California Partners for Advanced Transportation Technology UC Berkeley

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1 Calforna Partners for Advanced Transportaton Technology UC Berkeley Ttle: Estmaton of Truck Traffc Volume from Sngle Loop Detectors Usng Lane-to-Lane Speed Correlaton Author: Kwon Jamyoung Varaya Pravn Skabardons Alexander Publcaton Date: Seres: Workng Papers Permalnk: Abstract: An algorthm for real tme estmaton of truck traffc n mult-lane freeway s proposed. The algorthm uses data from sngle loop detectors-the most wdely nstalled survellance technology for urban freeways n the US. The algorthm works for those freeway locatons that have a truck-free lane and exhbt hgh lane-to-lane speed correlaton. These condtons are met by most urban freeway locatons. The algorthm produces real tme estmates of the truck traffc volumes at the locaton. It can also be used to produce alternatve estmate of the mean effectve vehcle length whch can mprove speed estmates from sngle loop detector data. The algorthm s tested wth real freeway data and produces estmates of truck traffc volumes wth only 5.7% error. It also captures the daly patterns of truck traffc and mean effectve vehcle length. Appled to loop data on I-710 near Long Beach durng the dockworkers lockout October the algorthm fnds a 32 % reducton n 5-axle truck volume. Copyrght Informaton: All rghts reserved unless otherwse ndcated. Contact the author or orgnal publsher for any necessary permssons. escholarshp s not the copyrght owner for deposted works. Learn more at escholarshp provdes open access scholarly publshng servces to the Unversty of Calforna and delvers a dynamc research platform to scholars worldwde.

2 CALIFORNIA PATH PROGRAM INSTITUTE OF TRANSPORTATION STUDIES UNIVERSITY OF CALIFORNIA BERKELEY Estmaton of Truck Traffc Volume from Sngle Loop Detectors Usng Lane-to-Lane Speed Correlaton Jamyoung Kwon Pravn Varaya Alexander Skabardons Unversty of Calforna Berkeley Calforna PATH Workng Paper UCB-ITS-PWP Ths work was performed as part of the Calforna PATH Program of the Unversty of Calforna n cooperaton wth the State of Calforna Busness Transportaton and Housng Agency Department of Transportaton; and the Unted States Department Transportaton Federal Hghway Admnstraton. The contents of ths report reflect the vews of the authors who are responsble for the facts and the accuracy of the data presented heren. The contents do not necessarly reflect the offcal vews or polces of the State of Calforna. Ths report does not consttute a standard specfcaton or regulaton. Report for Task Order 4301 July 2003 ISSN CALIFORNIA PARTNERS FOR ADVANCED TRANSIT AND HIGHWAYS

3 Estmaton of Truck Traffc Volume from Sngle Loop Detectors Usng Lane-to-Lane Speed Correlaton Jamyoung Kwon Pravn Varaya Alexander Skabardons

4 ACKNOWLEDGEMENTS Ths study s part of the PeMS proect whch s supported by grants from Caltrans to the Calforna PATH Program. We are very grateful to Caltrans Traffc Operatons engneers for ther support. The authors thank Ben Cofman Oho State Unversty for the BHL data and helpful dscussons and Joe Avs of Calforna Department of Transportaton for the AVC data from Los Angeles County and other helpful materal. The contents of ths report reflect the vews of the authors who are responsble for the facts and the accuracy of the data presented heren. The contents do not necessarly reflect the offcal vews of or polcy of the Calforna Department of Transportaton. Ths report does not consttute a standard specfcaton or regulaton.

5 Estmaton of Truck Traffc Volume from Sngle Loop Detectors Usng Usng Lane-to-Lane Speed Correlaton Jamyoung Kwon Pravn Varaya Alexander Skabardons Aprl 2003 ABSTRACT An algorthm for real tme estmaton of truck traffc n mult-lane freeway s proposed. The algorthm uses data from sngle loop detectors the most wdely nstalled survellance technology for urban freeways n the US. The algorthm works for those freeway locatons that have a truck-free lane and exhbt hgh lane-to-lane speed correlaton. These condtons are met by most urban freeway locatons. The algorthm produces real tme estmates of the truck traffc volumes at the locaton. It can also be used to produce alternatve estmate of the mean effectve vehcle length whch can mprove speed estmates from sngle loop detector data. The algorthm s tested wth real freeway data and produces estmates of truck traffc volumes wth only 5.7% error. It also captures the daly patterns of truck traffc and mean effectve vehcle length. Appled to loop data on I-710 near Long Beach durng the dockworkers lockout October the algorthm fnds a 32 % reducton n 5-axle truck volume. Keywords: freeways; automatc vehcle classfcaton; vehcle detectors; truckng; traffc survellance

6 Obectves and Methodology EXECUTIVE SUMMARY Accurate knowledge of the volume and pattern of truck traffc s crtcal for varous hghwayrelated plannng desgn and polcy analyses. Typcally such data are collected ether by Automatc Vehcle Classfers AVCs based on Wegh-In-Moton WIM technologes or by manual countng. AVCs produce onlne counts of traffc of dfferent vehcle types but they are costly to nstall and suffer varous lmtatons. When manual countng s used truck traffc s recorded for a short samplng perod and the counts are extrapolated to get an estmate for a whole year. Ths estmate can have a large margn of error even after adustng for seasonal and day-of-week trends. Improvng accuracy by ncreasng the frequency and length of manual counts s costly. Double loop detectors may also serve as a crude automatc vehcle classfer by usng the vehcle lengths as a surrogate for vehcle type. However the deployment of double loop detectors s lmted and addtonal hardware and software needs to be nstalled to extract vehcle length nformaton from double loops. We propose a novel algorthm for the real-tme estmaton of truck traffc volume on freeways from sngle loop detector data. In contrast to other technologes sngle loop detectors are much more wdely deployed. The algorthm makes use of the essental relatonshp between speed flow occupancy and effectve vehcle length accordng to whch vehcle length can be estmated f average speed s known. It also reles on the phenomenon that the average speed of a truck-rch lane s actually qute close to that of truck-free nner lanes that s there s a hgh lane-to-lane speed correlaton. Usng these two characterstcs of traffc flow we estmate the proporton of trucks wthn a sample gven representatve lengths of trucks and passenger cars. The algorthm s extremely easy to mplement requrng tunng of only a few generc parameters. Fndngs The algorthm s tested wth three real-world freeway datasets. The frst dataset s from double loop detector data from Berkeley Hghway Laboratory BHL on I-80 n Berkeley Calforna where speed measurements and the effectve lengths of ndvdual vehcles are avalable. The proposed algorthm produces estmates of truck traffc volumes wth only 5.7% error. Next the algorthm estmates were compared aganst WIM hourly vehcle classfcaton data from a ste on I-91 n Los Angeles Calforna. The algorthm was appled to the 5-mnute sngle loop flow and occupancy data collected from the freeway performance measurement PeMS database at the loop staton closest to the WIM staton. The algorthm captured well the daly patterns of truck traffc and mean effectve vehcle length. Fnally we used PeMS data from a locaton on I-710 near Long Beach to estmate the mpact on truck volumes durng the dockworkers lockout at the port of Long Beach durng the perod of October The algorthm found a 32 % reducton n 5-axle truck volume durng the lockout perod. The results from the applcaton of the algorthm demonstrate that the algorthm captures the qualtatve and quanttatve characterstcs of daly truck traffc satsfactorly wth acceptable bas. The mplementaton of the algorthm on the wdely avalable sngle loop detector nfrastructure wll produce onlne estmates of total truck volume as well as seasonal and daly truck patterns. Ths nformaton can facltate better freeway desgn and management. v

7 TABLE OF CONTENTS Acknowledgements... Abstract... Executve Summary...v Table of Contents...v Lst of fgures...v Lst of Tables...v 1. INTRODUCTION...1 Data PROPOSED METHOD...2 Dstrbuton of Effectve Vehcle Length...3 Two Key Assumptons and the Algorthm...4 Implcatons for G-factor estmaton...6 External Source of Speed ANALYSIS...6 Results...7 G-factor Estmaton...7 Comparson wth WIM Data Dscusson...8 Settng Parameters for Implementaton...9 Presence of Long Vehcles n Truck-Free Lanes...9 Bas at the Onset of Low-Speed...9 G-factor Estmaton CONCLUSION...10 References...11 v

8 LIST OF FIGURES FIGURE 1. Dstrbuton of Effectve Vehcle Length BHL Data...14 FIGURE 2 Tme-seres plots of 5-mnute aggregated double-loop speeds measured n four lanes at a locaton n BHL study. Each plot corresponds to a sngle day. Here and below when tme scale s 5 mnute tme s n 5-mnute ncrements from 0 to 288 startng wth 0 at mdnght...15 FIGURE 3 Lane-to-Lane Speed Correlaton. Each scatterplot depcts 5-mnute aggregated speeds mph; 1 mph = 1.61 km/h measured n lane a and b at a locaton n BHL study over 10 days total of 2880 samples. In each plot the thck lne s the least squares regresson lne wthout the ntercept fttng lane b speed on lane a speed and the thn lne s the reference lne y=x. Three numbers are the slope of the regresson lne R-squared values and correlaton coeffcent from top to bottom FIGURE 4 Observed and estmated daly pattern of lane-by-lane truck volume aggregated over 20 days. Here and below when tme scale s one hour tme s n one-hour ncrements from 1 to 24 startng wth 1 at mdnght FIGURE 5 Observed and estmated daly pattern of lane-total truck count top; lane-by-lane daly pattern of speed averaged over 10 days mddle; daly pattern of estmaton error of lane-total truck count bottom FIGURE 6 True and estmated daly trend of 5-mnute mean effectve vehcle length estmate averaged over 10 days FIGURE 7 Total vehcle volume estmated from WIM data top left and sngle loop data top rght; hourly volume of long truck traffc estmated from WIM data bottom left and sngle loop data usng the proposed algorthm bottom rght...20 FIGURE 8 Comparson of daly total traffc volume of all cars left trucks mddle and passenger cars rght durng port lockout and non-lockout perods FIGURE 9 Day-to-day trend of daly total truck traffc volume by lane top and lane-total bottom. The lockout perod s days LIST OF TABLES TABLE 1 Performance of the Algorthm for Data from BHL Study...12 TABLE 2 Comparson of Daly Traffc Volume durng Lockout and Non-Lockout Weekdays I-710 Port of Long Beach...13 v

9 1. INTRODUCTION Accurate knowledge of freght or heavy truck traffc s crtcal for varous hghway-related plannng desgn and polcy analyses. It s necessary to have estmates of such quanttes as truck Annual Average Daly Traffc AADT for dfferent sectons of a freeway 12. Typcally such data are collected ether by an Automatc Vehcle Classfer AVC or by manual countng. An AVC s usually based on technologes such as Wegh-In-Moton WIM consstng of nductve loops and a bendng plate or Pezo sensors or more sophstcated technologes such as vdeo magng laser and nght vson systems or acoustc sgnal analyss. These systems produce onlne counts of traffc of dfferent vehcle types. But they are costly to nstall and suffer varous lmtatons 3. When manual countng s used a person records the truck traffc dstrbuton for a short samplng perod usually a day or two and the counts are extrapolated to get an estmate for a whole year. Ths estmate can have a large margn of error even after adustng for seasonal and day-of-week trends Improvng accuracy by ncreasng the frequency and length of manual counts s costly. Double loop detectors can serve as a crude automatc vehcle classfer by usng the vehcle lengths as a surrogate for vehcle type. It s reasonable n many cases to assume that vehcles longer than say 50 ft m are heavy trucks. But deployment of double loop detectors s lmted. Moreover separate software or hardware needs to be nstalled to extract vehcle length nformaton from double loops. In ths report we propose an algorthm for the real-tme estmaton of truck traffc volume from sngle loop detectors. In contrast to other technologes sngle loop detectors are much more wdely deployed. In prncple they are unable to record vehcle lengths as double loop detectors can and only report flow traffc volume and occupancy. The algorthm makes use of the essental relatonshp between speed flow occupancy and effectve vehcle length accordng to whch vehcle length can be estmated f average speed s known. It also reles on the phenomenon that the average speed of a truck-rch lane s actually qute close to that of truckfree nner lanes that s there s a hgh lane-to-lane correlaton of speed. Usng these two characterstcs of traffc flow we estmate the proporton of trucks wthn a sample gven representatve lengths of trucks and passenger vehcles. Ths dea s elaborated n secton 2. Secton 2 also dscusses the relevance of the algorthm for estmatng the mean effectve vehcle length MEVL whose nverse s called G-factor. The G-factor s a crucal parameter n speed estmaton from sngle loop flow and occupancy data. It s shown that the algorthm produces as a byproduct an onlne estmate of the G-factor or the daly profle of the G-factor. The G-factor estmates can mprove speed estmates based on sngle-loop data. The algorthm s tested wth two data sets and the results are presented n secton 3. In secton 4 the algorthm s appled to data on I-710 near Long Beach CA durng the dockworkers lockout n October of Secton 5 dscusses the study methodology. Secton 6 summarzes the fndngs.

10 Data For the analyss as well as for an explanaton of concepts we use data from the Berkeley Hghway Laboratory BHL. 7. We study eastbound traffc at detector staton 6 near the Ashby Avenue ext. The data are collected for ten Mondays between March and May at eght double loop detector statons located on I-80 n Berkeley Calforna. The double loop speed measurements and the effectve vehcle lengths of ndvdual vehcles are avalable. Thus these measurements serve as ground truth. The algorthm of course only makes use of data from one of the double loops. Another test data set conssts of WIM hourly vehcle classfcaton data from eastbound I-91 at postmle 7.5 =12.1 km east of Avalon Boulevard n Los Angeles for the perod of May excludng May and 14 a total of 11 days. The 5-mnute sngle loop measurements of flow and occupancy from detector staton VDS closest to the WIM staton for the same tme perod were extracted from the freeway performance measurement PeMS database 8. We use the PeMS loop detector data to estmate the truck volumes and compare the estmates wth the WIM data. Fnally we use PeMS data from a locaton on I-710 freeway near the port of Long Beach from August to October to estmate the mpact on truck volumes durng the dockworkers lockout durng the perod of October PROPOSED METHOD Conventonal sngle loop detectors measure flow the number of vehcles that pass the detector durng a fxed sample perod and occupancy the percentage of the gven sample perod that the detector s occuped by vehcles. For each lane the flow q and occupancy O are defned as n q = 1 T tk k K O =. 2 T Here ndexes lane and ndexes the sample tme perod and n = number of vehcles that pass over the detector n lane durng tme perod T = samplng perod K = set of all vehcles that pass over the detector n lane durng tme perod and t k = vehcle k's on-tme.e. the tme nterval durng whch ths vehcle occupes the detector. The on-tme speed and length of a partcular vehcle are related by L = v t 3 k k k 2

11 3 where: k L = effectve length of vehcle k as seen by the detector k v = speed of vehcle k The sample mean speed at s defned to be n v v K k k =. 4 From equatons 1 and 2 = = 1 1 K k k k K k k k v L n q v L T O. 5 Assumng that ndvdual vehcle speeds are nearly constant durng each sample tme perod ths yelds v L q O 6 or O L q v 7 n whch = 1 K k L k n L s the mean effectve vehcle length MEVL. Equaton 7 has been used to estmate speeds from sngle loop detector flow and occupancy measurements. However ths requres knowledge of MEVL or G-factor. On the other hand f one knows the speed one can estmate MEVL by re-wrtng 7 as q O v L. 8 Observe that ths value s large f there are many long vehcles LVs and small f the traffc conssts mostly of passenger cars PCs. Dstrbuton of Effectve Vehcle Length Fgure 1 shows the dstrbuton of the effectve vehcle lengths EVLs observed for vehcles detected durng the 24-hour perod of March from BHL data. Only data from the loop detector nstalled n the fourth or outermost lane whch has sgnfcant truck traffc s used for the plot. The hstogram of the effectve vehcle length top of Fgure 1 s decomposed nto two separate hstograms correspondng to vehcles longer than 40 ft m mddle and shorter than 40 ft bottom.

12 The hghest peak s at 17 ft 5.18 m; there s another peak at 61 ft 18.6 m. It s lkely that the former corresponds to the typcal length of PC and the latter to that of LV. For our study we wll use nomnal representatve lengths 18.6 ft 5.67 m and 61.2 ft m as the typcal length of the two vehcle classes. These are the group means of those vehcles whose EVLs are smaller and larger than the threshold 40 ft m respectvely. A bmodal dstrbuton lke n Fgure 1 occurs when the vehcles mostly belong to two classes of vehcles wth apprecably dfferent lengths whch seems to be the case n these data. Several researchers 9 have notced ths bmodal characterstc of EVL dstrbuton n truck-rch traffc. In an deal settng when there are only two types of vehcles LV and PC each havng fxed lengths l t and l c we have the relatonshp: L = p l 1 p 9 t l c n whch p s the proporton of truck traffc n the sample. One can rewrte 9 as p L l l l c =. 10 t c Truck and passenger vehcle counts can then be calculated from n t = p n and n = 1 p n = n n. 11 c t Two Key Assumptons and the Algorthm As we have ust seen knowledge of the mean speed allows one to calculate the proporton of trucks and ther volume durng a tme perod. In ths regard several researchers [10] have observed that on mult-lane freeways vehcle speed over dfferent lanes tend to be synchronzed or v v '. 12 We call ths phenomenon a strong lane-to-lane correlaton of speed n mult-lane freeways. Also for most mult-lane freeways n the US heavy trucks are not allowed or dscouraged from drvng n nner lanes. Ths leads to the hypothess p 0 or L lc 13 n whch corresponds to nner or faster lanes say the frst or second lane from the medan. Suppose lane s almost truck-free and ' s truck-rch and the two lanes have hgh lane-to-lane speed correlaton. Then 4

13 q lc q L v O O 14 q ' L ' q ' p ' lt 1 p ' lc v ' θ ' O ' usng the speed equaton correlaton and truck-free lanes equatons 7 12 and 13 each. One can solve 14 for p ' drectly or solve t n two steps as follows: frst estmate the mean vehcle length by q O L ˆ / ' = l c q ' / O ' 15 and then the truck proporton by Lˆ ' lc pˆ ' =. 16 l l t c If the proporton estmate has a value outsde [01] due to detector nose the estmate must be approprately truncated. The truck count for sample s then estmated by nˆ t = pˆ n. The hgh lane-to-lane correlaton of speed s clearly observable n the data shown n Fgure 2 and 3 whch show the ont behavor of ndvdual lane speeds measured from BHL study. R- squared values and correlaton coeffcents are larger than 0.99 and 0.9 for all pars. Though the relatonshp v' v holds for all lane pars the speed s typcally slghtly lower n the outer lanes. Flow and occupancy are also moderately correlated over dfferent lanes but ther relatonshp tends to be noser and more nonlnear. As s llustrated by Fgure 3 the outer lanes exhbt slower speeds. The slopes of the leastsquares regresson lnes are and 0.89 for regressng lanes 3 4 and 5 on the fastest lane 2. Lane 1 s the HOV lane excluded from the analyss. Thus about 5% decrease of speed s observed as one drves on a lane further from the medan. Ths suggests the followng modfcaton of 12: v ' β ' v 17 n whch β ' s the estmated proporton of speeds n lane ' and. Usng a smpler dentty lke 12 when n fact β ' 1 leads to bas. But despte the bas the resultng estmate wll capture the seasonal or daly truck traffc pattern. In practce a generc constant may be used for β lke 5% slower traffc n outer lane although estmates tuned for an ndvdual detector staton usng another source of data may be benefcal. 5

14 Implcatons for G-factor estmaton The G-factor s a crtcal parameter for estmaton of the mean speed usng relaton 7. It s well known that a constant G-factor for speed estmaton from sngle loop data s a bad practce. Even though there have been some efforts to do so the real-tme estmaton of G-factor s a dffcult problem except durng free flow perods. Thus the hstorcal profle of G-factor s of great value for better speed estmaton. Our algorthm can be vewed as an alternatve procedure to estmate the G-factor. It produces 15 as a byproduct an estmate of the mean effectve vehcle length. For those freeways where our algorthm can be appled t can thus produce G-factor estmate ether onlne or to obtan the hstorcal pattern. External Source of Speed A speed estmate from a separate source may be avalable n some cases. In such cases nstead of usng the lane-to-lane speed correlaton one can drectly estmate the EVL by ~ v ' O ' L ' = 18 q ' nstead of 15 and then proceed as above to estmate the proporton and volume of trucks. Vdeo mages could provde such data. It s relatvely easy to extract the average speed of a group of vehcles from vdeo data 13. We wll dstngush between the orgnal algorthm that doesn t requre speed and the one that uses the speed from an extra source by the names sngle loop algorthm and exogenous speed algorthm. 3. ANALYSIS We frst examne detector data from the BHL study collected over ten Mondays between March and May The samplng rate of the loop detector s 60 Hz but we only use 5- mnute aggregated data to run the algorthm. Because we have the effectve vehcle length derved from double loop speed traps we know the actual truck volumes and we use these to assess the performance of the algorthm. The algorthm s appled usng the default parameters l c =18.6 ft 5.67 m and l t =61.2 ft m as the mean effectve vehcle lengths for the two classes and the regresson coeffcents and 0.85 for the speed correcton factors n 17. Lane 2 s assumed to be truck-free whch seems vald snce only 1% of the vehcles n that lane were longer than 40 ft m. Lane 1 s the HOV lane. We also calculate the alternatve estmate of truck volume usng the exogenous speed algorthm usng the double loop speed estmate as an extra source. Next we use PeMS loop data and the WIM data for the I-91 locaton over an 11-day perod. The algorthm s appled wth the parameters l c =12 ft 3.66 m and l t =55 ft 16.8 m whch were 6

15 determned from an algorthm outlned n 14. A set of generc coeffcents and 0.85 are used for the speed correcton factors. Lane 1 s assumed to be truck-free. Results The performance of the algorthms on the BHL data set s summarzed n Table 1 whch shows lane-by-lane and all-lane truck AADT the estmates from both sngle loop and exogenous speed algorthms and the error rate. All quanttes are averages over 10 days. The total percentage error n estmatng lane-total truck AADT s -5.7% and -3.3% usng the sngle loop and exogenous speed algorthms respectvely. Recall that speed s not needed for the sngle loop algorthm. The lane-by-lane breakdown of the statstcs shows that the sngle loop algorthm nherently estmates the truck traffc n lane 2 the reference lane as zero. The exogenous speed algorthm doesn t suffer from ths nherent lmtaton although the percentage error for the same lane s large 53%. Both algorthms underestmate truck counts for lane 3 and 5 and overestmate t for lane 4. The observed and estmated daly patterns of truck traffc for lane 3 4 and 5 are shown n Fgure 4. Qualtatvely both algorthms capture well the famlar daly pattern of truck traffc although the exogenous speed algorthm matches the daly trend better. The sngle loop algorthm s based n the afternoon commute hours. Fgure 5 shows that the bas s related to the varablty n speed. The sngle loop algorthm bas s most serous at the start of the congeston perod. We also compare our results wth the truck AADT reported n 2. We chose the locaton Route 80 postmle =7.37 kmat Berkeley ntersectng Route 13 Page 134 of the report whch s closest to our locaton. One half of the two-way total AADT s whch s larger than the current AADT by 23% and the source of the error s not clear. But the percentage of trucks wth more than 5 axles AADT n the total AADT s 4.8% accordng to the report agreeng closely wth the truck volume percentage of the BHL data. G-factor Estmaton Fgure 6 shows the results when the algorthm s used to estmate the G-factor. The true G-factor s calculated usng 8 assumng equalty n that relatonshp. As expected the true G-factor s close to constant for Lane 2 and vares sgnfcantly for lanes 3 4 and 5. The estmated G-factor follows the true G-factor surprsngly well. Comparson wth WIM Data The performance of the algorthm on the second data set s shown n Fgure 7. WIM data and sngle loop data produce smlar total traffc volume profle over days. The three days that do not show mornng and afternoon peaks are weekends. The hourly truck volume estmated from the sngle loop data usng the current algorthm also corresponds to that from WIM data. Even though there are some quanttatve dfferences our algorthm s overestmatng truck traffc by about 20% the two daly truck volume profles match each other qualtatvely. In partcular the trend of low truck volume over weekends s clearly vsble from both WIM data and the estmates by the algorthm. 7

16 4. APPLICATION: THE DOCWORKERS LOCKOUT OCTOBER 2002 At mdnght on Saturday September West Coast port operators shut down cargo termnals from Seattle to Los Angeles n effect lockng out unonzed longshore workers. On October 9 Presdent Bush nvoked the Taft-Hartley Act orderng the ports to reopen and the workers to return to ther obs. We analyzed sngle loop data at a locaton VDS that s lkely to have been affected by the lockout. Ths s a fve-lane secton near the port of Long Beach at postmle 7.3 =11.7 kmon I-710. Fve-mnute averages of flow and occupancy data between August 16 and October were retreved from the PeMS database. We use our sngle loop algorthm to estmate and compare the 5-axle truck volumes durng the non-lockout and lockout perods. The MEVL n the dfferent lanes s estmated usng 15. The ratos β ' of speeds are calculated from the ratos of representatve free flow speeds n the dfferent lanes obtaned from the Bay Area data. The medan values of free flow speeds ranged from 76 mph for lane 1 medan to 59 mph for lane 5 outer or shoulder lane. Lane 1 s assumed to be free of trucks. The unknown vehcle length L 1 of passenger cars n lane 1 s estmated usng the followng approach. We assume 1 lane 1 has a fxed MEVL L1 L1 correspondng to the representatve effectve vehcle length of passenger cars; and 2 the medan of lane 1 speed s same as the representatve medan free flow speed from the Bay Area. Then we have medan D4 q v1. medan D4 v medan D4 L1 O = =. 19 We solve ths equaton to get an estmate for L 1. It s found to be 16.6 ft 5.06 m from the data. We use ths as the representatve passenger car length for all lanes. We use 60 ft 18.3 m for the representatve truck length. Table 2 compares the truck volumes over non-lockout and lockout weekdays. The estmates suggest a 32% reducton n daly truck volume and only a 0.8% reducton n passenger car volume and an overall reducton n vehcle count of 3.4%. A statstcally rcher comparson s offered n the box plots of Fgure 8. Each plot gves fve numbers: the lowest and hghest lnes are drawn at the hghest and lowest daly estmates; the three lnes that form the box are drawn at 25% 50% and 75% of the daly estmates. Fgure 9 shows the daly truck volume over the study perod. The fgure shows both the weekly cycle the drop durng the lockout perod and the partal recovery followng the lockout. 5. DISCUSSION We dscuss some ssues concernng mplementaton of the algorthms and areas for future research. 8

17 Settng Parameters for Implementaton For practcal mplementaton of the algorthm a few key parameters need to be set. They are 1 the representatve vehcle lengths for the two vehcle classes and 2 rato of the speed between lanes. The parameter 1 would seem to be ndependent of locaton. In general dfferent locatons would have the same representatve lengths for long trucks as well as passenger cars unless very long trucks are used extensvely n a certan regon. A more subtle ssue s the presence of relatvely short less than 5 axles trucks whose volume typcally accounts for ffty to nnety percent of total truck volume 2. In many applcatons these short trucks are less sgnfcant than long trucks and our algorthm ams to capture only long vehcle volumes. However a sgnfcant volume of short trucks may lead to bas n the estmate of the long truck volume. How serous ths s a problem seems to depend on the specfc applcaton but further analyss of ths ssue s warranted. Another concern related to parameter 1 s the vehcle detector bas. Even though true vehcle speeds stay constant over dfferent locatons ndvdual detectors tend to see them dfferently often by as much as a few feet. Varous approaches are possble to estmate the detector bas; one approach that uses only 30-second sngle loop detector data s proposed n 14 and s employed n the current study. The parameter 2 s more lkely to vary wth locaton than parameter 1. Would usng a common set of speed rato factors for dfferent freeway locatons reasonable? Even the lnearty assumpton may not be reasonable for certan locatons. We may propose rules-of-thumb lke 5% speed decrease for outer lane and use locaton that are not close to on- and off-ramps. But the ssue s a challengng and nterestng topc for transportaton researchers and engneers. Presence of Long Vehcles n Truck-Free Lanes Presence of long vehcles n supposedly truck-free lanes can affect the accuracy of the proposed algorthm. It wll ncrease the occupancy n that lane and thus lead to a smaller estmate of mean effectve vehcle length n outer lanes and underestmaton of the proporton of long vehcles n the outer lanes see equaton 15. The degree of underestmaton wll depend on the abundance of long vehcles n the reference lane whch n turn should depend on the road geometry lke number of lanes among others. It would be useful to study the proporton of long vehcles n truck-free lanes for varous locatons under dfferent condtons. For the BHL data only less than 1% of the vehcles n lane 2 were longer than 40 ft so the bas s neglgble. Bas at the Onset of Low-Speed It was observed that the estmate of truck volume s based and unstable at the start of the congeston perod. Durng ths perod the occupancy and speed are unstable and the sgnal-tonose rato of the both parameters decreases. A quck soluton to ths may be puttng less confdence for the truck volume estmate when the perod shows sudden change of occupancy. But correctng ths bas seems a challengng problem whch requres careful study of traffc dynamcs. 9

18 G-factor Estmaton It s encouragng that the G-factor estmated by the current algorthm s surprsngly close to the real hstorcal G-factor. The estmated G-factor can be an nput for varous subsequent algorthms for speed calculaton ncludng 12. Usng the current algorthm for onlne G-factor estmates s nothng more than usng the speed of the reference lane multpled by a constant factor as the estmate for the speed at another lane. Ths may not be a good dea n general but t s an nterestng queston f usng a nosy onlne estmate of G-factor gves better speed estmate. 6. CONCLUSIONS We proposed an onlne algorthm for estmatng truck traffc volume. The algorthm s applcable to mult-lane freeways wth one truck-free lane and hgh lane-to-lane speed correlaton. Both condtons seem to be satsfed at most maor urban freeway locatons not close to on- and offramps. Ths makes the algorthm wdely applcable. The algorthm s extremely easy to mplement requrng tunng of only a few generc parameters. It can be also used for G-factor calculaton. In the emprcal study at two urban freeway locatons wth moderate long truck traffc volume the algorthm captures the qualtatve characterstcs of daly truck traffc satsfactorly wth acceptable bas. Quanttatvely t exhbts a 5.7% error n total truck volume estmates for data from BHL study. The algorthm also captures very well the hstorcal daly trend of G-factor provng benefcal for mprovng speed estmaton from sngle loop detector data. The bg advantage of the proposed algorthm s that t can collect truck volume profle for any gven day and locaton when loop data are avalable. Gven the wde deployment of sngle loop detector data t s feasble to apply the proposed algorthm to produce a census-type truck AADT for all many freeway locatons. The mplementaton of the algorthm requres mnmal effort. Snce the processng can be done on the aggregated data at the TMC no addtonal hardware or software s needed n the feld at the detector staton or cabnet level. Note also that our algorthm produces truck volumes at hourly or 5-mnute ntervals for dfferent days of week season etc. Such nformaton permts the study of the pattern of truck traffc over tme of day day of week and seasons. 10

19 REFERENCES 1. U.S. Department of Transportaton USDOT. Traffc Montorng Gude 3rd edton. FHWA Washngton DC Calforna Department of Transportaton Annual Average Daly Truck Traffc on the Calforna State Hghway System Sacramento CA Nhan N. L. Zhang X. and Wang Y. Evaluaton of Dual-Loop Data Accuracy Usng Vdeo Ground Truth Data Research Report TNW Unversty of Washngton. March Wenblatt H. Usng Seasonal and Day-of-Week Factorng To Improve Estmates of Truck Vehcle Mles Traveled. Transportaton Research Record pp Sharma S.C. B.M. Gulat and S. Rzak Statewde Traffc Volume Studes and Precson of AADT Estmates. In Journal of Transportaton Engneerng Vol Sharma S. C. Lu G. X. and Thomas S. Sources of Error n Estmatng Truck Traffc from Automatc Vehcle Classfcaton Data. In Journal of Transportaton & Statstcs. Volume 1 3 October Cofman B. Lyddy D. and Skabardons A. The Berkeley Hghway Laboratory- Buldng on the I-880 Feld Experment. In Proc. IEEE ITS Councl Annual Meetng IEEE 2000 pp Chen C. K. Petty A. Skabardons and P. Varaya. Freeway Performance Measurement System: Mnng Loop Detector Data. Transportaton Research Record No pp Wang Y. and Nhan N. L. Freeway Traffc Speed Estmaton Usng Sngle Loop Outputs accepted for publcaton by Transportaton Research Record January Helbng D. Traffc and Related Self-Drven Many Partcle Systems. In Revew of Modern Physcs vol 73 October 2001 pp Cofman B. Improved Velocty Estmaton Usng Sngle Loop Detectors. In Transportaton Research: Part A Vol pp Ja Z. Chen C. Cofman B. and Varaya P. The PeMS algorthms for accurate realtme estmates of g-factors and speeds from sngle loop detectors. In Proc. IEEE ITS Councl Annual Meetng IEEE 2001 pp Beymer D. McLauchlan P. Cofman B. and Malk J. A Real-Tme Computer Vson System for Measurng Traffc Parameters. In Proc. IEEE - Computer Vson and Pattern Recognton IEEE 1997 pp Kwon J. Estmaton of Free Flow Speed and Detector Bas from Sngle Loop Data Usng Vehcle Length Profle. PATH workng paper August

20 TABLE 1 Performance of the Algorthm for Data from BHL Study Observed Sngle-Loop Algorthm Exogenous-Speed Algorthm Total Traffc Volume veh/day Truck Traffc Volume veh/day and Percent of Total Volume Estmated Truck Volume veh/day and Percent of Total Volume Error n Truck Volume Estmate veh/day and Percent Error Estmated Truck Volume veh/day and Percent of Total Volume Error n Truck Volume Estmate veh/day and Percent Error Lane HOV Lane % 0 0% % % % Lane % % % % % Lane % % % % % Lane % % % % % Total % % % % % Caltrans Report for Year % A dash - means that data s not applcable. 2. Caltrans Report quanttes are calculated assumng the same AADT for both drectons. 12

21 TABLE 2 Comparson of Daly Traffc Volume durng Lockout and Non-Lockout Weekdays I-710 Port of Long Beach Average Daly Traffc Volume veh/day All Cars Trucks Passenger Cars Non-lockout Weekdays 1 Lockout Weekdays 2 Dfference % % % 1. Medan over 38 non-lockout weekdays 2. Medan over 5 lockout weekdays 13

22 Effectve Vehcle Length Count ft = m Length ft Length>40 ft Count Length ft Length<40 ft Count Length ft FIGURE 1. Dstrbuton of Effectve Vehcle Length BHL Data 14

23 Speed mph Lane 2 Lane 3 Lane 4 Lane 5 Speed mph Lane 2 Lane 3 Lane 4 Lane Tme 5 mn Tme 5 mn Speed mph Lane 2 Lane 3 Lane 4 Lane 5 Speed mph Lane 2 Lane 3 Lane 4 Lane 5 1 mph = 1.61 km/h Tme 5 mn Tme 5 mn FIGURE 2 Tme-seres plots of 5-mnute aggregated double-loop speeds measured n four lanes at a locaton n BHL study. Each plot corresponds to a sngle day. Here and below when tme scale s 5 mnute tme s n 5-mnute ncrements from 0 to 288 startng wth 0 at mdnght. 15

24 16 Lane Lane Lane Lane 5 FIGURE 3 Lane-to-Lane Speed Correlaton. Each scatterplot depcts 5-mnute aggregated speeds mph; 1 mph = 1.61 km/h measured n lane a and b at a locaton n BHL study over 10 days total of 2880 samples. In each plot the thck lne s the least squares regresson lne wthout the ntercept fttng lane b speed on lane a speed and the thn lne s the reference lne y=x. Three numbers are the slope of the regresson lne R-squared values and correlaton coeffcent from top to bottom.

25 Lane 3 Volume veh/hr Tme hour Lane 4 Volume veh/hr Tme hour Lane 5 Volume veh/hr True Sngle-Loop Algorthm Exogenous-Speed Algorthm Tme hour FIGURE 4 Observed and estmated daly pattern of lane-by-lane truck volume aggregated over 20 days. Here and below when tme scale s one hour tme s n one-hour ncrements from 1 to 24 startng wth 1 at mdnght. 17

26 Truck Count veh/hr True Sngle-Loop Algorthm Exogenous-Speed Algorthm Tme hour Mean Speed mph Lane 2 Lane 3 Lane 4 Lane 5 1 mph=1.61 km/h Tme hour Error veh/hr Sngle-Loop Algorthm Exogenous-Speed Algorthm Tme hour FIGURE 5 Observed and estmated daly pattern of lane-total truck count top; lane-bylane daly pattern of speed averaged over 10 days mddle; daly pattern of estmaton error of lane-total truck count bottom. 18

27 Lane 2 Lane 3 Length ft true estmate Length ft true estmate Tme 5 mn Tme 5 mn Lane 4 Lane 5 Length ft true estmate Length ft true estmate 1 ft = m Tme 5 mn Tme 5 mn FIGURE 6 True and estmated daly trend of 5-mnute mean effectve vehcle length estmate averaged over 10 days. 19

28 Total Vehcle Count Sngle Loop Total Count Countveh/hr Tmehour Total Truck Count Countveh/hr Countveh/hr Tmehour Sngle Loop Truck Estmate Countveh/hr Tmehour Tmehour FIGURE 7 Total vehcle volume estmated from WIM data top left and sngle loop data top rght; hourly volume of long truck traffc estmated from WIM data bottom left and sngle loop data usng the proposed algorthm bottom rght. 20

29 Total Truck Passenger Car Yes No Yes No Yes No Lockout Lockout Lockout FIGURE 8 Comparson of daly total traffc volume of all cars left trucks mddle and passenger cars rght durng port lockout and non-lockout perods. 21

30 Truck Volume veh/day/lane Lane 1 Lane 2 Lane 3 Lane 4 Lane Day Truck Volume veh/day Day FIGURE 9 Day-to-day trend of daly total truck traffc volume by lane top and lanetotal bottom. The lockout perod s days