Allocating Travel Times Recorded from Sparse GPS Probe Vehicles into Individual Road Segments

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World Conference on Transport Research - WCTR 2016 Shanghai. 10-15 July 2016 World Conference on Transport Research - WCTR 2016 Shanghai. 10-15 July 2016

Allocating Travel Times Recorded from Sparse GPS Probe Vehicles Allocating Travel Times Recorded from Sparse GPS Probe Vehicles into Individual Road Segments into Individual Road Segments a a

a Porntep Puangprakhon a,* a,*, Sorawit Narupiti a Porntep Puangprakhon , Sorawit Narupiti

Department of Civil Engineering, Chulalongkorn University, Bangkok, 10330, Thailand Department of Civil Engineering, Chulalongkorn University, Bangkok, 10330, Thailand

Abstract Abstract Probe-based data collection system, which deploys movable sensors in traffic streams to collect traffic records, is commonly used Probe-based collection system, movableof sensors in on traffic to collect traffic records, is commonly used for area-widedata measurement of travelwhich timesdeploys and conditions traffics roadstreams networks. However, due to sparse distribution of for area-wide measurement travelsampling times and conditions trafficsthe on sampled road networks. However, to sparse distribution of polling positions from a lowofprobe frequency in of practice, points from probedue vehicles do not necessarily pollingwith positions from a low probelink, sampling practice,two theconsecutive sampled points from probe vehicles not necessarily match the end points of each and thefrequency travel timeinbetween polling points needs to be do positioned into an match withlink the for endlink points of each and theThis travelpaper timepresents betweenthe twonew consecutive points needs to be positioned an individual travel time link, calculation. techniquepolling that addresses the allocation of travelinto times individual linkgathered for link travel time calculation. paperThe presents new technique that addresses the allocation of travelamong times based on data from sparse GPS probe This vehicles. travel the time allocation procedure by applying the relationship based on data speeds, gatheredsampled from sparse GPS and probe vehicles. The travel timeThe allocation procedure byisapplying theand relationship instantaneous positions tracked times is proposed. proposed technique discussed comparedamong with a instantaneous speeds, sampled positions andfield tracked is proposed. The roadway proposedcorridor technique discussed and and compared with a ground truth benchmark of high resolution datatimes recorded from urban in isboth congested uncongested ground truth benchmark of high resolution field data recorded from urban roadway corridor in both congested and uncongested traffic conditions. Results suggest that addressing travel time allocation problems by the proposed method significantly traffic conditions. Results suggest that addressing time allocation problems by the proposed method significantly outperforms the benchmark method in both complete travel link and local levels which are demonstrated by an increasing estimation outperforms benchmark method in both complete linklevel and analysis local levels are demonstrated an increasing estimation accuracy up the to 60%. It is also observed from the local thatwhich the accuracy figures arebylower at the intersections accuracy uphigh to 60%. It isdelays, also observed from thecontain local level thatspeed the accuracy are lower at the intersections comprising stopped which normally highlyanalysis fluctuated profiles. figures Nonetheless, the proposed technique comprising high stopped approach delays, which normally contain highly speeddelays. profiles. Nonetheless, the proposed outperforms the baseline in both intersections with low fluctuated or high stopped The proposed technique offerstechnique superior outperforms baseline approach in both intersections withon low high stopped The proposed technique results to the the baseline technique in all scenarios, particularly theorsegments with delays. highly fluctuated speed profiles. offers superior results to the baseline technique in all scenarios, particularly on the segments with highly fluctuated speed profiles. © 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier B.V. B.V. © 2017 © 2017 The Authors. Published by Peer-review under responsibility responsibility of Elsevier WORLDB.V. CONFERENCE ON ON TRANSPORT TRANSPORT RESEARCH RESEARCH SOCIETY. SOCIETY. Peer-review under of WORLD CONFERENCE Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY. Keywords: travel time; travel time allocation, travel time decomposition; travel time estimation; probe data; arterial road; GPS Keywords: travel time; travel time allocation, travel time decomposition; travel time estimation; probe data; arterial road; GPS * Corresponding author. Tel.: +668-9682-9877; fax: +662-988-3666 ext. 3213. * Corresponding Tel.: +668-9682-9877; fax: +662-988-3666 ext. 3213. E-mail address:author. [email protected] E-mail address: [email protected]

2214-241X © 2017 The Authors. Published by Elsevier B.V. 2214-241X 2017responsibility The Authors.of Published Elsevier B.V. ON TRANSPORT RESEARCH SOCIETY. Peer-review©under WORLDbyCONFERENCE Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY.

2352-1465 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY. 10.1016/j.trpro.2017.05.423

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Porntep Puangprakhon et al. / Transportation Research Procedia 25C (2017) 2213–2226 Puangprakhon, P. and Narupiti, S./ Transportation Research Procedia 00 (2017) 000–000

1. Introduction Data recorded from probe vehicles is considered as one of the promising sources of traffic information for intelligent transportation systems (ITS). In this data collection system, the movable sensors that travel in the traffic stream, such as vehicles equipped with GPS devices, are used as tracking instruments for collecting real-time locations and speeds of vehicles along the travel route. Generally, the identification (ID) of vehicle, position, instantaneous speed, and time stamp are basic information recorded in probe data. Consequently, the travel time and speed between any two recorded points on the travel route can be directly measured. This technique is regarded as a cost-effective approach and has higher potential in area-wide implementation compared with the fixed sensor system as it does not require any instrument or infrastructure to be installed alongside the road networks, and requires small investment, operating and maintenance cost. In the past decade, numerous research on travel time study in both freeway and arterial settings were carried out using probe-based data from various sources e.g. taxi probes (Herring et al. (2010) and Wei et al. (2007)), bus probes (Pu and Lin (2009), Uno et al. (2009), Bejan et al. (2010) and Vanajakshi et al. (2009)), test vehicles (Puangprakhon and Narupiti (2015), Jiang et al. (2009), Billings and Yang(2006)), or synthetic data simulated from traffic simulation software (Esawey and Sayed (2009), Nanthawichit et al. (2003), Li et al. (2008)). Up to now, most of the previous studies require high resolution data, e.g. sampling every 1 second or less, to address the complete link travel time estimation or prediction problems (Zheng, and Van Zuylen (2013)). Conversely, in reality, the probe data fed to the traffic data collecting center come from a variety of sources with different sampling time intervals such as taxies, logistics vehicles, public buses or private cars, etc. Therefore, the transmission rates can be varied from very high frequency to low resolution depending on the data providers (the sampling time interval up to 60 seconds could generally be observed). Additionally, the polling positions or sampling points in probe-based data are randomly distributed and do not necessarily correspond with the end points of the link on the road segment. As a consequence, the allocation of travel time between two consecutive sampled GPS points across the end points of the link is considered as one crucial task in the link travel time estimation procedure. One of the simplest and easy-to-implement ideas for travel time allocation is by assuming the constant driving speed between two consecutive sampling points. Then, the decomposed travel time in each link can be allocated by direct interpolation between the stamped times and reported positions of each vehicle. This technique provides reasonable estimation results in the traffic with nearly constant speed profiles such as on freeways or motorways with the under-saturated traffic condition. However, in the urban context where the road network typically comprises traffic signals, intersections and numerous access points and the vehicle speed profiles are generally fluctuated and far from constant, the estimation based on the constant speed assumption technique has difficulty in providing precise outcomes (Neumann (2013)). For the above reason, various techniques have been proposed to address the travel time allocation problem. For instance, Hellinga et al. (2008) proposed the model which considers the probability of stopping and congestion delays based on the positions of vehicles along a road segment. Although the overall result from simulated data showed that this approach performed well compared to the benchmark technique, the link travel time was overestimated on the segment without traffic signals and the limitation on the number of stops in each link and this was a drawback of this technique. Hofleitner and Bayen (2011) demonstrated the use of the statistical traffic flow theory in travel time decomposition problems. Their technique showed good agreement with the next Generation Simulation (NGSIM) data. Still, this technique is quite complex and requires many assumptions e.g. stationary traffic, probability of delay, etc. to allocate the travel time into individual links. Although a number of works attempted to construct more complex models for representing the urban traffic, a finding from Zheng et al. (2010) proved that the more complicated models did not always offer better outcome than the simple and widely used technique (time-distance relationship technique). Conversely, in some cases e.g. in the less frequent polling time interval or in the sparse data, the simple model tends to offer the healthier result than the complicated ones. This could be resulted from complex movement and delay behaviors on urban roadways that face many unexpected influencing factors e.g. a bus waiting at a bus stop, double-parked vehicles or other causes. Therefore, Zheng and Van Zuylen (2013) overcame the complexity of modeling by utilizing the Artificial Intelligent (AI) method in travel time allocation for urban roads. They employed the three-layer neural network with positions, link IDs, time stamps and speeds as the model inputs for complete link travel time estimation. The result from synthetic data illustrated



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that their approach outperformed the analytical model from Hellinga et al. (2008), particularly when the traffic demand was increasing. They also suggested that the position could be the critical factor influencing the accuracy of the ANN model while adding of instantaneous speed as the input could improve the accuracy marginally. Yet, the ANN technique requires a lot of historical data for training and the ambiguous process going underneath with regards to the decisions of ANN is questioned. As aforementioned, accurate prediction on delays and trajectories of vehicles along the urban roads is not an easy task. However, the condition of the traffic movement at any point can basically be informed by the instantaneous speed detected from the probe vehicle. Therefore, Puangprakhon and Narupiti (2014) demonstrated the integration of the instantaneous speed data together with time and position in the travel time allocation procedure. In their approach, the speeds at the end points of the link and travel times were approximated and tuned until convergence using the speed-time-distance relationship. Verification through the results from field data also confirmed the betterquality of the results from this technique over the simple distance-time method in all scenarios. Moreover, the speedtime-distance techniques can easily be implemented and efficiently address the travel time allocation problem as proved by more precise complete link travel time estimation results. Research by Neumann (2013) pointed out the importance of individual decomposed travel time study particularly at the local level (e.g. an individual intersection) and also suggested that the travel time decomposition could be a crucial negative factor affecting the accuracy of probe-based link travel time as errors from each decomposed travel time do not accumulate but could balance out when being recombined into the complete link travel time. Therefore, study on quality of the decomposing technique at the local level is a necessitated task for ensuring the quality of travel time estimation at both local and complete link levels. This paper illustrates the allocation of travel times on arterial roads from probe data using the speed-time-distance technique. The paper begins with details and procedures of travel time allocation using the speed-time-distance technique, followed by details of studied corridors, data gathering techniques, and verification and evaluation of the proposed technique compared with the baseline approach at both local and complete link levels, respectively. The results and main conclusions of the study are discussed last. TTT = t2 -t1 (a)

Link 1

(P1,t1,v1 )

Link 2 L1 (known)

(P2,t2,v2 )

...

Link n

TTT = t2 -t1

tL1,dec (b)

Link 1 (P1,t1,v1 ) L1 (known)

tL2,dec Link 2

(P2,t2,v2 )

...

Link n

L2 (known) TTT = t2 -t1

tL1,dec (c)

Link 1

(P1,t1,v1 )

L1 (known)

tL2,dec Link 2 L2 (known)

...

tLn,dec Link n

(P2,t2,v2 )

Ln (known)

Fig. 1. Three possible travel time allocation cases from probe-based data. (a) sampled points lie on the same link; (b) sampled points lie on adjacent links; (c) sampled points lie on different links with at least one link in between.

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2. Travel time decomposition techniques Link travel time or time spent for traversing through each link is considered as one of the most understood indicators for representing the condition of traffic on road networks. In probe-based data, the travel time between two consecutive observed points can be directly considered as the travel time between those points. However, in general, the locations of sampled points from probe vehicles are randomly located on the road and usually do not correspond with the end points of the link. Therefore, in measuring link travel time, the time between two consecutive sampled points across the end points of the link needs to be allocated into an individual link as depicted in Fig. 1. There are three possible cases from two observed points from probe-based data; two observed points lie on the same link (Fig. 1(a)), two observed points lie on adjacent links (Fig. 1(b)), and two observed points lie on different links with at least one link in between (Fig. 1(c)). In the first case, since both observed points lie on the same link, travel time between those points can be directly measured from sampling time interval without travel time allocation problems. While in the second and third cases, the measured travel time between two observed points (t 2 - t1 ) needs to be allocated or decomposed into existing links ( t L1,dec , t L 2,dec ,..., t Ln ,dec ) between those points. 2.1. Distance-time relationship method Travel time allocation by the distance-time relationship assumes “the speed of the probe vehicle is constant during traversing between two consecutive sampled points”. The decomposed travel time in each component link can be approximated by interpolating among locations and recorded times from sampled data regardless of instantaneous speed of those points. From Fig. 1, Let n be the number of incorporated links between two consecutive sampled points, time stamps at the first and second points are t1 and t 2 respectively, TTT is the travel time or time difference between those two points (calculated by t 2 - t1 ), which is generally equivalent to probe sampling time interval, Li , is the distance between two sampled points projected on link i . The decomposed travel time of link i , t Li,dec , can be estimated by:

t Li,dec = TTT

Li

n

åL

(1)

i

i =1

2.2. Speed-Time-Distance relationship method The state or movement of traffic at each sampled location can be reflected by instantaneous speed information recorded in probe data. Previous research from Zheng and Van Zuylen (2013) has demonstrated the improvement of travel time estimation when the instantaneous speed was integrated into the estimation process. Therefore, not only information from time stamped and sampled location of probe vehicles, but also the instantaneous speed of those positions are assimilated into the approximation procedure of the speed-time-distance approach. In this technique, firstly, the speed at the end point of the link is approximated by direct interpolation assuming linear relationship between speeds and location of two sampled points. Then, the estimating of individual link travel time using the speed and distance relationship is estimated and a tuning of individual link travel time is compared with the sampling time interval. Afterward, the speed at the end point of the link is re-calculated from the adjusted individual link travel time from the previous step. All the above mentioned processes are repeatedly performed until the individual link travel time is convergent. The procedure for allocating travel time into an individual link by the speed-time-distance approach can be outlined into six steps and is illustrated in Fig. 2. • Step 1: Approximation of speed at the end of link. Assuming a linear relationship between instantaneous speed and recorded location from two consecutive sampled points across the end points of the link, the speed of the vehicle at the end points of the link, ve , can be estimated using the proportion among instantaneous speeds and distances as follows:



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START T Approximation of speed at the end of link



Approximation of decomposed travel time from speed-distance relationship

Re-adjusting speed at the end point of link

Calculation of time difference between sampling time interval and estimated travel time

Re-estimation of speed at the end point of link from adjusted decomposed travel time





Tuning the decomposed travel time to sampling time interval

No Is convergence attained?

Yes END Fig. 2. Calculation flowchart for travel time allocation of the proposed technique.

ve = v1 + Dv(

L1 L2 ) = v 2 - Dv( ) L1 + Ln L1 + L2

(2)

where Dv is the difference of instantaneous speeds between two sampled points, computed by ( v2 - v1 ), v1 and v2 are instantaneous speeds recorded at first and second points, respectively. It should be noted that ve will be used as the dividing term in the next step. For that reason, in the special case where ve = 0 (in case of v1 = v2 = 0 ), the small speed value (e.g. 1 km/h) should be applied to ve for solvable purpose instead of 0 km/h. • Step 2: Approximation of decomposed travel time from the speed-distance relationship Due to the clear relationship among travel speed, travel time and traversing distance ( Dx during time t1 and t 2 ) can be expressed in terms of speed profile as Dx = ò vdt (in the case that dt is small enough). Consequently, the decomposed travel time of each link can be roughly estimated by applying the above relationship as follows:

ì2L /(v + v1 ) t Li ,dec = í i e î Li / ve

for i = 1, n otherwise

(3)

• Step 3: Calculation of time difference between sampling time interval and estimated travel time The travel time between two consecutive sampled points must correspond to the sampling time interval. Thus, the time difference between decomposed travel times from the previous step and a sampling time interval can be expressed as follows:

Dt = TTT -

n

åt

Li , dec

i =1

• Step 4: Tuning the decomposed travel time to sampling time interval

(4)

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As discussed previously, summation of decomposed travel times calculated in Step 2 needs to be equivalent with the sampling time interval. For that reason, in the tuning procedure, time difference calculated in Step 3 is added to the decomposed travel time in each link according to the ratio between individual link decomposed travel time and total decomposed travel time as illustrated in Eq. (5). It should be noted that to ensure that the adjusted decomposed travel times always have positive values and lie within the sampling time interval, the minimum and maximum boundaries 0 £ t Li, dec £ TTT should be applied.

æ ç t ¢Li ,dec = min{max{t Li , dec + Dt ç ç è

t Li ,dec

å

n

i =1

t Li , dec

ö ÷ ÷, 0}, TTT } ÷ ø

(5)

• Step 5: Re-estimation of speed at the end points of the link from adjusted decomposed travel time From the speed-time-distance relationship, the speeds at the end points of the link calculated from adjusted decomposed travel time in each link ( ve ,i ) can be estimated using Eq. (6). It should be noted that the lower and upper boundaries for ve ,i should be applied to ensure that the adjusted speeds in this step have positive values and are not more than the rational driving speed. In this paper, the speed limit was employed as the upper boundary. However, another appropriate value could be used instead; for instance, free flow speed.

¢ ,dec ) - vi ,0}, speed li mit} ìmin{max{(2 Li / t Li v e ,i í ¢ ,dec ) - vi ,0}, speed li mit} îmin{max{( Li / t Li

for i = 1, n otherwise

(6)

• Step 6: Re-adjusting speed at the end point of link The adjusted speed at the end point of link ( v e¢ ) can be approximated from the adjusted decomposed travel time in each link ( ve , i ) by weighing with the distance proportion as follows:

ve¢ =

n

å i =1

(ve,i ( Li /

n

å L )) i

(7)

i =1

Substitute ve¢ calculated from Eq. (7) into Eq. (3) in place of ve and recalculate Step 2 to Step 6 until the adjusted decomposed travel time of each link ( t ¢L ,dec ) is convergent. 3. Experiments and methodology 3.1. Studied corridor and data gathering technique In order to validate the proposed technique, the 4.07 km in-bound urban roadway comprising 6 links with different length varying from 0.2 to 1.24 km partitioned by 5 signalized intersections in Bangkok Metropolis was selected as the test corridor for gathering high resolution probe data. The field data were collected from 15 GPS equipped probe vehicle runs throughout the study site with a sampling time interval of every 1 second. The time period for data collection was from 6:00 am to 4:00 pm to ensure that both congested and uncongested traffic conditions were included in the dataset. From high resolution probe data, the testing scenarios were simulated to the sparsely distributed data into three testing campaigns for representing the more often used sampling time interval in reality; sampling every 15, 30 and 60 seconds, respectively. As the bias on the estimation results could occur if only one sampling position on the link was used, in this study various initial conditions of samplings were used. Therefore, the re-sampling technique was applied in this study for diminishing the bias in the sampling process. From each re-sampling time interval, for instance sampling every 30 seconds, the combination of different starting times can be expressed as follows: Combination 1: j, j+30, j+60, j+90,…



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Combination 2: j+1, j+31, j+61, j+91,… … Combination 30: j+29, j+59, j+89, j+119,… The expected link travel time from vehicle k which traversed throughout link i can be calculated by averaging the results from all combination cases as:

TTk ,i =

1 m

m

å tt

(8)

k, j

j =1

where m is the number of combination cases (or sampling moment), tt k , j is the estimated travel time of link i using data gathered from vehicle k with the sampling moment j . 3.2. Performance indicators To display the effectiveness of the proposed technique, the estimation results from the speed-time –distance technique in both complete link and local contexts were assessed and compared with the baseline technique by means of various indicators. The Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) were applied as the accuracy indicators for complete link travel time estimation, since MAPE can express the error in generic percentage whereas RMSE presents the differences between values from estimation and observation.

MAPE =

100 n

n

å

TTk ,i ,est - TTk ,i ,obs TTk ,i ,obs

k =1

n

å (TT

k ,i , est

RMSE =

k =1

(9)

- TTk ,i ,obs ) 2 n

(10)

where TTk ,i , est denotes the estimated travel time of link i using data recorded from vehicle k , TTk ,i , obs is the observed travel time of link i from vehicle k , and n is the total number of probe runs throughout link i . In comparing the two approaches, the Percentage of Improvement (PoI) was selected as the indicator for performance measurement. The PoI of travel time estimation from the proposed technique compared to the benchmark technique on segment j , can be calculated as follows:

PoI j =

RMSE baseline, j - RMSE prop osed , j RMSE baseline , j

(11)

where RMSEbaseline, j denotes the RMSE on segment j from the estimation using the baseline method (simple timedistance method), RMSE proposed, j denotes the RMSE on segment j from the estimation using the speed-timedistance method.

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4. Results and discussions As discussed previously, the investigation on the validation and performance of travel time allocation techniques can be evaluated in both complete link and local levels. Therefore, in this section, the results are presented and discussed in both complete link and intersection levels for examining the correctness of the proposed technique compared with the baseline approach. For representing the application of probe vehicles in reality, the testing scenarios were simulated from the high resolution observed data (ground truth) and divided into three testing campaigns with sparsely sampling time intervals from 15, 30 and 60 seconds, respectively. 4.1. Complete link travel time estimation Based on data collected from 15 probe runs throughout the studied corridor which comprises 6 links and 7 intersections, the accuracy on travel time allocations from both the proposed (speed-time-distance relationship) and baseline techniques (time-distance relationship) in complete link travel time estimation is illustrated in Table 1. From Table 1, it can be observed that the less frequent sampling time interval decreases the correctness of estimation from both models. In the proposed technique, as the sampling time interval increases from 15 to 60 seconds, average MAPE increases from 1.14 to 6.59%, and average RMSE also increases from 1.05 to 6.17 seconds. On the other hand, the baseline technique provides poorer estimation results as reflected by the steep increase on average MAPE from 2.04 to 10.46% and average RMSE from 1.85 to 9.26 seconds, while the sampling time interval rises from 15 seconds to 60 seconds respectively. In addition, as depicted by PoI values, the accuracy of estimation is significantly boosted in all test campaigns when employing the proposed technique, compared to the baseline approach. As shown in Fig. 3, the total time spent in each link affects the accuracy level of link travel time estimation in the case that MAPE is employed as the indicator for accuracy. In this case, since the accuracy is represented by the error time per total travel time, in the longer link or link with higher travel time, the accuracy from both techniques are higher than in the shorter ones indicated by lower MAPE values, as illustrated in Fig.3a. This occurred because the portion of the known travel time (travel time in this section does not need to be allocated, as illustrated in Fig. 1(a)) is a lot greater than the unknown cases (Fig. 1(b), (c), which need to be allocated) in the more time consuming link. In comparison, the relationship among link travel times and the time difference between estimated and observed values indicated by RMSE are fluctuated as illustrated in Fig. 3(b). This could be caused by the local characteristics (e.g. traffic movement behaviors at each intersection) and the error combination from both ends of link as discussed previously. Even so, the proposed technique still provides superior results to those from the baseline approach as seen by the lower RMSE in all test scenarios. Table 1. Performance measurements at complete link level of proposed and baseline method in different sampling time intervals. Link Average observed travel time (s) Average observed speed (km/h) Sampling time 15 seconds Sampling time 30 seconds Sampling time 60 seconds

MAPE (%) RMSE (s) PoI (%) MAPE (%) RMSE (s) PoI (%) MAPE (%) RMSE (s) PoI (%)

Baseline Proposed Baseline Proposed Baseline Proposed Baseline Proposed Baseline Proposed Baseline Proposed

AB 66.67 17.56 3.38 1.97 3.23 2.23 31.02 7.37 4.67 6.74 4.68 30.56 16.38 10.13 12.56 9.01 28.23

BC 102.00 28.08 1.96 1.11 2.18 1.26 42.15 4.35 2.6 4.97 2.82 43.22 8.94 6.01 10.19 7.57 25.74

CD 38.20 20.25 4.79 2.84 2.23 1.27 42.99 11.7 5.47 5.4 2.31 57.35 23.73 16.13 10.86 6.89 36.58

DE 315.13 28.43 0.56 0.22 1.31 0.63 51.76 1.54 0.64 3.46 1.69 51.09 3.77 1.91 7.92 5.06 36.09

EF 196.67 20.62 0.39 0.24 0.74 0.41 44.92 1.06 0.49 1.96 0.97 50.62 3.58 1.35 6.09 2.68 56.09

FG 119.73 15.43 1.16 0.44 1.39 0.5 64.18 3.1 1.41 3.85 1.92 50.20 6.34 4.03 7.93 5.84 26.35

Average 2.04 1.14 1.85 1.05 46.17 4.85 2.55 4.40 2.40 47.17 10.46 6.59 9.26 6.17 34.85



Porntep Puangprakhon et S/ al.Transportation / Transportation Research Procedia0025C (2017) 2213–2226 Puangprakhon, P and Narupiti, Research Procedia (2017) 000–000

(a)

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(b)

Fig. 3. Relationship between MAPE, RMSE and link travel time from the proposed and baseline method in various sampling time intervals.

4.2. Travel time allocation at local level (intersection level) As described previously about the effects of balancing out of errors from both ends of link and also effects of portion of known travel time within the link (as illustrated in Fig. 1(a)), which could create biases in the complete link travel time estimation, this section introduces the analysis at local level (intersection level) for diminishing the bias and provides the closer look at the effectiveness of travel time allocation by the baseline and proposed techniques. In this section, the results and discussions on travel time allocation from both techniques at local level (or at intersection instead of complete link) is demonstrated. The section starts with the definition of local level and time region used in this study, followed by the travel time allocation results at each intersection, then the results according to the different movement behaviors at each intersection are demonstrated and discussed. • Definition and time region for evaluating local level travel time In this study, the time region for evaluating local level or intersection level was defined and shown in Fig. 4. Fig. 4 displays an example of the speed and time tracked from the probe vehicle during traversing through link AB. The time spent for traversing within this link can be determined by the time difference between entrance and exit time of the link (the entrance time is when the vehicle passed intersection A and the exit time is when vehicle passed intersection B which were 08:08:00 and 08:09:19 respectively). In the case that sampling time interval is 15 seconds, the time region used for evaluating the accuracy of travel time allocation at local level at intersection A will cover the region from 15 seconds before and after the time that the vehicle passed intersection A (from 08:07:45 to 08:08:15 as depicted in Fig.4). This is because, in the analysis part, this time period will cover all the combinations of sampling time at intersection A that are used for testing the accuracy of travel time allocation as previously described in section 3.1. Therefore, in this example, totally 15 combinations from 15 sampling cases starting from the first case recorded at 08:07:45 and 08:08:00 , second case at 08:07:46 and 08:08:01,…, and the fifteenth case at 08:08:00 and 08:08:15 will be combined together and used for evaluating the accuracy of both techniques at local level of intersection A.

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Time region for analyzing intersection B

Time region for analyzing intersection A

Traffic movement direction Fig. 4. Time region for local level (intersection level) analysis in the case that sampling time interval is 15 seconds.

• The evaluation of travel time allocation at local level As illustrated in Table 2, travel time allocation resulted from the proposed technique is superior to that of the baseline approach in all intersections and sampling intervals. The estimation error is smallest in the shortest sampling interval, but increases as the sampling interval increases. MAPE values in Table 2 are significantly greater than in Table 1 as all the allocation cases in local context are unknown as depicted in Fig. 1(b) and 1(c), unlike in complete link level in Fig. 1(a). Additionally, the average PoI values ranging between 30-40% also show considerably better results than the proposed technique in the local context. • Effects of stopping behavior at intersection region The movement behavior of the vehicle within the area of intersection (within the time region as depicted in Fig.4.) could affect the accuracy level of both models due to different basic assumptions. Therefore, besides the overall picture at each intersection given in Table 2, an in-depth analysis by considering stopping behavior from the vehicle speed profile is performed. In this study we defined the “intersection with stopping behavior” as the intersection where the probe vehicle has at least one stopped delay within one sampling interval prior to or after the recorded time at the intersection point (as depicted by red region in Fig.4). As shown in Fig. 5, the estimation errors from both techniques are significantly higher at the intersection with stopping behavior (which generally contained a highly fluctuated speed profile). Still, the proposed technique offers better outcomes in all cases. This is because the baseline approach allocates travel time by assuming a constant speed profile among two consecutive probe points and this is far from the real traffic behavior particularly with stop and go movement. On the other hand, the proposed technique could reflect the fluctuation of the speed profile by assuming a linear relationship among recorded instantaneous speeds and speed at the end points of the link using the speed-time-distance relationship in the tuning process to find speed at the end points of the link from travel time allocation. In Fig. 5, although the proposed technique can represent better speed variation than the baseline approach, the PoI values at the intersection without stopping behavior are higher than the stopping ones. This is because the RMSE (or dividing term) of the “no stopping cases” are significantly lower than the “stopping case”. Therefore, even though the proposed technique can reduce higher quantity of RMSE in the “stopping cases”, the effect from the smaller dividing term in “no stopping cases” will lead them to the higher PoI value.



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Table 2. Performance measurement at intersection level of proposed and baseline method in different sampling time intervals. Intersection

A B C D E F G Average Baseline 33.21 15.53 20.22 16.35 7.72 7.92 16.59 16.79 MAPE (%) Proposed 23.64 10.53 15.09 7.83 5.64 5.77 9.12 11.09 Sampling time 15 RMSE Baseline 3.30 1.28 1.79 1.37 0.68 0.75 1.42 1.51 seconds Proposed 2.63 0.88 1.37 0.74 0.45 0.58 0.77 1.06 (s) PoI (%) 20.46 31.16 23.64 46.03 33.41 23.11 46.10 31.99 Baseline 31.52 18.51 21.37 22.87 11.81 9.51 21.92 19.64 MAPE (%) Proposed 23.35 14.17 14.78 11.20 5.40 4.92 12.04 12.27 Sampling time 30 RMSE Baseline 5.85 3.48 4.05 3.73 2.23 1.62 4.07 3.58 seconds Proposed 4.67 2.37 2.44 2.17 0.93 0.95 2.11 2.23 (s) PoI (%) 20.16 31.86 39.81 41.75 58.32 41.10 48.21 40.17 Baseline 31.73 23.32 22.38 34.94 22.97 12.61 22.55 24.36 MAPE (%) Proposed 23.81 18.55 18.32 25.44 10.03 6.70 18.67 17.36 Sampling time 60 RMSE Baseline 10.74 7.81 8.45 11.49 7.92 4.32 8.89 8.52 seconds Proposed 8.46 6.50 6.45 8.48 3.68 2.14 6.98 6.10 (s) PoI (%) 21.19 16.82 23.65 26.16 53.59 50.54 21.50 30.49 *Average decomposed travel times in each link (upstream and downstream links) at intersection are 7.5, 15 and 30 seconds for sampling time interval 15, 30 and 60 seconds respectively.

PoI (%)

(a) MAPE

(b) RMSE and PoI

Fig. 5. MAPE, RMSE and PoI of decomposed travel time from the baseline and proposed technique categorized by stopping behavior.

• Effects of the average speed within time region of each intersection The average travel speed at intersection could be used to represent the state of traffic at that location, the higher movement speed the better traffic conditions. Therefore, the relationship between the average travel speed within the intersection region and the error from each allocation technique were presented. In Fig.6, the percentage of error from travel time allocation per size of sampling interval is represented in the vertical axis (e.g. if allocation error is 3 seconds and sampling time interval is 15 seconds, the error in decomposed travel time per sampling time interval will be 20 %), while the horizontal axis indicates the average travel speed of the probe vehicle inside the intersection region. From Fig. 6, the errors of travel time allocation from both techniques decrease when the average travel speed at the intersection region increases. This points out the advantages of both techniques in the uncongested traffic condition. Besides, the speed profile in the uncongested condition (higher average speed) is smoother and close to the constant value due to the better agreement with the results from the baseline technique with constant speed assumption. However, in all sampling time intervals and all states of traffic, the proposed technique yields the superior results.

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• Effects of the speed fluctuation within the time region of each intersection A closer consideration is made on the effects of speed fluctuation at intersection level on the accuracy of both techniques. The relationship between the travel time allocation errors and the standard deviation of speed is illustrated in Fig.7. The standard deviation of speed on the horizontal axis can be calculated from all recorded instantaneous speeds (recorded every 1 second) within the intersection region, while the vertical axis can be determined as described in the previous section. From Fig.7, as the speed fluctuation increases (higher standard deviation), the error of estimation from the baseline technique increases massively; e.g. from 5% to 20% approximately when the standard deviation in speed changes from 5 km/h to 25 km/h, while the error from the proposed technique is still at the same level (approximately 5%). Results illustrated in this section imply the superior outcomes from the proposed technique particularly in the region with highly fluctuated speed e.g. at signalized intersection, congested condition or interrupted flow.

(a) Sampling time interval 15 sec

(b) Sampling time interval 30 sec

(c) Sampling time interval 60 sec Fig. 6. Relationship between the average travel speed within intersection region and travel time allocation error.

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(a) Sampling time interval 15 sec

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(b) Sampling time interval 30 sec

(c) Sampling time interval 60 sec Fig. 7. Relationship between standard deviation of speed within intersection region and travel time allocation error.

5. Conclusions This paper addresses the problem of travel time allocation which is considered as one of the vital steps required in obtaining the link travel time from probe data. In this paper, we have proposed the new analytical algorithm for allocating travel time into individual links by integrating instantaneous speed together with tracked locations and time stamp. From traffic state information represented by instantaneous speed data, the proposed model applies the speed-time-distance relationship for model tuning and then allocates travel time into each link. The performance of the proposed model in travel time allocation was tested and compared with the widely used technique in both complete link and local levels using high resolution (ground truth) field data. It is found that the proposed technique provides a significant improvement in travel time allocation in both complete link and intersection levels compared to the benchmark technique. Moreover, from the in-depth analysis at local level, the stopping (traffic) behavior within the intersection region affects the level of accuracy on both

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models. Accuracy from both techniques is lower at the intersections with stopping behavior due to its complicated movement behavior. Still, the proposed technique outperforms the baseline approach in both intersections with low and high stopped delays. The average speed of vehicle within the intersection region, which represents the local traffic state, also influences the model accuracy. Intersections with the higher average speed can achieve the higher accuracy level in both methods. Furthermore, analysis on the effects of speed fluctuation at local level points out the outstanding performance of the proposed model in addressing the complicated movement behavior compared to the baseline approach. It is recommended for the future research to validate this technique based on a larger dataset which comprises various types of road, types of intersection, traffic conditions, and turning movements. References Bejan, A.I., Gibbens, R.J., Evans, D., Beresford, A.R., Bacon, J. Friday, A., 2010. Statistical Modelling and Analysis of Sparse Bus Probe Data in Urban Areas. 13th International IEEE conference on Intelligent Transportation Systems. Madeira Island, Portugal. Billings, D., Yang, J.S., 2006. Application of the ARIMA Models to Urban Roadway Travel Time Prediction - A Case Study. IEEE International Conference on Systems, Man, and CyberneticsTaipei, Taiwan. Esawey, M. E., Sayed, T., 2009. Travel Time Estimation in an Urban Network Using Sparse Probe Vehicle Data and Historical Travel Time Relationships. 88th meeting of the Transportation Research Board. Washington D.C., USA. Hellinga, B., Izadpanah, P., Takada, H., Fu, L., 2008. Decomposing Travel Times Measured by Probe-based Traffic Monitoring Systems to Individual Road Segments. Transportation Research Part C, 16, 768-782. Herring, R., Hofleitner, A., Abbeel, P., Bayen, A., 2010. Estimating arterial traffic conditions using sparse probe data. 13th International IEEE conference on Intelligent Transportation Systems. Madeira Island, Portugal. Hofleitner, A., Bayen, A., 2011. Optimal Decomposing of Travel Times Measured by Probe Vehicles Using a Statistical Flow Model. 14th International IEEE conference on Intelligent Transportation Systems. Washington, D.C., USA. Jiang, G., Chang, A., Zhang, W., 2009. Comparing of Link Travel-time Estimation Methods based on GPS Equipped Floating Car. International Conference on Transportation Engineering. Chengdu, China. Li, Q., Miwa, T., Morikawa, T., 2008. Preliminary Analysis on Link Travel Time for Probe-Based Estimation Method by Microscopic Simulation. International Journal of ITS Research, Vol. 6, No.1, 21-27. Nanthawichit, C., Nakatsuji, T., Suzuki, H., 2003. Application of Probe Vehicle Data for Real-Time Traffic State Estimation and Short-Term Travel Time Prediction on a Freeway. Transportation Research Record, Journal of the Transportation Research Board, No. 1855, 49-59. Neumann, T., 2013. Accuracy of Distance-based Travel Time Decomposition in Probe Vehicle Systems. Journal of Advanced Transportation, published online DOI: 10.1002/atr.1251. Pu, W., Lin, J., 2009. Real-Time Estimation of Urban Street Segment Travel Time Using Buses as Speed Probes. Transportation Research Record: Journal of the Transportation Research Board, No. 2129, 81–89. Puangprakhon, P., Narupiti, S., 2015. Arterial Speed Studies Based on Data from GPS Equipped Probe Vehicle. Journal of the Eastern Asia Society of Transportation Studies, Vol.11, 30-43. Puangprakhon, P., Narupiti, S., 2014. Probe-Based Travel Time Decomposition Using Speed-time-distance Approximation Technique. 21th ITS World Congress, CD-ROM, Michigan, USA. Uno, N., Kurauchi, F., Tamura, H., Iida, Y., 2009. Using Bus Probe Data for Analysis of Travel Time Variability. Journal of Intelligent Transportation Systems, Vol.13(1), 2-15. Vanajakshi, L., Subramanian, S.C., Sivanandan, R., 2009. Travel Time Prediction under Heterogeneous Traffic Conditions using Global Positioning System Data from Buses. IET Intell. Transp. Syst., Vol. 3, No. 1, 1–9. Wei, Z., Jianmin, X., Haifeng, W., 2007. Urban Traffic Situation Calculation Methods Based on Probe Vehicle Data. J Transpn Sys Eng & IT, Vol.7, Issue 1, 43−49. Zheng, F., Van Zuylen, H., Chen, Y., 2010. An Investigation of Urban Link Travel Time Estimation based on Field Sparse Probe Vehicle Data. 89th meeting of the Transportation Research Board. Washington D.C.,USA. Zheng, F., Van Zuylen, H., 2013. Urban Link Travel Time Estimation based on Sparse Probe Vehicle Data. Transportation Research Part C, Vol. 31, 145-157.