traffic data using probe vehicles, an algorithm was
developed to estimate the minimum probe vehicles required to report a reliable link travel
time in a network.
Studies on this subject across the country have shown a great disparity in the estimates due
to the specific network characteristics, such as the variation in link capacities and volumes.
In this paper, the authors developed a procedure considering the following criteria;

Reliability corresponds to the number of replications of travel times from probe
vehicles for each link, during each measurement period desired to estimate of the
number of probe vehicles.
Adequacy relates to the proportion of links to be sampled at least one (based on the
reliability criterion) during the measurement period.
In addition, trip length distribution, and mix of link classes is also considered.
The first measure of reliability is in terms of the probability of the absolute error not
exceeding a threshold on relative error. As the authors noted, for this measure the
allowable variance on larger values of travel times is more stringent than that on smaller
values of mean travel times. This measure ignores the possible dependence of the standard
deviation on the mean travel time. Hence, the authors did not recommend this measure.
The second measure is defined as the minimum probability that the absolute value of
relative error is less than the maximum allowable relative error threshold. The relative error
of the probe travel times is the ratio of the difference between the mean travel time of the
probes and the overall mean travel time to the overall mean travel time. Therefore, the
reliability is expressed in terms of the number of probes required for a link and time during
any period of interest.

r|pit = minimum number of probes required to reliably measure travel times
during the measurement period;
pelt = estimated number of probe vehicles required to reliably measure link travel
times based on historical data;
aelt = estimated standard deviation based on historical travel times.
The second major aspect of determining the total number of probe vehicles required is
adequate area coverage; routing played a major role in this aspect. The objective is to
determine the number of probe vehicles required in the network given that a desired
proportion of the links is to be covered reliably in a peak period. The problem of adequate
area coverage involves the consideration of overlapping in the paths of the probe vehicles.
The estimate of the number of probes would vary with the route assignment criterion.
Also, with more control over the routing decision of the probe vehicles, fewer probe
vehicles will be required. A probe vehicle routing assignment was proposed by using a
stochastic or dynamic approach instead of the static user-optimal routing assignment. The
procedure described as follows:
1. Determine the minimum number of probe vehicles required from the reliability
criterion on each link, during each measurement period.
2. Solve a stochastic or dynamic route assignment model for the network.
3. Sample a number of probe vehicle trips from the pool of all vehicle trips
occurring in the network during the peak period.

4. Assign the sampled probe vehicle trips by using the route assignment model
from step 2.
5. Determine the proportion of links covered reliably by probes. Average the link
coverage proportion over all measurement periods in the peak period to obtain
the average proportion link coverage.
A simulation was developed to implement this algorithm. The model used in this
simulation assumed a majority of the users will choose paths that minimize their travel
times, such as a stochastic shortest-path route assignment model with a normal distributed
travel time. The simulation seeks a desired proportion of the links covered which varies
the input values of number of probe vehicles per link per measurement period, and the
duration of the measurement period. The results from the simulation model suggested that
if the variance in travel times on a link is small, then fewer probes are adequate to reliably
represent travel times. Also, a substantial number of probe vehicles is required to estimate
link travel times if minor arterial and local and collector streets are included in the covering
area. Finally, in order to minimize the cost of using probe vehicles, the authors concluded
the best approach in using probe vehicle to collect traffic information is applying the probe
vehicles to the freeways and major arterials during a peak period. Other sources of travel
time data are needed during off-peak hours, and on local, collector streets and minor
ADVANCE Experience from Chicago
In 1994, an Advanced Traveler Information System (ATIS) experiment on signalized and
unsignalized arterials, ADVANCE (Advanced Driver and Vehicle Advisory Navigation
Concept) project in Chicago, conducted studies to estimate link travel time using probe

vehicles. Several papers were published that addressed data collection as well as the
assessment of probe data.
One of the papers on the ADVANCE project by Sen, Soot and Berka [Sen, Soot and
Berka, 1995]paper summarized the technology, methodology and the experience gained.
This paper discussed the effectiveness of estimating link travel times from probe vehicle
reports generated in the ADVANCE project. The paper concentrated on travel time
estimation from both detectors and probes during recurrent congestion. Non-recurring
congestion or incidents were not covered in this report.
In the ADVANCE project, the probe vehicles equipped with Mobil Navigation Assistant
(MNA) measure travel time on each link traversed. They also measured congested time
and congested distance for each link. These were reported back to the TIC via radio-
communications channels.
The travel time is represented as step functions. The day is divided into several intervals
and a single number would yield the travel time during intervals. For static estimates, a
weekday was divided into 48 intervals and weekends and holidays divided into 24 intervals.
More intervals were assigned to the peak hours. These numbers were chosen based on
comparisons of estimated and MNA data. There were some difficulties representing travel
times as a step function in static profiles. Link travel times is continuous function of time
of day. Therefore, the static estimates near the end of each interval were approximate. A
linear function was recommended to represent the interval individually for a better
A network equilibrium model was used to estimate initial travel times, which were then
revised using actual probe travel times. Though this procedure would produce quite

accurate travel time, it also could lead to imprecise travel times on a congested system of
arterial with signalized links.
ADVANCE project examined the quality of the reports collected by the probe vehicles.
These reports were tested on three critical elements of travel: travel time, congested time
and congested distance. This information was computed in the vehicles on-board MNA
and it was recorded in two different ways, directly onto a memory card in the vehicle and
also from radio frequency at files tabulated at the project offices TIC.
Quality of the Probe Reports
Another paper assessed the quality of the information accumulated in the vehicles on-
board Mobile Navigation Assistant (MNA)[Soot and Condie, 1995]. Two types of
assessments were performed to evaluate the travel time/speed, congested travel time, and
congested distance. The first assessment compared the MNA report data with expected
results to consider the reasonableness of the data. The second assessment compared the
probe data to the data recorded by human observers.
In the summer of 1995, as part of the ADVANCE project, 12 probe vehicles equipped
with MNA were used in a link travel time study for four days a week over an eleven-week
period. This data collection exercise yielded 50,620 reports in Traffic Information Center
(TIC). These reports provided information on three critical elements of travel: travel time,
congested time and congested distance. This information was computed in the probe
vehicle in its on-board MNA and it is recorded in two different ways, directly onto a
diskette in the vehicle and from files transmitted to the TIC by radio frequency. Data
reported from the TIC were formatted in a form indicating the data, time, travel time,
congested time, and congested distance.

The paper also described in detail the background information with this probe vehicle data
collection. The probe vehicle collection was performed from Monday to Thursday. Data
were collected by probe vehicles driven in the study area between 1 PM and 7 PM. During
the data collection period, the temperature the MNA unit installed in the trunk of each
probe vehicle experienced up to 149 F, which may have lead to malfunction of the MNA
unit. A tracking system and the Global Positioning System (GPS) were used to determine
the vehicle position. Each probe vehicle was equipped with a set of electronic equipment.
This included
Compact disc drive,
Radio transmitter and receiver,
Satellite signal receiver,
RF antenna,
GPS antenna,
Transmission sensor,
Display head, and
Cellular telephone.
The first aspect of this evaluation was to compare MNA data from the probe vehicles with
expected results, such as speed, congested time and congested distance. The report send to
TIC from MNA was analyzed for unusually high speed and congested distance. High-
speed reports are defined as those reports in which the average speed for the probe vehicle

on a link is substantially higher than the link speed limits. The analysis showed that less
than 0.2% of all probe reported high speed, and most of these high speed reports occurred
in particular probe vehicles. This suggested problems with the on-board MNA, because
different drivers were assigned to different vehicle, every day. High-congested distance
reports are those reports where the congested distance exceeds the link length. A sample
of data was analyzed to determine the accuracy of the congested distance. Less than 0.2%
of all probe reports with the congested distance exceeding the link length by at least 10%.
Most of these reports occurred in specific links and vehicles. Congested distance and
congested time comparison were made to establish any logical inconsistency. In most of
the case, the malfunction of MNA contributed to the mismatch of congested distance and
congested time.
The second aspect of the evaluation was to assess the compatibility of the probe and
human-observer data. The human-observer data was manually recorded by the traveling
passengers in the probe vehicles. In the travel time comparison, 87.6% of the probe data
were within 5 seconds, and 94% were within 10 seconds. This indicated a very good fit
between the observed and probe data. The congested distance and congested time
reported by MNA also indicated a very close relationship to the observed data.
In the first aspect of the assessment of reasonableness of the probe data, three criterions
were applied to detect faulty reports. Each identified approximately one hundred reports
out of 50,640 reports that appeared incorrect. Some of these reports were identified more
than once. The authors concluded that this was due to the MNA malfunctioning. Second
assessment was by comparison of the human-observed and probes data. The link travel
time and both congested time and congested distance indicated a sufficiently good match
between probe and the observed data. Authors concluded that there were some faulty
records in these data collection exercises. The faulty data were easy to identify and was

deleted. These reports constituted a very small proportion of the total data collected.
Overall, the probe vehicle data collected using MNA represented a valuable resource for
traffic analysis.
Probe Data Fusion
A paper by Tarko and Rouphail [Tarko and Rouphail, 1996] examined the methodological
aspects of detector and probe data for signalized arterials. This study presented the
concept of the basic data fusion algorithm to process the data from probe vehicle reports,
detector outputs, historical and other data.
Two data fusion algorithms were presented, off-line and on-line. On-line algorithm was
discussed in detail in the paper. The algorithm was designed to fuse data from historical
profiles, probes and detectors, and to execute the algorithm in real-time.
The data fusion algorithm was proposed in following steps:
1. Estimate the expected link travel time from detector data (EDIT) using a
regression model developed off-line,
2. Calculate the mean probe travel time (EPTT) from probe reports received
during the last interval,
3. Fuse EDIT with EPTT in order to obtain the on-line link travel time estimate
4. Obtain the final link travel time (EFl'l) by fusing EOTT with historical
(static) travel time estimate (ESTl).

Step 1 involved the conversion of detector data to the expected link travel time. On any
signalized link, detector data conversion considered three factors: traffic stream
parameters, traffic control and link geometry. Regression model was applied off-line to
estimate the link travel time. The relationship between detector data and mean link travel
time in 15-minute intervals was investigated, with control parameters unchanged. The
results indicated the detector occupancy has superior explanatory capability than volume.
In the second step, the average probe travel time EPTT was calculated as:
s = standard deviation of the probe travel time in the historical data base, and
N = the number of probe reports during the update interval.
Step 3 calculated the fused mean travel time from on-line sources, EOTT,
2 1 ~
a D
Step 4 fused the EOTT with ESTT to find the overall travel time estimate,

2 2
CT s____CT o
1 1
2 + 2
CT s CT o
This paper described an approach to estimate travel time on-line by data fusion.
Variance of Travel Time
An 1997, another paper on the ADVANCE project reported the variance of the probe
reports as a function of number of probe vehicles deployed [Sen, Thakuriah, Zhu and
Karr, 1997]. The key conclusions reached by the authors is that given the correlation
between probe vehicle travel times on a link,
High levels of deployment may not offer substantial improvement in guidance
quality because of the marginal improvement in the precision of link travel
time estimates drops off after only a few observations per discrete time
interval are obtained.
The variances of the estimates under high levels of congestion never go to
zero and one must explicitly account for this in constructing route guidance
In order to estimate the required number of the probes, the paper provided a method to
estimate the variance of the mean link travel time. Given that link travel time observations
are correlated, the variance and covariance of mean travel time were estimated based on
the level of dependency.
The mean probe travel times is

x = n > x
^i=\ 1
Where, x, = individual probe travel time within a given interval, n = number of probe
reports. And the variance of the mean as:
n __
vafx)=n2 J\Mx,)+Yf^x: xj )
Where, Cov() = covariance, the average variance of x as
= [n(n-\)Y'Y,Cov(Xi,Xj)
With the average covariance of all pairs (x,, x^ as 7] Yl 1 ^ var( X( )
And, finally the variance of the average travel time can be written as
var(x) = v + x{tj-v)
A null hypothesis of zero covariance was tested. With v = 0 or cov = 0, there would be no
correlation between the each measured travel time in the field. The correlation tests
revealed the following conclusions:

The variance of mean link travel time remains quite far from zero no matter
how many probes are reporting the travel time.
Beyond certain number of probes per unit time, additional probes do not
change the variance substantially.
The paper presented an empirical analysis of variance and covariance of the link travel
time. The analysis concluded the variances of the link travel time would never go to zero.
Thus, a high level of probe vehicle deployment is not necessary in order to have a link
travel time estimate of reasonably good quality. It is important to identify the important
links within the network, and provide probe vehicle coverage for a more accurate measure
of the travel time.
Review Summary
Several major studies that examined the use of probe vehicles to estimate link travel time
were presented in this chapter. The Sirinivasan and Jo vans paper presented a procedure to
estimate the required number of probe vehicle based on the reliability of the data, and the
adequacy of the coverage area. This procedure requires historical data to estimate the
number of probe vehicles required for each link.
In the ADVANCE project, a large probe-based ATIS experiment in Chicago was
conducted to collect extensive probe data. The results of the deploying probe vehicles
were documented in various reports and papers presented. ADVANCE project offered
many perspectives, from the managerial to the technical view of the experiment. One of
the papers examined the dependence of probe reports and its impact on the estimation of
average link travel time was an important contribution.
It is important to note the following about most of these studies:

(a) link travel time was reported by the probes
(b) only one study considered the dependence or correlation of probe travel time
(c) none of the studies considered the the supply function to evaluate the variance of
probe travel time

Sen et al (1995) and other studies have examined estimation of average link travel time
based on link travel time reported by probe vehicles, over a given interval. Probe vehicle
travel time is calculated as:
Link travel time = TM Tm
Tm = time vehicle enters a link, and
Tm = time vehicle exits a link.
For example, as shown in the figure 1 below, several probe vehicles may report their full
link travel time (e.g. Vehicle# 1) within a 5-min time interval. However, probe vehicles may
not complete their link journey within the time interval (Vehicle #2,3,4). A traffic
operation center scanning the availability of probe vehicles every 5-min may identify
Vehicle #2,3,4. Though these probe vehicles may not have completed their link journey,
this data could be used to estimate average link travel time.

#3 £22*
Di=L= T,
#2 0
Dj, Ti

Figure 1: l ink travel time estimation

Link travel time is estimated based on time-stamped probe location data as follows:
A 1
-d- = u,=>- = t,
T; M,
LTT, = Ltt L
___ 1 " T n 1
ltt = -Yltti=-Y
n ,=i n ,=1 u,
This study examines the use of unit travel time or space mean speed of probe vehicles to
estimate average probe vehicle travel time. A previous study (Sen et al, 1995) has shown
that the variance of average travel time estimated from n probe reports does not tend to
zero, as n increases. The variance of average travel time was shown based on the following:
v = average covariance of probe travel time
r) = average variance of probe travel time
According to equation above, as n tends to infinity, variance of average travel time tends to
the average covariance of probe travel time. This study examines the average variance and
covariance of probe vehicle travel time under congested and uncongested conditions.
Under uncongested conditions, the average covariance of travel time is very low since
vehicles move through the link unimpeded by the presence of other vehicles. However, as
congestion develops, vehicle following occurs and therefore travel times are correlated.
The correlation increases with increasing flow. This suggests that it is important to analyze
the variance of travel time under different flow conditions separately, to assess the
standard error of estimate of the average link travel time or speed. More specifically, the

value of v and r| and their difference determines how sharply the standard error decreases
with increasing number of probes in the traffic.
Figure 2: Travel time function
A typical travel time function is shown in Figure 2 and can be determined for any link
under different flow conditions. Based on probe reports, the range of flow condition can
be identified. Therefore, flow specific v and r\ can be used to assess the standard error of
average probe information (travel time, speed, etc.)
Study Approach
This study models a section of the 1-70 corridor from SH-40 to US-6 in CORSIM (details
in Chapter 5). Congested and uncongested flow conditions were simulated for half an
hour, based on flow profiles developed from 5-min field data. Field data was collected to
validate the model. For congested and uncongested flow conditions, 1, 3, 5, 10 and 15

probe vehicles were randomly selected from a 5-min period to estimate average probe
travel time (details in chapter 5) as discussed in the previous section.
For each flow condiuon the following was estimated:
average ^LTT j
variance (LTT )
average of 5-min average probe vehicle travel time, based on n
(=1,3,5,10,15) probe reports
variance of 5-min average probe vehicle travel time, based on n
(1,3,5,10,15) reports
For a given flow condition, variance (Z.7T j and n over 5-min periods provide the data to
estimate average variance and average covariance v and r| by regressing
variance! LTT 1 against l/n to determine v and r|-v.

This chapter describes the data collected to develop a representation of a section of the I-
70 interstate corridor from east of SH40 to the Eisenhower Tunnel, in a traffic simulation
model to simulate vehicles reporting their location and speed. Traffic information required
to coding and calibrating the corridor in CORSIM is as follows:
Freeway geometry,
Lane configuration and road grades;
Freeway traffic volume;
Vehicle turning movements;
Point-to-point travel time.
The following sections present the details.
Study Network
The study network represented in this project is a section of rural US interstate highway, I-
70. A section of the freeway located in a mountainous terrain, just east of the Eisenhower
Tunnel, is a gateway to the ski countries on west of Denver, Colorado (figure 3). The limits
of the network is between the tunnel to the east of SH40 on 1-70. This freeway segment
was selected because it carries high traffic volume during the ski season. This study
network consists of a 17-mile westbound stretch of the freeway. Each direction of the
section has two-lanes and twelve one-lane on and off ramps. The distance between each
interchange is approximately 3 miles. Because of the mountainous terrain, severe vertical

Figure 3: Study area is a section of rural interstate highway 1-70 located in mountainous terrain

grades exist throughout this section of the freeway. Mountain rocks on the shoulder of the
roads also cause limited horizontal sight distance. Queues and saturated flow conditions
occur during the peak hour flow. Therefore, this section of the freeway served as an
excellent test-bed for this research.
Data Sources
Colorado Department of Transportation (CDOT) provided freeway geometry and limited
detector data. Most of the data was collected by a research team involved with the larger
project. Tube counters and video cameras were used to collect freeway and ramp traffic
volume. Vehicles were also deployed to measure the freeway travel time within the study
network. At a later stage of this research project, vehicle equipped with Global Position
System (GPS) receivers traversed the network to detailed geometry and link travel time
Freeway Geometry Data
Network geometry data including lane configuration, length of acceleration and
deceleration lanes, roadway grades, and the distances between on and off ramps for this
study section was collected from construction plans provided by Colorado Department of
Transportation (CDOT). Additional data on roadway geometry was subsequently based on
data collected using survey-grade GPS receivers. Figure 4 shows the variation of the
grades, as determined by GPS elevation reported along the roadway. As the figure
indicates, severe grades exist along the entire study segment. Grades vary from -1% to 7%.

Roadway Grades o nno/
o.uu /o 7 nno/ (
f. UU 70 c nno/
O.UU 70 c nno/ * -) l_ J \ J
jg O.UU /o T3 ffl a nno/ X h 1 4 l
i- 4.UU/0 CD l\ J- i ,! -1 ] X.
o o.UUvo ] i r / J L h \ L
O ^.UU /o <5 H a nno/ L ! ( Sj X *
1 .UUyo n nno/ < 1
U.UUyo i nno#?* - £ K iSl. n. 4i &
-1.Ul^9 1 * v <: _ <5 ' > s b s>
Zl.VJU /o Milepost
Figure 4: Network roadway grades.
Freeway Traffic Volumes and Travel Time
CDOT maintains many in-pavement detectors along Interstate 70 freeway. Two detectors
are located just outside of the study area, at the upstream and downstream end. The
upstream detectors are located about 5 miles east of SH40 and the downstream detectors
are located in the tunnel. These detectors provided historic data to identify the peak hour
of traffic flow. The peak-period freeway and ramp volumes were collected by setting up
temporary, mechanical tube counters on the upstream and downstream locations. Data
was collected on Saturday during the morning peak hours between the period of 7 AM to
10 AM, and non-peak hours of 11 AM to 1 PM. These periods were chosen based on the

flow pattern in the corridor. Generally, most skiers head toward the ski resorts over the
weekend during the winter season. Locals travel to the ski countries from the metropolitan
area of Denver, and visitors from the Denver International Airport usually travel early
Saturday mornings, and return to the urban cities Sunday afternoons. Peak hour traffic on
the westbound freeway is usually observed Saturday morning, during the ski season.
Data was collected on a mid-March Saturday morning. Counters were set up at each of
the twelve on and off ramps. Speed traps were also set up at two locations on the mainline
of the freeway. Approximately 12 miles apart, the counters were located at the beginning
and the end of the network. While the vehicle volume and speed were recorded
automatically by the counters, three probe vehicles were traveling within the network to
collect the travel time information. Speed, location, (distance from the origin) and time was
recorded by each driver. This information was recorded on an audio recorder. Probe
vehicle drivers also recorded other information. Each driver traveled the study section four
times during the first study period with 15 minutes headway between probe vehicles. A
similar procedure was also applied to the non-peak period data collection.
Additional data was collected during the model calibration process. Two good vantage
points were identified to setup video cameras to record the mainline traffic volumes. The
two vantage points were selected to collect traffic data at the upstream and downstream of
the study network. Upstream camera located on the elevated section of the 1-70 and SH40
ramp. The downstream setup of the camera located on a typical overhang diamond-
interchange bridge of 1-17 and Bakerville. Videos tapes were later processed using a video
image processing (VIP) tool (Aries Corp., 1995) to extract the traffic volumes and speed at
two locations on the freeway.

L/i i
Figure 5: Video cameras on 1-70 near US 40 and Bakerville
In addition to the VEP tool, GPS receivers were utilized to collect elevation, location, time
and speed data. The data was transmitted via a TCP/IP protocol to a lab computer. Data
was transmitted as text string. Data transferred was also differentially corrected to reduce
selective availability error. Using linear referencing tools available in a Geographic
Information System (GIS), the exact location of the GPS instrumented vehicle was
represented on a map. Data were transfer in real time, and updated every second.

In summary, this data collection effort combined information from several sources and
was pieced together using GIS and other customized programs. Figure 6 illustrates all the
data collected and utilized to model and calibrate CORSIM.
CDOT n Mechnical
Existing ^ Tube
Data V Counters
i Autoscope J| GPS
Video ^ Instrumented
Detection W Vehicle
Figure 6: Collection of Traffic Data.

There are several microscopic traffic simulation programs available for research and
design. One of the objectives of the study was to simulate probe vehicles on freeway
network. This chapter provides an overview of the simulation model used, details of the
test network coded, inputs to the model, and a description of the special routines written
to collect probe data from the simulation.
CORSIM is a traffic CORridor SIMulation software developed by Federal Highway
Administration (FHWA). CORSIM combines NETSIM and FRESIM, two microscopic
stochastic simulation models. NETSIM simulates a surface street network, and FRESIM
models a freeway network. The simulation environment is represented as a network
consisting of nodes and links. Generally, the nodes represent a change in geometry, and
the links represent freeway sections and urban streets. Links are uni-directional segments
of freeway and are defined by their upstream and downstream node numbers. CORSIM
models the movement of individual vehicles, including driver behavior and vehicle
characteristics. Time-varying traffic volume can be specified in CORSIM using user-
defined time periods. The simulation reports measures of effectiveness (MOEs) such as
average vehicle speed, vehicle stops, delays, vehicle-hours of travel, vehicle-miles of travel,
fuel consumption, and pollutant emission. Results are summarized for a transportation
network, sub-network, and links by time period.
The traffic environment in CORSIM is represented in the following ways:
Topology of the roadway system
Roadway geometry

Lane channelization
Motorist behavior
Traffic control
Traffic volumes entering the roadway system
Turn movements
Fleets characteristics
Figure 7 illustrates the basic process used to code a network using the CORSIM model.
Data Input Output Data
- Geometric data CORSIM - Network average
- Freeway volumes Model -Link summary
Turning movements -MOE
Figure 7: Basic CORSIM model process.
CORSIM simulates individual vehicle, and reports network or link statistics. Vehicle
trajectory data is developed, but is not available as standard output. One of the tasks in
simulating probe vehicles is collecting individual vehicle data from the model. Figure 8
shows a schematic of the node and link representation of the test network.


In the CORSIM simulation model, 8000s nodes are identified as external nodes, one and
two-digit numbers are the dummy nodes, and the three-digit numbers are the internal
nodes. For example, in the beginning of the westbound node is 8004, followed by a
dummy node of 4, and an internal node 331 at an off ramp intersection. T ink 8004 to 4
specifies the traffic volumes entering the network, link 4 to 331 defines the through
volume, and link 331-28 as the off ramp movement.
Probe Vehicle File Data
The simulation of probe vehicle in CORSIM is based on individual vehicle trajectory data
generated by the program In CORSIM, a unique identification number is assigned to each
vehicle in the simulation. Associated with each vehicle ID is its trajectory information.
Vehicles were randomly selected to represent a probe vehicle.
CORSIM program provides output in two formats. One format is an ASCII file that
includes summary tables of average measures for links and sub-networks. The other
output file that CORSIM generates is in binary format and includes the information
needed for CORSIM's animation tool.
Initially, a post-process was developed within the CORSIM source code sub-routines to
report individual vehicle trajectory data. CORSIM has a few hundred sub-routines for the
freeway simulation alone. The VTRAJ routine saves all the vehicle trajectory data in binary
form. In this effort, an additional vehicle trajectory data output file was generated to report
vehicle ID, location, speed, acceleration, upstream and downstream node. The additional
sub-routine added to CORSIM does the following :
1. At the entry node, identifies sets of 3 consecutive vehicles of a certain type, at user-
defined intervals

2. Stores the vehicle ID in a two-dimensional array
3. The selected vehicles are tracked throughout the network at user-defined interval
and the location and speed data is stored in a two-dimensional array
4. The array is used to report vehicle-specific data for selected vehicles only,
5. Stores the selected vehicle trajectory data in an external file
Three vehicles, instead of just one vehicle was selected to ensure that the same vehicle
could be tracked through the entire simulation period as a probe vehicle. Some vehicles
generated exit the network through off-ramps. The probe vehicle reporting interval and
headway can be user-defined in an external file. Figure 9 defines the relationship between
the original model input and the additional sub-routine in CORSIM source code.
Figure 9: CORSIM source code modification

With this modification, the network was tested to ensure that the vehicles tracked through
the modified routines were reporting correct values by comparing the probe vehicle output
generated by the new routine against the animation data in TRAFVU [Federal Highway
Administration, 1997].
Subsequently, new versions of CORSIM was released (without its source code) and to take
advantage of the improved model, an external program was written to read CORSIM's
binary file to extract the same probe data. This external program provided more flexibility
in gathering probe vehicle data from the model.
The binary file reader was programmed to output the probe vehicle data in the text format.
Each field of the output is comma separated, and therefore easily imported into any
standard spreadsheet software. Table 1 shows the individual vehicle data available from the
binary file. The trajectory data in Table 1 shows each vehicle with a unique identification
number (VehID) in the traffic stream (column 4). Therefore, any specific vehicle can be
tracked through the entire network. The time stamp in column 1 indicates the simulation
time. Vehicle Position (VehPos) refers to the vehicle location from the upstream node
(USN). A link is identified by the USN and the downstream node number (DSN). Other
vehicle data includes speed and vehicle type.

Time USN DSN VehID Fleet VehType VehPos Vel
6010 316 416 4015 0 2 27 89
6011 316 416 4015 0 2 116 89
6012 316 416 4187 1 3 59 83
6012 316 416 4230 0 2 105 89
6012 316 416 4015 0 2 206 89
6013 316 416 4204 0 2 20 84
6013 316 416 4234 0 2 39 102
6013 316 416 4187 1 3 143 84
6013 316 416 4230 0 2 195 89
6014 316 416 4204 0 2 104 84
6014 316 416 4234 0 2 142 103
6014 316 416 4187 1 3 227 84
6015 316 416 4207 0 2 65 75
6015 316 416 4204 0 2 188 84
6015 316 416 4234 0 2 246 102
6016 316 416 4207 0 2 138 67
6016 316 416 4204 0 2 265 62
6017 316 416 4203 0 2 87 96
6017 316 416 4207 0 2 207 70
Table 1: Individual vehicles trajectory data from GORSIM.
Using a spreadsheet, the individual vehicle output can be sorted to find any given VehID
and its path followed throughout the entire network. Based on simulation time-stamp in
link data and vehicle position from the upstream node, speed and travel time is calculated
to measure individual vehicle travel time on any particular link.
A separate report presents the details of the effort to calibrate CORSIM for the 1-70 test
network. Link travel speed estimated based on the GPS and CORSIM data was compared.
This figure shows the percent difference between GPS and CORSIM link speed for 27
links in the test network.

Figure 10: Difference between GPS and CORSIM link speed
The links showing higher than 10% percent difference were not included in the study.

This chapter presents the travel time function for several sections of the 1-70 corridor. The
estimations of average variance and covariance of probe vehicle travel time are under
congested and uncongested conditions. The standard error of average travel time is
estimated as a function of the number of probes.
Selection of Links
The following links were selected to develop average travel time estimates based on probe
Link 431-532: 7,292 ft link between US-40 and Georgetown, 0% grade
Link 534-552: A 1991 ft. link between US-40 and Georgetown, 0% grade.
Link 557-558: A 2735 ft. link between Bakersvile and Herman Gulch, 5% grade
Link 316-416: A 258 ft. link between the US-6 on-ramp and off-ramp, 3% grade.
Flow Rates
High, medium and low flow rates for the test section of the 1-70 network were modeled.
The following table summarizes the model flow rates on the various links as estimated
from the detectors simulated in each link.

Link Number Low Flow Rates Medium Flow Rates High Flow Rates
431 to 532 1450 2270 3650
534 to 552 1460 2280 3660
557 to 558 1700 2290 3900
316 to 416 1500 2100 3500
Table 2: Model detector output flow rates.
Based on detector data, the speed-flow plots for links 431-532, 534-552, 557-558 and 316-
416 are shown in figure 10, figure 11, figure 12 and figure 13. The speed-flow relationship
for link 431-532 and link 534-552 is a parabola. However, the plots for link 557-558 with a
5% grade and link 316-416, a weaving section between on and off-ramp (316-416), show
some difference. For example, for link 557-558, speed variation is quite high at medium
flow levels. The plots highlight the importance of analyzing variance of travel time under
uncongested and congested conditions separately.

Link 431-532
How (vph)
o Low A Med Higfi
Figure 11: Speed-flow plot for link 431-552, 0% grade
Figure 12: Speed-Flow plot for link 557-558, 5% grade

Figure 13: Speed-flow plot for Link 534-552, 0% grade
Link 316-416
O Low
A Med
Flow (vph)
Figure 14: Speed-flow plot for link 316-416 between US-6 on
and off-ramp

Link Travel Time-Flow Relationships
Link travel time plots were developed for the four links, based on flow measurements
from loop detectors, and link travel time estimated for all vehicles, for 5-min intervals. It
may be mendoned here that the link travel time provided by CORSIM is cumulative. Even
the intermediate output included in CORSIM is cumulative. Therefore, link travel time
reported by CORSIM could not be used. Based on the vehicle trajectory data extracted
from CORSIM's binary file, individual vehicle travel was time calculated to estimate
average link travel time for all vehicles in a 5-min period.
Figure 14 and figure 15 show that for low flow levels, the variation of link travel time is
minimal. However, the high flow level link travel time variation is considerably higher as
indicated by the spot mean speed plots.
Link 431-532
Volume (vph)
Measured by Detectors
O Flow: 1300-1650 vph A Flow: 2100-2400 vph Flow: 3670-3680 vph
Figure 15: Travel time plot for Link 431-532

Travel time of link 557-558
4) 70
E 60
F ci c
> o 40
u H 0) 30
2L C 20
_o__o n
o High
0 1000 2000 3000 4000 5000
Flow (vph)
Figure 16: Travel time plot for link 557-558 (5% grade)
Variance of Average Travel Time
Probe vehicle travel time was averaged over 5-min periods based on 1, 3, 5, 10 or 15
probes reporting. The variance of the average travel time was also estimated. Based on
equation of travel time variance, the average variance and average covariance were
estimated and the fit of the regression is presented in Table 3.
Average Average
Covariance Variance
R2 V t q-v t T1
Link 431-532 Low 0.92 0.93 0.53 21.46 5.85 22.40
High 0.89 644.46 2.34 1948.87 3.42 2593.33
Link 557-558 Low 0.35 31.35 1.99 41.32 1.27 72.67
High 0.63 124.38 6.01 95.54 2.22 219.92
Link 316-416 Low 0.82 0.06 1.38 0.34 3.74 0.40
High 0.19 1.05 7.13 0.25 0.83 1.30
Table 3: Average variance and average covariance estimates of probe travel
rime for four links under congested and uncongested conditions

For a typical Link 431-532, under uncongested conditions, the average covariance is not
significantly different from zero (t-value) and average variance is low. That is, for low flow
conditions, link travel times are uncorrelated as vehicle interaction is low. However, for
congested conditions, vehicle's follow each other closely and vehicle interaction is high -
therefore the average covariance is significantly higher. For link 557-558 with a 5% grade,
the average covariance and average variance is high under congested conditions. For link
316-416, a short weaving section, the average covariance and average covariance is not
significantly different.
These results clearly showed the need to evaluate the variance and covariance under
congested and uncongested conditions separately. It also showed that even for a large
number of probe vehicles in traffic, variance of average travel time is higher for high flow
conditions compared to low flow conditions. Depending on link characteristics, the
variance of average travel time could tend to zero, with increasing number of probes in the
traffic stream, e.g. low flow conditions. It may also be noted that the reduction in variance
of travel time decreases more sharply under high flow conditions compared to low flow
conditions. Therefore, higher gains may be obatined for increasing probe vehicles under
congested conditions compared to the same level of deployment under low flow
Standard Error of Average Travel Time
The standard error of average travel time for link 431-532, 557-558, and 316-416 is shown
in figure 16, figure 18, and figure 19, respectively. For the typical link 431-532, the rate at
which standard error reduces as number of probes deployed increases, is greater under
congested conditions compared to uncongested conditions. Therefore, average probe
travel time and a corresponding supply function or travel time function can provide a
better assessment of the accuracy of a travel time estimate (figure 17).

Link 431-532
Number of probes
Low Row High Row
Figure 17: Standard error of estimate of average travel time for
congested and uncongested conditions
Figure 18: Interaction of supply and demand to assess probe
estimate accuracy

For link 557-558, the reduction in standard error with increase in probes is not as sharp
under congested conditions. For link 316-416, a weaving, the reverse seems to be the case.
It is expected that under stop-and-go conditions, the average covariance will decrease and
may also show the need for fewer probe vehicles (similar to the low flow condition). As
CORSIM does not model stop-and-go conditions well, this could not be tested as part of
this study.
Link 557-558
Number of probes
o Low Flow High Flow
Figure 19: Standard error of travel rime estimate for link 557-
558 for congested and uncongested conditions

Link 316-416
H- C o .E a -
L. P 1 o V UJ £ q
55 > 0 2 < n .
10 20 30 40 Number of probes High Flow Low Flow
Figure 20: Standard error of travel time estimates using probe
data for uncongested and congested flow conditions

The objective of this study was to examine the relationship between number of probe
reports and the variance of link travel estimate under different flow conditions.
A literature review revealed that the major studies that addressed the use of probe vehicles
to estimate travel time included Srinivasan [Srinivasan et al, 1996], and the ADVANCE
project reports [Sen et al 1995; Soot et al, 1995; Tarko and Rouphail, 1996]. The Srinivas
study [Srinivasan et al, 1996] and one of the ADVANCE studies [Tarko and Rouphail,
1996] did not consider the temporal correlation of probe reports in analyzing the variance
of average travel time. A second ADVANCE study included the temporal correlation of
probe reports and reported that the variance of travel estimates does not decrease to zero,
even with a large number of probes per discrete time interval.
This study has shown that the variance of travel time estimates depends on the flow
condition. Under low flow conditions, the variance of average travel time could reduce to
zero. However under higher flow conditions, this is not the case, as also shown by the Sen
[Sen et al, 1995] study. This study has also shown that significantly better assessment of the
variance of travel time could be made if flow-specific average variance and covariance
estimates are developed. In addition, when probe reports for a link is received and used
with its corresponding travel time function, a proper assessment of its standard error in
estimating average link travel time can be made.
It may also be mentioned that CORSIM, though widely used in traffic modeling, does not
model stop-and-go conditions adequately. It was also observed that the simulation time or
warm-up period currently provided to reach network equilibrium condition is not adequate

to ensure steady state condition for large networks. Though vehicle trajectory data is
generated by CORSIM, this data is not readily available. In addition, the intermediate
network or link-based output statistics available over user-defined period reports are
limited to cumulative output only. Modifications to CORSIM that address these issues
would significantly enhance the model.
The findings of this study were based on simulated probe data. Future work that includes
field data from probe vehicles under highly congested conditions would be useful.

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