Computer-Aided Civil and Infrastructure Engineering17(2002)53–60
INDUSTRIAL APPLICATION
Probe Vehicle Population and Sample Size for
Arterial Speed Estimation
Ruey Long Cheu,*Chi Xie&Der-Horng Lee
Intelligent Transportation and Vehicle Systems Laboratory,Department of Civil Engineering,
National University of Singapore,Singapore117576,Singapore
Abstract:Equipping probe vehicles with global posi-tioning system(GPS)receivers is a cost-effective way of collecting real-time location and speed information.A large-scale,nationwide travel speed information acquisi-tion and dismination system has already been in opera-tion in Singapore,using a largefleet of taxis equipped with differential GPS(DGPS)receivers.This paper discuss the u of simulation approach to study the reliability of estimated average arterial link speed from probe vehicles. This study is bad on the road network at the Clementi town area in Singapore.Simulation
runs were made with a variety of traffic volumes,and with different percentages of probes in the total traffic volume.The reliability of link speed estimate is analyzed with respect to(1)overall probe vehicle percentages;and(2)number of probe vehicles sam-pled in a link.Results indicate that for an absolute error in estimated average link speed to be less than5km/hr at least95%of the time,the network needs to have4%to5% of active probe vehicles,or at least ten probe vehicles must pasd through a link within the sampling period.
1INTRODUCTION
With the progressive implementation of advanced traveler information systems(ATIS)and advanced traffic manage-ment systems(ATMS),it is increasingly important that accurate estimation of link(and hence route)travel times be provided to drivers,travelers,and traffic managers.In trip planning,route travel time is the primary concern in route choice,departure time,and other related decisions.How-ever,route travel time is origin–destination(O–D)specific. *To whom correspondence should be addresd.E-mail: cvecrl@nus.edu.sg.In view of the numerous O–D combinations demanded by urs,ATMS and ATIS rvice providers normally dis-minate traffic information at link or ction level.For example,in Singapore,the Land Transport Authority pro-vides travel times from major expressway entrances to major interchanges via variable message signs(VMS)in its Expressway Mo
nitoring and Advisory systems(EMAS). The travel times are calculated from individual link/ction speeds measured by loop detectors.In addition,all the four major taxi companies have had their vehicles equipped with DGPS receivers.Using more than10,000taxis from the largest company as probe vehicles(PVs),the Land Trans-port Authority(LTA)is acquiring real-time position and speed information from the vehicles over the nation’s road network of3000km.The measured average speeds at different links,translated into color codes,are available for the public free of charge at a website called TrafficScan (affiv.sg).
Several quantitative measures of link performance have been discusd by D’Este et al.(1999).To the traveling public,two indicators that are easily understood are aver-age link travel time and average link speed.Compared to travel time,link speed is independent of link length.It can be measured easily and objectively,for example,by loop detectors or probe vehicles.Link speed may be converted into link travel time,or qualitative measure of level of r-vice,like the color code commonly found in traffic condi-tion maps.
The work reported in this paper is an ongoing rearch project that aims to analyze the spatial and temporal char-acteristics of GPS-equipped PV data in arterial link speed estimation.Within this rearch,two issues related to link speed estimation using PVs need to be addresd.The are(1)th
e error magnitude of estimated average link speed under a variety of traffic conditions,and(2)the number of
©2002Computer-Aided Civil and Infrastructure Engineering.Published by Blackwell Publishers,350Main Street,Malden,MA02148,USA, and108Cowley Road,Oxford OX41JF,UK.
芍药功效54Ruey Long Cheu,Chi Xie &Der-Horng Lee
PVs in a link and over the entire network in a sampling period that would be required to give a reasonably accurate estimation of average link speed.This paper prents the finding of a simulation study that attempts to answer the above questions.
2REVIEW OF LINK SPEED MEASUREMENT TECHNIQUES
A number of traffic speed estimation models have been developed over the years (Zhang,1998).Several existing approaches are bad on data,such as volume and occu-pancy,collected by single-loop detectors.With double-loop t-up,it is possible to measure spot speed (time-mean speed)directly.Due to the disadvantage of only spot mea-surement,this approach has its inherent deficiency in com-prehensive reflection of speed over the entire link.This type of model is link and detector location specific,it requires careful calibration.
Several studies have demonstrated the u of GPS in travel time or speed survey (Zito et al.,1995;Quiroga and Bullock,1998b).Compare to stationary loop detectors,the estimation of link speed by PVs has the obvious advantage that traffic data are collected over the link,permitting the measurement of space-mean speed.However,only a small percentage of vehicles in the entire traffic stream (such as the taxi fleet in Singapore)is equipped with GPS receivers.Although the fraction of GPS-equipped vehicles is expected to increa with the gradual implementation of ATMS and ATIS rvices,the capacity and cost of wireless communi-cation links between the in-vehicle devices and traffic man-agement center will still limit the sample size of PV reports.With the limited number of PVs as a scenario,Srinivasan and Jovanis conducted a simulation study for a traffic net-work in Sacramento,California (1996).They found that for at least 80%of the links to have at least three PVs during a sampling period of 10min,at least 5%of the total vehicle population must be equipped with probe devices.
At link level,PV sample size can be estimated from sta-tistical sampling theory.For a ur-lected allowable error in estimated speed εa and sample standard deviation of speed s ,the minimum PV sample size is given by:
n ≥ t α/2,n −1s εa 2
(1)
where t α/2,n −1is the t-distribution statistic for 1−αcon-fidence interval with degree of freedom n −1.This equa-tion is termed standard deviation formulation by Quiroga and Bullock (1998a).A slightly different approach,but still bad on the standard deviation formulation,is to make u of the relative speed error εr (Chen and Chien,2000):
n ≥
t α/2,n −1s εr ¯
x 2
(2)Here,¯x is the average speed computed from n samples.
Note that (1)and (2)have no clod form solution,and an iterative procedure has to be applied.This is becau,in practice,s has to be computed from n samples.The above formulation is bad on the assumption that the speed of vehicles in a link follows a normal distribution.This may not be the ca when the traffic flow in an arterial is in mi-congested or congested conditions.However,the above equations are widely ud and are expected to give a reliable sample size estimate (Quiroga and Bu
llock,1998a).
3TESTBED SIMULATION
3.1The testbed network
The road network of the Clementi town area in Singapore (e Figure 1)has been chon as the simulation testbed for this study.The link speeds along two major arterials,namely Commonwealth Avenue West and Clementi Road,are of interest.The major arterials have three through-lanes in each direction.To better reprent the network traffic conditions due to a mass rapid transit station,a bus interchange,and a commercial town center surrounded by medium/high density residential areas,other condary arterials (most of them have two lanes in each directions)and the Ayer Rajar Expressway that runs parallel to Com-monwealth Avenue West are also included as parts of the testbed.
3.2Simulation tool
In this rearch,Version 2.0of INTEGRATION model (Van Aerde,1995)was employed to model traffic flow in the testbed and to generate PV data for analysis.INTEGRA-TION was lected mainly becau
(1)it is a microscopic model;and (2)it is capable of simulating PVs as part of the total O–D demand and recording individual PV’s speed at link level in an output file.
The network in Figure 1,which consists of 74nodes and 120links,was coded into the INTEGRATION input file.The baline traffic volume was the morning peak period from 8: 9:00A.M.in a typical weekday.The signal plans and interction turning volume were obtained from LTA.The traffic volume was further supplemented by field survey and then translated into an O–D matrix by the QueensOD software (Van Aerde,1998).
The INTEGRATION model was calibrated with field travel time data on four lected routes along the major cor-ridors of Commonwealth Avenue West and Clementi Road (Yuan,2001).Average vehicle travel times between nodes 1and 5,and 2and 10in both directions were obtained from licen plate surveys during the morning peaks.Average route travel times from the INTEGRATION model were calculated from PV data of approximately the same sample
Probe vehicle population and sample size for arterial speed estimation55
xx Link Fig.1.Node and link diagram of simulated testbed.
sizes as in the licen plate surveys.Four parameters—vehicle speed variability factor,free-flow speed,speed at capacity,and saturationflow rate—within the INTEGRA-TION model were adjusted s
o that the individual route’s average PV travel time matched cloly with that obtained from thefield survey.For the four routes,the standard deviations of the PV travel time andfield survey data also matched cloly.This also suggests that simulated PVs exhibited travel time variation similar to that of actual vehi-cles in the testbed.
3.3Probe vehicle modeling
In INTEGRATION modeling,the number of PVs for a par-ticular O–D pair was specified as a percentage of the total O–D volume(hereafter referred to simply as PV%).Once a PV is generated,the INTEGRATION program traces and records its movement from the origin to destination.Indi-vidual PV statistics,such as the travel time and average speed at each link,may be directed to an outputfile for analysis.
In INTEGRATION,the recorded PV travel time is the time between two interction stop lines.For a vehicle equipped with a GPS or differential GPS(DGPS)receiver, some assumptions have to be made.First,it was assumed that instantaneous speed measured by a kinematic GPS or DGPS receiver(using Doppler effect)is not desirable,as this spot speed measurement may not be reprentative of the link speed and will tend to overestimate the space-mean speed(May,1995).The
refore,average link speed has to be computed from location differencing ,divid-ing the distance between two points by travel time).It was further assumed that each active GPS(or DGPS)receiver continuously surveys its position(latitude and longitude)at 1c or2c intervals.The instantaneous position is then compared with an on-board digital roadmap databa.If the computed coordinate is near an interction,the vehicle’s position and time stamp are then recorded in the in-vehicle unit.Similar data are acquired for successive interctions, from which link speeds between interctions could be cal-culated and stored in the on-board memory and later trans-mitted to the traffic management center at the end of a sampling period.The GPS approach may be supplemented or replaced by a combination of(1)roadside positioning devices,such as beacons,at or near interction stop lines
56Ruey Long Cheu,Chi Xie&Der-Horng Lee
(e.g.,installed on top of traffic signal poles),and(2)in-vehicle units.When a PV cross a stop line,the in-vehicle unit receives a message from the associated beacon and registers the beacon’s identification and position,plus the in-vehicle unit’s clock time.Average link speed can then be calculated upon passing successive interctions.
3.4Simulation experiment
A total of216simulation runs were conducted in INTE-GRATION under a variety of traffic ttings.The varied conditions included the following:
1.Six different O–D ,at the bad O–D in
the morning peak period,and60%,70%,80%,90%, and110%of the bad O–D;
2.Six different percentages of PVs in the total O–D vol-探险故事
我想回到过去,PV%=3%,6%,9%,12%,15%,and18%;
and
3.Six different degrees of randomness in vehicle head-
way generation.For this,the fraction of random vehi-cle headway was t at0.5,0.6,0.7,0.8,0.9,and
1.0of the mean uniform headway.This is to inject
randomness into the vehicle arrival pattern so as to reduce the bias of using the default random number ed.
In each simulation,a warm-up period of500c was first carried out.This is followed by a data collection inter-val of700c.The700c interval was lected becau (1)it is within the practical range of pooling frequency for communication between the vehicles and the manage-ment center,and(2)it is a multiple of signal cycle time of 140c.The average traffic conditions and link level probe statistics outputfiles were post-procesd for analysis.The average traffic conditions outputfile provides the average link speed of all vehicles using a link during the700c sampling period.In our analysis,the statistics were ud as the accurate measurement from which error in PV sam-pling was calculated.
The travel speeds of interest were along the eight directional links along Commonwealth Avenue West and Clementi Road.The are links19,53,106,115,117,126, 107,and128.Their length ranges from141m to407m. Other links along the two arterials were not included becau their lengths were too short to render any estima-tion to be meaningful.
3.5Incorporating GPS positioning errors in link
speed calculation
Since the link speed and travel time extracted from the INTEGRATION model are believed to be mor
e preci than tho calculated from DGPS data obtained fromfield environment,artificial errors were introduced into the sim-ulated PV data during the post-processing stage.
Afield test was conducted on the university campus (located at the southern end of the Clementi Road,at node 10in Figure1)in January2000,when lective availabil-ity(SA)in the positioning data was still in existence.A GPS receiver,acting as a rover or mobile unit,was placed at a spot with partial blockage of satellite ,at ground level20m from a ven-story building).This is to simulate the effect of apartment buildings in the testbed and an elevated mass rapid transit track along Commonwealth Avenue West.The latitude and longitude readings were recorded at a30c interval continuously for3hr.Another GPS receiver,ud as the reference unit,was placed and simultaneously recorded positioning data at an established reference point(ba station)within the campus.The lat-itude and longitude readings of the reference unit were compared to the actual coordinates of the ba station, from which differential corrections of the two compo-nents were obtained and applied to the data collected by the rover unit at the same time.This process simulated the DGPS correction applied to positioning data with SA.The standard deviations of the latitude and longitude were found to be2.89m and4.84m,respectively.This error magni-tude is consistent with the DGPS error ranges reported by Quiroga and Bullock(1998b)and D’Este et al.(1999).The auto-correlation co
efficients for latitude and longitude were 0.69and0.82,respectively.Assuming the errors in lati-tude and longitude are independent,it can be shown that,a conrvative estimate of the standard deviation of distance traveled in a straight link with length ,error in loca-tion differencing)is
σL=
√
2σ
1−ρ(3) whereσis the greater value of the two standard deviations of latitude and longitude,andρis the smaller value of the auto-correlation coefficients in the latitude and longitude readings.The computedσL was3.79m,which was then rounded up to4.0m.
It can safely be assumed that in DGPS measurement,the impact of positioning error is much larger than the error in the receiver’s clock time.Therefore in the post-processing stage,the average speed with DGPS error,s pl,of a PV p in a link l was computed from
s pl=s pl+
L
矾石t pl
(4)
where t pl is the link travel time of probe vehicle p at link l,and L is the DGPS measurement error in distance trav-eled,and s pl is the average speed of PV p in link l.Both s pl and t pl are readily available in the INTEGRATION’s Link Level Probe Statistics outputfile. L was assumed to follow a normal distribution with meanµ=0and standard deviationσL=4.0m.
Probe vehicle population and sample size for arterial speed estimation57
With the removal of SA in the GPS positioning data by the U.S.Department of Defen in May2000,the position-ing accuracy for GPS without differential correction is in the same order of magnitude as that obtained from DGPS with SA.It has been mentioned that the taxis in Singa-pore are equipped with DGPS receivers.Our recentfield experiments similar to the above have shown thatσL is between0.5m to1.0m for DGPS readings without SA, and between4.0m and5.0m for GPS readings with SA. To provide an analysis for a conrvative scenario when differential correction signal is not available,the magnitude ofσL=4.0m has been injected to the probe vehicle data in speed calculation.This also provides an analysis for sys-tems with probe vehicles that u the relativ
ely low-cost GPS receivers(without differential correction).
4RESULTS
4.1Effect of probe vehicle percentages at
network level
Figure2plots the average speed of all PVs that had tra-verd a link within the sampling period(hereafter referred to as PV speed),versus the average speed of all vehicles using the same link(referred to as all-vehicle speed),at six different levels of PV%.It is obvious that the error in the average speed calculated from the PVs reduces with increasing number of PV%.This is reflected in the increa in R2value.The standard deviation of the error in aver-age link speed,as shown in Figure3,reduces with increa in PV%.But the reduction in standard deviation levels off at PV%of approximately15%.This suggests that,when the PV%in the network has reached15%,any further investment in DGPS receivers and communication infras-tructure would yield marginal improvement in the accuracy of link speed estimation.The above analysis may provide an insight for the policy makers and ATMS and ATIS sys-tem designers on the number of vehicles that is desirable in a network in order to achieve certain accuracy in link speed estimation.
It has been mentioned that the TrafficScan system in Singapore makes u of approximately10,000taxis with DGPS receivers as probes.This is only approximately 1.67%of the entire vehicle population.However,the usage of taxis is higher than that of an average pasnger car. In TrafficScan,probe reports from taxis on empty cruis-ing mode are not ud becau the taxis always travel at slower speeds when looking for pasngers.Even if the data from tho empty cruising taxis are not ud,the frac-tion of“active”taxis in the entire traffic stream is still much higher than1.67%.A manual survey at lected spots along Commonwealth Avenue West and Clementi Road within the testbed showed that the percentage of taxis in the traf-fic stream was approximately14%.After discounting tho empty cruising taxis,and taxis not associated with the Traf-ficScan system,the authors have estimated that the percent-age of active probe should be in the range of3%to6%. The PV%could even be higher during an off-peak traf-fic period when the overall traffic volume in the network is lower.Using the2-standard deviation curve in Figure3, it can be deduced that,at95%of the time,the estimated average link speed has an absolute error of not more than 6.06km/hr for3%of PV,and4.16km/hr for6%of active PVs in the testbed.If the absolute error is limited to less than or equal to5km/hr in at least95%of the estimated average link speed,by intrapolation,the network’s PV% should be in the range of4%to5%.From another point of view,if the PV population is between4%and5%,at most one out of20links has an absolute error in average spee
d of more than5km/hr.This is assuming that(1)the PV link speeds are calculated using the location differenc-ing approach as described in this paper;and(2)for afixed PV%,the error in estimated average speed follows a nor-mal distribution with mean0.
4.2Effect of probe vehicle sample size in a link
In day-to-day operation of an ATMS or ATIS system,a traffic engineer would be more concerned with the relia-bility of link speed estimation,as this could translate into error in travel time calculation.Of all the simulation runs, it is found that all the lected links have at least one PV during the sampling interval of700c.To provide an indi-cation of the reliability of link speed estimate at various PV sample sizes,the errors between the PV’s average link speed and that computed from all vehicles in a link are plotted against the PV sample size in Figure4.Thisfigure also shows the95%confidence envelopes,assuming that the error at a given sample size follows a normal distribu-tion with mean0.From the confidence envelopes,one can deduce that,if the absolute error in the estimated average link speed is to be less than5.0km/hr at least95%of the time,there should be at least10PVs within a sampling period.If such sample size is not achievable,one has to consider a longer sampling interval,or u a smaller con-fidence interval,or accept a larger absolute error.
4.3Comparison with statistical formulation
It has been mentioned that(1)and(2)give the minimum sample sizes for PV in link speed estimation.Comparisons have also been made between the estimates given by(1) and(2),and the results obtained from this simulation study. In this rearch,it has been found that,in general,the minimum sample sizes(n)given by the standard deviation formulation is link specific and is far lower than the sample size derived in Figure4,for an average link in a network. Becau of the large number of variables involved,an anal-
58Ruey Long Cheu,Chi Xie &Der-Horng Lee
3% of total O-D volume as probe vehicles (a) 6% of total O-D volume as probe vehicles (b)
9% of total O-D volume as probe vehicles (c)
12% of total O-D volume as probe vehicles (d)
15% of total O-D volume as probe vehicles (e) 18% of total O-D volume as probe vehicles (f)
0.010.020.030.040.050.060.00.0
10.0
20.030.040.050.060.0
All-Vehicle Speed (km/hr)
All-Vehicle Speed (km/hr)
P r o b e V e h i c l e S p e e d (k m /h r )
P r o b e V e h i c l e S p e e d (k m /h r
)
0.0
10.0
20.030.040.050.0孔子学堂
60.0
0.0
10.0
20.030.040.0
50.0
60.0
All-Vehicle Speed (km/hr)
P r o b e V e h i c l e S p e e d (k m /h r
)0.010.020.030.040.050.060.00.0
10.0
两弹一星作文20.030.040.050.0朱泰祺
60.0
如何泡脚最养生All-Vehicle Speed (km/hr)
P r o b e V e h i c l e S p e e d (k m /h r
)
0.0
10.0
20.030.040.050.0
60.0
All-Vehicle Speed (km/hr)
P r o b e V e h i c l e S p e e d (k m /h r
)0.010.020.030.040.050.060.00.0
10.0
20.030.040.050.0
60.0
All-Vehicle Speed (km/hr)
P r o b e V e h i c l e S p e e d (k m /h r )
Fig.2.Comparison between all-vehicle speed and speed from probe vehicles.
