An Investigation in the Use of Vehicle Reidentification for Deriving Travel Time and Travel Time Distributions

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1 An Investigation in the Use of Vehicle Reientification for Deriving Travel Time an Travel Time Distributions Carlos Sun Department of Civil an Environmental Engineering, University of Missouri-Columbia, E2509 Engineering Builing East, Columbia, MO , Tel: , Fax: , Glenn Arr Department of Electrical an Computer Engineering, Rowan University, 201 Mullica Hill Roa, Glassboro, NJ , Ravi P. Ramachanran Department of Electrical an Computer Engineering, Rowan University, 201 Mullica Hill Roa, Glassboro, NJ , Tel: , Fax: , ABSTRACT This paper presents the results from an investigation in the use of vehicle reientification for eriving travel time an travel time istributions using loop an vieo etectors. Vehicle reientification is the process of tracking vehicles anonymously from site to site thus yieling iniviual vehicle travel times an overall travel time istribution. Travel time an travel time istribution are measures of the performance an reliability of the transportation system an are useful in many transportation applications such as planning, operations, an control. This paper will present the following finings: 1) the results from a platoon reientification algorithm that improve upon a previous iniviual vehicle reientification algorithm, 2) sensitivity analysis on the effect of time winows in eriving travel times, an 3) the erivation an gooness-of-fit of travel time istributions using vehicle reientification. Arterial ata from Southern California are use in testing the algorithm performance. The test results show that the algorithm can reientify vehicles with an accuracy of over 95.9% when using 92.4% of total vehicles, calculate iniviual travel times with approximately 1% mean error using the most effective time winow an erive travel time istributions that fit actual istributions at a 99% confience level. INTRODUCTION One motivation for performing vehicle reientification is to aress the nee for section measures of traffic performance as oppose to point measures. As the names imply, point measures are those obtaine at a particular point on the roaway while section measures are those obtaine for an entire section of roaway. Point measures such as spee, flow an occupancy are measure over the istance of a traffic etector s fiel-of-view, which is aroun 2m (6.6ft) in the case of an octagonal loop. Traffic engineers an travelers on the other han, require information about entire sections of roaways. It is true that uner certain traffic conitions, point measures can approximate section measures. However in general, the use of point measure surrogates for section measures can lea to inaccuracies. The irect measurement of section travel times can avoi the inaccuracies involve with estimating section travel times using point spees. The practical traffic applications of vehicle reientification are many. The erivation of section travel times is useful to transportation engineers for the purpose of traffic operations, planning, an control. The metho of floating car stuies is comparatively more labor intensive an only prouces mean or meian travel times instea of travel time istributions. Accurate travel times can be instrumental in feeback control, vehicle routing, traffic assignment, ynamic origin/estination eman estimation, an traveler information systems. The usefulness of travel time istributions has been iscusse by many for ifferent applications in transportation. Travel time istribution or variability has been use in measuring the performance of transportation systems. For example in the Minnesota ramp metering stuy, travel time reliability is use as a performance criterion in aition to travel time an traffic volume (1). Rickman points to the use travel time istribution for quantifying traffic signalization service (2). Bates mentions that meian an travel time istribution are better measures than the mean (3). From the traveler s perspective many times a reuction in variability is just as valuable as the reuction in the mean travel time since it reuces anxiety or stress cause by uncertainty. Bates points to the

2 Sun, Arr, Ramachanran 2 notion of isutility from arriving at a estination earlier or later than esire. The placement of confience intervals aroun mean travel times improves the information for travelers (4). Travel time istributions are also valuable in simulation an moeling of networks (5). Hellinga highlights the ifference between minimum travel time paths an paths of optimal travel time reliability in simulation (6). Dany mentions that stuies on travel time istribution can help improve iscrete choice moeling in route selection since travelers are more concerne with maximum likelihoo travel time rather thanthe average (7). Wakabayashi iscusses the applicationof travel time variability in roa network management an construction (8). Cohen mentions the importance of consiering travel time variability in the erivation of traveler cost functions (9). RELEVANT LITERATURE Even though few surveillance systems highlight the fact that they are able to prouce travel time istributions, there are a number of existing technologies that have the potential to prouce accurate travel time istributions. One class of techniques uses point measures an stochastic traffic flow moeling. One such example is Dailey s use of cross-correlation for measuring the propagation time of traffic (10). Another is Petty s use of the assumption that upstream an ownstream travel times have the same probability istribution (11). Another class of techniques for obtaining travel times involves vehicle reientification or the matching of vehicle signatures that come from locations along roa sections. In other wors, etector signatures from an upstream station are compare with the signatures from a ownstream station for a match. Some algorithms match iniviual inuctive loop signatures or lengths from vehicles by correlating such signatures from two contiguous sites (12)-(14). One traitional metho of vehicle reientification is license plate matching (15). Some examples of vieo reientification inclue the use of color (16) an vieo signature vectors (17). Other etector technologies that have been use for vehicle reientification incluing laser profiles (18), weigh-in-motion axle profiles (WIM) (19), an ultrasonic etectors (20). There are some in-vehicle technologies that coul be employe to erive travel time istributions (21)-(23). One is the use of so-calle toll tags or AVI (Avance Vehicle Ientification). This system requires vehicles to have a toll tag or transceiver to communicate with the reaers at points on the transportation network. A rawback to this system is that toll tags currently have a limite market share thus only a subset of vehicles are etecte. An avantage of this system is that the accuracy in ientification is high since each toll tag transmits a unique ientification number. Another system is the use of probe vehicles often equippe with GPS an/or cellular telephones. This system is also accurate an allows almost a continuous tracking of vehicles. However, this system is also epenent upon consumer acceptance. The two aforementione systems in use in the private sector can augment the information obtaine by the public sector. DATA The traffic ata use for this experiment are collecte on June 30, 1998 in Irvine, California. The ata site consists of two etector stations bouning a two-lane section of Alton Parkway within the intersections of Telemetry an Jenner streets. Each etector station has ouble inuctive loops in a spee trap configuration, 3M Canoga etector cars, an vieo etectors. The ata collecte from the loops an vieo are time synchronize so that the inuctive signature an the vieo image from the same vehicle can be ientifie. Figure 1 shows an example of the fiel ata that was collecte incluing the inuctive signature, original vieo image, backgroun subtracte image, an the extracte color feature. The istance between the two etector stations is 130m (425 ft). The inuctive loops are stanar 1.83mX1.83m (6ftX6ft) rectangular loops that are commonly use by many transportation agencies. The vieo camera use was a consumer grae Hi-8mm camcorer. The ata are collecte uring the morning peak between approximately 8:00am an 9:30am at the ownstream station. This ataset contains 581 vehicle pairs or 1162 vehicles. The time consuming nature of groun truthing makes the formation of large ata sets very ifficult. This process requires a researcher to ientify an upstream vehicle on a monitor, search an fin the corresponing ownstream vehicle on another monitor, an recor the time stamp of the vehicles at both locations in orer to obtain travel times. The set of over 500 samples seem to be large compare to floating car runs of 20 samples, but this is necessary since the goal is to erive travel time istributions an not just the mean travel time. The first 200 vehicle pairs are use for training an the rest for testing. Table 1 shows the characteristics of the actual travel time an spee istributions of the fiel ata. A high skewness value implies that the istribution is not symmetrical. The kurtosis value represents the fatness of the

3 Sun, Arr, Ramachanran 3 tails of the istribution. The information in Table 1 explains the reasons for using both travel time an spee time winows as presente in the results section. The table shows that the travel time istribution is relatively skewe while the spee istribution is not. The right tail of the travel time istribution which correspons to the slower travel times is relatively fat (large kurtosis value). The mean an the meian travel times are not the same for the travel time or the spee istributions which shows that neither istribution is normal. This is consistent with ata from other research which show significant positive skewness for the travel time istribution (7). Other research also points to normal istributions as inappropriate but suggests that log-normal or gamma istributions might be better for characterizing travel time istributions. METHODOLOGY Instea of treating vehicles as iniviual images, traffic flow consierations can be use to further constrain the vehicle reientification problem. The propose platoon algorithm uses the fact that vehicles ten to travel in groups or platoons. Platoon in this context refers to a group of vehicles in chronological sequence in close proximity to each other. This is a more general formulation than the previous iniviual reientification since the size limits of vehicle platoons are iniviual vehicles in the least congeste case an all existing vehicles in the extremely congeste case. By comparing multiple vehicles instea of iniviual vehicles, the algorithm performance shoul be improve while iniviual vehicle matches are still maintaine. An intrinsic step in the algorithm formulation of the vehicle reientification problem is the process of feature extraction. Traitionally, vehicle reientification or more generally system ientification is split into two separate components: feature extraction an classification. Within feature extraction, there are so-calle irect methos an also parametric methos. Since the reientification system nees to be fiel implementable, there are many "real-life" constraints that limit the algorithm. The various trae offs between accuracy, computational intensity, an information banwith are carefully weighe. Feature extraction seeks to extract the salient components of vehicle images that woul sufficiently ifferentiate vehicles. In orer to avoi reunancy, features obtaine from the vehicle images nee to contain ifferent information. This is similar to the process of eriving a basis in linear algebra or fining the principal components in ata analysis. In a likewise fashion, the goal here is to fin an orthogonal set of vectors that woul span the space of possible vehicles images. Direct feature extraction methos have been employe for this research since parametric estimation involves the assumption of a specific moel structure an require more computation. The features use in the algorithm inclue inuctive signature, color, velocity, inuctive amplitue (proportional to the suspension height), electronic length (similar to physical length), an platoon travel time or the heaway between the first an last vehicles of the platoon. Once the salient features from various etectors images are extracte, they are combine in the platoon vehicle reientification algorithm which performs the ientification or classification. In other wors, the algorithm performs the vehicle reientification an matches the images prouce by the same vehicle along various points on the roaway. A multi-objective optimization approach is use in the platoon vehicle reientification algorithm because it allows the incorporation of various objectives associate with the ifferent features. A sequential multiobjective optimization approach calle lexicographical optimization (LO) is use for the following reasons (24). First, LO enables objectives with ifferent units to be place at ifferent priority levels. Secon, LO progressively reuces the feasible set from level to level thus improving computational efficiency. The separation into multiple optimization levels allows sensitivity analysis to be conucte at every level. Multi-objective has the notion of Pareto optimality which is efine as a certain position when it is impossible to fin a way of moving from that position very slightly in such a manner that the ophelimity enjoye by each of the iniviuals of the collectivity increases or ecreases (25). The following paragraph gives an overview of the platoon vehicle reientification algorithm. The algorithm starts by selecting a platoon etecte at the ownstream site. A list of upstream caniate platoons are generate subject to a time winow objective that eliminates platoons that are not within a reasonable time frame. In other wors, caniate vehicles that travel at excessive or unreasonably low spees are eliminate from caniate platoons. Each upstream platoon is then compare with the ownstream platoon. A minimum absolute istance classifier (L1) is use as the objective in etermining the best match. The classifier uses the feature vectors escribe previously. An iniviual vehicle time winow objective is use in the en to exclue vehicles with unreasonable travel times effectively eliminating outliers in the ata set. The trae off in this final objective

4 Sun, Arr, Ramachanran 4 involves an improvement in the fit in the majority of the travel time istribution at the cost of the eges of the istribution. Because there is a one-to-one corresponence between the iniviual vehicles of the upstream an ownstream platoons, the results from this algorithm yiel iniviual vehicle reientifications. Therefore iniviual vehicle are tracke from point to point an vehicle travel times are measure. The minimum absolute istance measure (L1) between an upstream feature f u an ownstream feature f is given by ( f, f ) = u q i= 1 f ( i) f u ( i) where i enotes the i th component of the feature vector an q is the vector imension. If the number of components of the signatures is ifferent for ifferent vehicles, then the feature vector with fewer components is pae before taking the L1 istance. If the size of the platoon is enote as N p, the L1 istance for the overall platoon, D, is where f j u D N p ( fu, f ) = an f j j = 1 ( f j u, f j ) are the upstream an ownstream features for vehicle j. The optimum number of vehicles in a platoon is etermine by the platoon size that achieves the highest reientification accuracy using the training set. For this ata set, the optimal platoon size is three. The first level of the lexicographic optimization is formulate as a time winow objective in the fashion of a goal criterion. Goal programming is useful in establishing target or threshol values. State verbally this objective has the goal of retaining vehicles whose upstream an ownstream travel times are greater than L t an less than U t. The time winow objective is { D( t t ) = z }, ( z [ L U ]) f, 1 = goal u, 1 1 The goal value z 1 is efine by upper an lower bouns U t an L t an efine as t t U t = t l t min an L t = t f t max where t min an t max are the minimum an maximum vehicle traversal times base on the training set, t l is the travel time for the last vehicle from the ownstream platoon an t f is the travel time of the first vehicle from the ownstream platoon. Each feasible upstream vehicle will nee to have a travel time that is greater than L t an less than U t. If the number of feasible upstream vehicles is efine as N v an N f is efine as the number of feasible upstream platoons then N f = N v N p + 1. For example, if N v =10 an N p =3, then there woul be 8 consecutive upstream platoons of 3 vehicles that nee to be examine. Then, the platoon comparison nees to be performe 8 times to fin the upstream platoon that best matches the ownstream platoon. The secon level objective involves the comparison of feasible caniate upstream platoons with the ownstream platoon. How closely two platoons are matche to each other is efine by a linear program which is a weighte-average of feature istances. If two images are prouce from the same vehicle, then the features from the images shoul not iffer significantly resulting in small feature istances. As the platoon is compose of iniviual vehicles the feature istances are summe up to obtain an overall platoon istance. The secon level objective is formulate as { f = min w D( s, s ) + w D( c, c ) + w D( v, v ) + w D( m, m ) + w D( l 2 s u c u v u m u l u + w p ( pu, p )}, l )

5 Sun, Arr, Ramachanran 5 where w s is the weight applie to the vehicle signature istance D s u, s ),w c is the weight applie to the color ( information feature istance D c u, c ),w v is the weight applie to velocity feature istance D v u, v ),w m is the ( ( weight applie to the maximum inuctive amplitue feature istance D m u, m ),w l is the weight applie to the ( ( electronic length feature istance D l u, l ) an w p is the weight applie to the platoon traversal time feature istance ( p u, p ). As before, the subscripts u an refer to upstream an ownstream, respectively. Also, the superscript j refers to the j th vehicle in the platoon. Note that the platoon traversal time feature applies to the entire platoon an not for any iniviual vehicle. The linear weights a up to one an are etermine uring training by searching an n-imensional gri of real numbers an fining the optimum combination that gives the best performance on the training ata alone. The upstream platoon that achieves the objective f 2 or the smallest istance is matche to the ownstream platoon. The last level objective involves an iniviual vehicle time winow. This objective is use in orer to eliminate vehicles that travel at unreasonable spees for the segment in question. For example, if the vehicle ha a travel time of the mean travel time minus 4 stanar eviations, then the vehicle woul be traveling at approximately 212 fps (144 mph). Effectively, this objective helps to eliminate some vehicles that were erroneously reientifie as a travel time sample. The iniviual time winow objective is j j { ( t t ) = z }, z [ l u ] 3 = goal u, 2 2 ( ) f, t t The goal value z 2 is efine by lower an upper bouns l t an u t an efine in two ways. One way is to use the mean travel time t an form the limits of the time winow by aing an subtracting multiples of the sample stanar eviation of the travel time, s. For example, if a four stanar eviation range is esire, then l t = t 2s an u t = t + 2s. Due to the fact that the travel time istribution is skewe compare to the spee istribution (see Table 1), a secon way of using the mean an stanar eviation of spee is also use. In this case, for example, l t = s 2s an u t = s + 2s,where s is the mean spee an s is the sample stanar eviation of spee. In this initial evelopment of the platoon reientification algorithm, the two lanes of traffic were treate separately. This is ue to several reasons. First, this is a simpler case upon which more complicate scenarios such as overtaking can be ae. Secon, if vehicles are not require to be sequential in a platoon, then the problem becomes a combinatorial problem an the solution becomes more computationally intensive. Thir, on certain short stretches of roaway, lane changes are infrequent. The test ata use is from such a site an the number of lane changes amounte to only 2% of the traffic. RESULTS One of the goals of this research is to improve upon a previous algorithm for vehicle reientification that use iniviual vehicle reientification (14). Table 2 compares the results of the new platoon algorithm with the previous algorithm. Column one lists the ifferent time winows use for extracting a subset of the total number of vehicles for reientification. The etails of the time winow are iscusse in the methoology section. The first four time winows, rows one through four, use the stanar eviation, s, of travel times. For example, the time winow in row one has the lower limit of mean travel time minus two stanar eviations an the higher limit of mean travel time plus two stanar eviations. The next four time winows, rows five through eight, use the stanar eviation of spees translate into equivalent travel times. Because of the inverse relationship between spee an travel time, the time winows using spee are skewe towar the right of the mean when translate into equivalent travel times. Columns two an six show the reientification accuracy (rate) for the two algorithms. Columns three an seven show the percentage of vehicles that are exclue using the time winow. Columns four, five, eight, an nine show values relate to the accuracy of the travel time erive using the reientification algorithms. Columns five an nine show the variance of the percent travel time error. The variance is important to examine because it gives an inication as to the consistency of the erive travel times over a range of values. The results in column nine show that the travel time errors o not fluctuate wiely but are consistent among the erive travel times of iniviual vehicles.

6 Sun, Arr, Ramachanran 6 The results show that the reientification algorithm using the platoon reientification algorithm is superior in all aspects to the iniviual vehicle reientification algorithm. This is true in the reientification accuracy, the mean percent error for travel time, an the variance of the percent error. Table 2 also shows encouraging results for the use of the platoon reientification algorithm for eriving travel times. In the best case, the reientification accuracy is close to 96%, the mean travel time error is approximately 1% an the variance in the travel time error is 0.36% while over 90% of the vehicles are still use in eriving travel times. The trae offs in the use of iniviual vehicle time winows is between accuracy an the percentage of vehicles use in reientification. In three of the four sets of cases, as the time winow become narrower an as the percentage of vehicle use ecreases the reientification accuracy increases. The exception is the platoon reientification with a time winow using travel time. In this case, the reientification accuracy ecreases as the time winow was ecrease from +/- 3.5 stanar eviations to +/- 3 stanar eviations before the accuracy increase again with a time winow of +/- 2 stanar eviations. To summarize, the narrowing of time winow can exclue outliers that are most often erroneous reientifications, however this is not universal as is shown in one of the four cases. One of the goals of this research is to investigate the ability of the reientification algorithm for eriving travel time istributions. A qualitative way of accomplishing this is by visually comparing the plots of the erive an actual travel time istributions. Figure 2 shows an example of travel time istribution plots using a time winow of mean spee +/- two stanar eviations. From the plot, the two istributions look very similar. Two quantitative ways of evaluating the performance of the reientification in eriving travel time istributions are chi-square an Kolmogorov-Smirnov (K) tests (26). These tests measure the gooness-of-fit between observe istributions an expecte istributions. The two tests operate on slightly ifferent principles. The chi-square test assesses how closely the erive frequency istribution represents the actual istribution by classifying ata into I istinct intervals an summing the results of comparison between each travel time interval. The chi-square test statistic is 2 χ = I i= 1 ( f f ) o f t t 2 where f o is the observe or erive frequency, f t is the theoretical or actual frequency, an I is the number of travel time intervals. The statistic has I-1 egrees of freeom (DF). The Kolmogorov-Smirnov is a statistic base on the maximum eviation between two cumulative relative frequencies over the entire range of the variable an epens on the sample size N. Itisexpresseas D( N ) = max E( x) O( x) where E(x) is the expecte (actual) cumulative frequency istribution an O(x) is the observe (erive). Briefly, some trae-offs between chi-square an K test inclue K test s more moerate assumptions about ranom sampling an sample size, its use of ungroupe ata, an efficiency; while chi-square oes not require that the hypothesize population be specifie in avance, it s values can be meaningfully ae, an it can be easily applie to iscrete populations. See (27) for more iscussions on the relative merits of chi-square an K test as well as iscussions on other maximum eviation tests such as Cramer-von Mises. The following hypothesis is teste using the aforementione statistics: H o : The frequency istribution of the erive an actual travel times are the same. The results from testing the frequency istribution generate by the platoon reientification algorithm at 99% confience level are shown in Table 3. Similar to Table 2, values for 8 cases are shown relate to the ifferent time winows that are employe. In terms of the chi-square test, the results from rows 1-7 show that the null hypothesis can not be rejecte inicating a goo fit. Even in the case of row 8 where the null hypothesis is rejecte, the test statistic is very close to the chi-square value at a 99% confience level. The number of intervals chosen in the chisquare test is a function of the number of 0.5 secon intervals that resulte after the application of the time winow. In terms of the K test, the null hypothesis is rejecte in none of the cases inicating a goo fit for all cases. Even though there are some ifferences in the results from the chi-square an K tests, the results have shown statistically that it is possible to erive travel time istributions that fit actual istributions well using platoon reientification.

7 Sun, Arr, Ramachanran 7 CONCLUSION The use of the platoon reientification algorithm is shown to be superior to the iniviual vehicle reientification algorithm. However, the optimal static size of the platoon or a criterion for establishing ynamic platoon sizes shoul be further investigate for ifferent traffic flowconitions an facilities. The platoon behavior between freeways an arterials shoul necessitate ifferent platoon sizes in the algorithm. Even though every time winow prouce promising results of over 90% reientification accuracy an travel time error of less than 4%, the narrower time winows such as v ± 2s prouce the best results while still retaining a significant amount of vehicles use (95.85%). The narrower time winows also prouce travel time istributions that fit the actual istribution the best. The length of the test segment was too short for the collection of useful trip time, an it i not span an intersection to allow for the erivation of intersection control elays. However, this section was useful in proving the feasibility of vehicle reientification an erivation of travel time istribution which are precursors to the erivation of trip travel times an trip reliability. To valiate the ability of the algorithm to reientify vehicles accurately, a close segment is investigate in orer to control for vehicles which o not appear at both upstream an ownstream stations. In the future, ata shoul be collecte from longer segments such as freeway corriors an arterial segments that span intersections. There are many research issues relate to the evelopment of the platoon reientification that are yet unresolve. The current algorithm shoul be generalize for the case where lane changing is consiere. There is also nee for assessing the transferability of the algorithm to ifferent sites. This will necessitate the collection of ata from more traffic sites. However, such an effort is a long term process, since implementing fiel instrumentation takes time an groun truth ata evelopment is extremely labor intensive. In aition, incient travel times will be esirable to collect since the variability in travel time uner incients is of great interest to rivers an public agencies. It is esirable to further examine the application of travel time istributions in ifferent transportation areas. One such area is its use in performance evaluation of transportation systems. This can involve more than just variability of travel time an inclue assessment of the shapes of the istributions. For example a peake istribution seems to be more esirable than a relatively uniform istribution. Travel time istributions can be use in safety applications similar to the use of spee ifference. Also, there are many opportunities where travel time istributions can be use for improving moeling an simulation of traffic in terms of route choice, travel cost functions, an river behavior. ACKNOWLEDGEMENT The ata use for this research was provie by the California Department of Transportation (Caltrans) an PATH (Partners for the Avance Transit an Highways). The contents of this paper reflect the views of the authors who are responsible for the facts an the accuracy of the ata presente herein. The contents o not necessarily reflect the official views or policies of any state agencies. This paper oes not constitute a stanar, specification, or regulation. REFERENCES 1. Cambrige Systematics. (2000) Twin Cities Ramp Meter Evaluation. 2. Rickman, T, Hallenbeck, M., an Schroeer, M. (1990) Improve Metho for Collecting Travel Time Information. Transportation Research Recor Washington, D. C., pp Bates, J., Polak, J., Jones, P., an Cook, A. (2001) The Valuation of Reliability for Personal Travel. Transportation Research Part E, Vol. 37, pp Eisele,W. an Rilett, L. (2002) Estimating Corrior Travel Time Mean, Variance, an Covariance with Intelligent Transportation Systems Link Travel Time Data. Proceeings of the Annual Transportation Research Boar Meeting, January 13-17, Washington, D. C.

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9 Sun, Arr, Ramachanran 9 LIST OF TABLES AND FIGURES TABLE 1 Comparison of Travel Time an Spee Distributions TABLE 2 Iniviual Versus Platoon Algorithm Results TABLE 3 Gooness-of-fit Test for Derive Travel Time Distribution FIGURE 1 Example of features extracte from inuctive an vieo etectors. FIGURE 2 Example of erive an actual travel time istributions.

10 Sun, Arr, Ramachanran 10 TABLES TABLE 1 Comparison of Travel Time an Spee Distributions istribution mean meian variance skewness kurtosis range travel time 6.73 s 6.94 s s spee m/s fps mph m/s fps mph m/s fps mph

11 Sun, Arr, Ramachanran 11 TABLE 2 Iniviual Versus Platoon Algorithm Results Iniviual Platoon Time Winow Rei Rate % Veh s Mean % Error Var % Error Rei Rate % Veh s Mean % Error Var % Error t ± 2s t ± 3s t ± 3. 5s t ± 4s v ± 2s v ± 3s v ± 3. 5s v ± 4s

12 Sun, Arr, Ramachanran 12 TABLE 3 Gooness-of-fit Test for Derive Travel Time Distribution Time Winow t 2s t 3s t 3. 5s t 4s v 2s v 3s v 3. 5s v 4s %Veh Use calc. chisquare DF ± ± ± ± ± ± ± ± Chisquare 99% calc. K N K 99%

13 Sun, Arr, Ramachanran 13 FIGURES Color Vector = [ ] FIGURE 1 Example of features extracte from inuctive an vieo etectors.

14 Sun, Arr, Ramachanran Relative Frequency Travel Time (s) Derive Actual FIGURE 2 Example of erive an actual travel time istributions.