Variation Based Online Travel Time Prediction Using Clustered Neural Networks

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1 Variation Based Online Travel Time Predition Using lustered Neural Networks Jie Yu, Gang-Len hang, H.W. Ho and Yue Liu Abstrat-This paper proposes a variation-based online travel time predition approah using lustered Neural Networks with traffi vetors extrated from raw detetor data as the input variables. Different from previous studies, the proposed approah deomposes the orridor travel time into two parts: ) the base term, whih is predited by a fuzzy membership-value-weighted average of the lustered historial data to reflet the primary traffi pattern in the orridor; and 2) the variation term, whih is predited through the alibrated luster-based artifiial neural network model to apture the atual traffi flutuation. To evaluate the effetiveness of the proposed approah, this paper has onduted intensive numerial experiments with simulated data from the mirosopi simulator ORSIM. Experimental results under various traffi volume levels have revealed the potentials for the proposed method to be applied in online orridor travel time predition. A I. INTRODUTION S is well reognized, travel time information plays an important role in the Advaned Travelers Information Systems (ATIS), whih has the potential of providing dynami route guidane for travelers, inreasing the reliability in road networks, and alleviating ongestion and its negative environmental/soial side effets []. Travel time predition, whih refers to the alulation of the travel time at the time the vehiles start their trips, is a highly omplex and hallenging problem, as travel times are the results of omplex nonlinear interations of heterogeneous groups of driver-vehile ombinations. Furthermore, exogenous fators (suh as availability of vehile detetor system, traffi delay and missing of real-time data) are often beyond ontrol of the predition model. In review of the literature, researhers have attempted to implement both parametri and nonparametri approahes to foreast travel times. Among parametri models, promising results were ahieved using regression models [2], time-series models [3], and Kalman Filter models [4]. Meanwhile, lots of researhers have devoted onsiderable Manusript reeived May 3, Jie Yu is Researh Assoiate at University of Maryland, ollege Park, MD 20742, USA ( yujie@umd.edu). Gang-Len hang is professor at University of Maryland, ollege Park, MD 20742, USA ( gang@umd.edu). H.W. Ho is Researh Assoiate at University of Maryland, ollege Park, MD 20742, USA (orresponding author; phone: ; hwho@umd.edu ). Yue Liu is Researh Assistant at University of Maryland at ollege Park, ollege Park, MD USA troybest@ umd.edu) attention to nonparametri models, whih inlude artifiial neural network (ANN) models [, 5, 6, 7, 8], nearest neighborhood models [9], and simulation models [0,, 2], due to their robust performane. Many studies have demonstrated that ANNs have the potential to aurately predit travel time on freeways, inluding modular neural network model [5], spetral basis neural network model [6], and state-spae neural network model [, 7] et. Nearest neighborhood model an provide reasonably good performane when a suffiient number of similar historial ases an be obtained. Simulation-based approahes (e.g., SBOTTP [0], DYNAMIT []) an also be used as a ost-effetive tool for travel time predition. Despite the promising work by previous studies, the following drawbaks remain to be further addressed: Most studies predited travel times in a link-based way assuming that orridor travel time is the addition of the travel times on its onsisting links during the predition period. However, those approahes may not be reliable due to the neglet of time lag between predition periods of different links and aumulation of link predition errors; Some studies use travel times in previous time periods as inputs, whih limits them to be applied online beause travel times in previous time periods may not be available before they are realized; Previous studies treated the travel time as a single omponent and predit it diretly, whih may have large predition errors. To aommodate the aforementioned issues, this paper presents a variation based approah for real-time travel time predition fous on the following speifi issues: The proposed predition model predits travel time at the entire orridor level rather than the link-based level to overome the aumulation of link travel time predition errors, as well as to fully take advantage of the historial orridor travel time data; The proposed predition model takes detetor data instead of travel time in previous intervals as inputs and is more suitable to be eligible for online appliation; The proposed predition model tries to make the predition results more robust by deomposing the orridor travel time into a base term and a variation term. The base term an make full use of the historial data to apture the primary traffi pattern in the orridor, while predition of the variation term will represent the traffi

2 flutuation. This paper is organized as follows. A model framework that onsists of online and offline proedures will be introdued in Setion II. Setion III presents five key funtional modules of the proposed model, inluding data olletion module, data proessing and pattern identifiation module, base travel time predition module, travel time variation predition module, and final travel time output module. Setion IV evaluates the performane of the proposed model on a segment of US50 eastbound to Oean ity, Maryland under different demand senarios using data from ORSIM. Finally, a onluding disussion follows in Setion V, inluding a summary of the proposed approah and future extensions. II. MODEL FRAMEWORK This setion presents the model framework (see Fig. ) for the proposed online travel time predition approah. As shown in Fig., the entire framework for online travel time predition onsists of two main proedures: Off-line proedure: Integrated with a omprehensive historial database, the off-line proedure funtions to ) ollet, store and provide required traffi data (i.e. volume, speed, and historial travel time); 2) lassify different traffi patterns based on lustering tehniques and alulate the mean travel time for eah luster; and 3) alibrate ANN models for eah luster; On-line proedure: Based on the lustering results and alibrated models from the off-line proedure, the on-line proedure serves to fulfill the following five tasks. ) Proess real-time detetor data and extrat the input traffi vetor; 2) alulate fuzzy membership values of the extrated traffi vetor for all lusters; 3) Predit the base travel time term based on the membership-value-weighted average of all luster means; 4) Apply the lustered ANN model to predit the variation term for eah luster, and alulate their membership-value-weighted average as the travel time variation term; 5) Sum up the base term and variation term to output the total predited travel time. During the real-world operation, the offline and online proedures will interat with eah other through various seamlessly integrated modules, inluding data olletion module [(A), (B), and (F)], data proessing and pattern identifiation module [() and (G)], base travel time predition module [(D) and (H)], travel time variation predition module [(E) and (I)], and final travel time output module [(J)]. Eah of its five funtional modules will be elaborated below. Fig. A oneptual framework for online travel time predition

3 A. Data olletion Module III. KEY MODULES This module provides basi input information to both online and offline models for travel time predition. It inludes two parts: historial data arhiving and real-time detetor data olletion. A omprehensive offline database plays a key role in arhiving and organizing historial data, inluding the following information: Historial traffi volume & speed data (from roadside detetors) representing different traffi patterns at the target orridor in different time periods; Historial orridor travel time in one time period ahead (either from diret measurement or offline estimation approahes). For example, for the reord of historial speed and volume data olleted in the time period k, historial orridor travel time in time period k+ will be mathed with it. This module is also responsible for olleting real-time traffi volume & speed (from detetion equipment) in eah time period to represent the urrent traffi pattern on target orridor and update the predition results. B. Data Proessing and Pattern Identifiation Module Traffi data olleted from the entire orridor in the preeding time periods are important parameters for identifying future travel time patterns. However, it is diffiult to diretly apply those raw data to represent the traffi pattern when the number of detetors and seleted preeding time periods is large. This module funtions to effiiently redue the dimensionality of raw data by extrating one traffi vetor whih an represent the dynami traffi patterns for the target orridor, as shown in Equation () - (2): r r r r ϕ( k) = { ϕ( k), L, ϕi ( k), L, ϕn( k) } () Δki r si ( k j + ) wi ( j) r j= (2) ϕi ( k) = Δki w ( j) j= i i : Index of link; k : Index of time periods; j : Index of previous time intervals from to Δ k ; i n : Number of links in the target orridor; r ϕ(k) : A 2n-dimensional vetor at the time period k; r ϕi (k) : A 2-dimensional vetor (volume, speed) on link i at the time period k; r s i (k) : A 2-dimensional traffi data vetor (volume, speed) for the i th detetor at the time period k; w i ( j) : Weight of previous time period j for link i; Δ k i : Num. of the preeding time periods used for link i. In this module, the 2n-dimensional vetor r ϕ(k) whih onsists of those different 2-dimensional vetors r ϕi(k) represents the speifi traffi pattern for the entire orridor up to time period k (inluding both urrent and previous time period). r ϕi(k) is a weighted measure of traffi status of link i up to the time period k. To aount for the maximal possible impat of previous traffi data, the number of previous time periods ( Δ ) used for alulating r ϕ (k) is hosen to be the ki maximal estimated travel time from detetor i to destination based on historial data, as shown in Fig. 2. It would be reasonable to expet that weights for traffi data in the more reent time period are higher, based on the assumption that the more reent information would influene the future states more. Fig. 3 demonstrates the potential weight funtions used for different time periods. In this module, we take the linear form weight funtion as shown in Equation (3): [ Δki j] wi ( j) = wmin + [ wmax wmin] j [, Δki ] (3) [ Δki ] w max : Maximal weight (.0 in this paper); w min : Minimal weight (0. in this paper). Fig. 2 Num. of the preeding time periods used for different links Fig. 3 Weight funtions for different time periods. Base Travel Time Predition Module This module funtions to predit the base travel time in order to apture the primary traffi pattern at the target orridor. As is reported in the literature and observed in the field survey, traffi patterns on a orridor may vary signifiantly during the morning peak hours, evening peak hours, and off-peak hours due to the omplex interations of many fators with time-varying natures. Therefore, it would be more aurate to predit the base travel time by pre-lassifying the traffi patterns into several simpler lasses. i

4 onsidering the atual lassifiation sheme is not known as a priori, an unsupervised learning model may be more suitable for lustering traffi patterns. This module employs a fuzzy -means lustering algorithm, whih had given outstanding results in previous related studies [5]. As shown in Fig. 4, the proedure for base travel time predition inludes both off-line and on-line parts. Based on the omprehensive historial database provided by data olletion module, the off-line proedure aims to identify luster enters, and as well as alulate the mean travel time TT for eah luster, whih is a fuzzy membership value weighted average of historial travel time samples. On the other hand, the on-line part first aquires real-time traffi pattern vetors at time period k, and then alulates luster membership values μ ( ϕ(, whih defines the degree to whih the vetor r ϕ(k) belongs to the th luster. Finally, this module predits the base travel time by onduting a μ( ϕ( weighted average of eah luster mean TT, as shown in Equation (4): TT ( k b TT = + ) = = μ ( ϕ( μ ( ϕ( TT b ( k +) : Predited base travel time at time period k+ for the orridor; TT : Mean travel time orresponding to luster ; μ ( ϕ( : Fuzzy membership value of vetor r ϕ(k) orresponding to luster ; : Number of lusters. (4) D. Travel Time Variation Predition Module This module aims to predit the variation of travel time to reflet the real-time traffi flutuation in the target orridor through pre-alibrated lustered Neural Network models. For eah luster, the feed-forward Multilayer ANN was seleted and the bak-propagation algorithm was implemented to train the neural network in order to minimize the errors between the atual and desired output. Fig. 5 illustrates the topology of the Neural Network model for eah luster. Eah neuron in the input layer reeives inputs from r ϕi(k), and the output layer onsists of one neuron whih is the predited travel time variation on the target orridor at time interval k+ for eah luster. One hidden layer was determined for the bak-propagation struture. Similar to the proedure of alulating the base travel time, the travel time variation is predited as a fuzzy-membership -value-weighted average of the outputs from all luster based Fig. 4 Proedures for base travel time predition using fuzzy -means lustering algorithm ANNs, as shown in Equation (5): ΔTT( k + ) = = ΔTT ( k + ) μ ( ϕ( = μ ( ϕ( ΔTT ( k +) : Predited travel time variation at time period k+; ΔTT ( k +) : Predited travel time variation at time period k+ for the th luster. E. Final Travel Time Output Module The total predited travel time at time period k+ is the sum of base travel time and travel time variation, given by the following Equation: (5)

5 Fig. 5 Topology of the Neural Network model for travel time variation predition TT( k + ) = TTb ( k + ) + ΔTT( k + ) (6) A. Test Network IV. NUMERIAL EXPERIMENT An approximately 7. mile setion of US50 eastbound to Oean ity, MD was modeled in ORSIM (see Fig. 6) to generate the data for lustering, ANN training, and testing. This arterial setion was omprised of 2-lane links and 0 signalized intersetions with speed limits varying between 35 and 55 miles per hour. detetors, whih programmed to reord flow and speed data, were loated at the upstream of eah link. B. Experiment Design Fig. 6 Illustration of the study area To reate a training and testing dataset under different traffi onditions, the travel demand loadings on the network lasting from 7:30am to 8:30pm were varied hourly based on the observed real world traffi pattern, as shown in Table I, in whih free-flow traffi, moderated ongested traffi, and heavily ongested traffi are all onsidered. As the first 30 minutes of simulation is used to warm-up and some of the vehiles departure in the last 30 minutes ould not arrive the destination before the end of the simulation, 2-hour (8:00 am ~ 8:00 pm) detetor data and travel times are used for analysis data reords (0days x 2 hours/day x 60 time periods/hour) are generated for training and testing the proposed models. Among these 7200 data reords, nearly 6,500 samples (9 days x 720 periods a day) were employed to ) identify luster enters (the number of luster we hose in this paper is 0) and alulate the fuzzy-membership-value-weighted mean travel time for eah luster; and 2) alibrate ANN models for eah luster. Meanwhile, 720 samples were used to validate the performane of the proposed models. TABLE HOURLY VARIED TRAVEL DEMAND LOADING. Performane Evaluation Fig. 7 shows the omparison of the predited travel time and the ORSIM results. The x-axis denotes the departure time of day (i.e. from 8:00am~8:00pm) whereas the y-axis denotes the travel times in minutes. From the figure below, we an see that the predited travel times showed a very similar trend to the simulated results. Fig. 7 omparison of predited travel time with ORSIM simulation results Table II evaluates the performane of the developed models by two indies: Root Mean Square Error (RMSE) and

6 Root Mean Square Perentage Error (RMSP). As indiated in the table below, one an reah the following findings: As a whole, the proposed models produe reasonably good results with.29 minute RMSE and RMSP; and For the peak hours in whih prediting travel time reliably is a hallenge, the proposed models an provide promising predition auray (with RMSP equal to 0.083) due to the embedded base term whih is apable of apturing primary traffi patterns. V. ONLUSION AND FUTURE EXTENSIONS This paper proposes a variation-based online travel time predition approah using lustered Neural Networks with traffi vetors extrated from raw detetor data as input variables. The total predited travel time is omprised of two parts: base travel time and travel time variation. The base term is predited by a fuzzy-membership-value-weighted average of the lustered historial data to reflet the primary traffi pattern, while the variation term is predited through the alibrated luster-based artifiial neural network model to apture the atual traffi flutuation. Numerial experiments on a segment of US50 eastbound to Oean ity, Maryland under different demand senarios using data from ORSIM illustrate that the proposed appoah is apable of reliably prediting orridor travel time. Although the results of the proposed approah are promising, a number of issues still need to be resolved in future studies: () The proposed models will be tested with field data under more omplex real world traffi onditions; (2) Advaned ANN strutures ould be employed to ahieve better predition performane; (3) Sensitivity analysis of the number of luster should be taken into aount to obtain the optimal number of lusters with the minimal predition errors. Researh Reord, No.768, pp. 57 6, National Researh ounil, Washington, D.., 200. [5] D. Park and L. Rilett, Foreasting multiple-period freeway link travel times using modular neural networks, Transportation Researh Reord, No.67, pp , National Researh ounil, Washington, D.., 998. [6] D. Park, L. Rilett, and G. Han, Spetral basis neural networks for real-time travel time forasting, J. Transp. Eng., vol. 25, no. 6, pp , November/Deember, 999. [7] J. W.. Van Lint, S. P. Hoogendoorn, and H. J. Van Zuylen, Aurate freeway travel time predition with state-spae neural networks under missing data, Transportation Researh Part 3, pp , [8]. H. Wei and Y. Lee, Development of freeway travel time foreasting models by integrating different soures of traffi data, IEEE Trans. Veh. Teh., vol. 56, no. 6, pp , November 2007 TABLE II PERFORMANE EVALUATION FOR TRAVEL TIME PEDITION [9] N. Zou, A reliable travel time predition system with sparsely distributed detetors, Ph. D. Dissertation, University of Maryland, [0] Y. Liu, P. W. Lin, X. R. Lai, G. L. hang and A. Marquess, Developments and appliations of simulation-based online travel time predition system: Traveling to Oean ity, Maryland, Transportation Researh Reord, No.959, pp , National Researh ounil, Washington, D.., [] M. Ben-Akiva, M. Bierlaire, D.Burton, H. N. Koutsopoulos, and R. Mishalani, Network state estimation and predition for real-time transportation management appliations. 8 st Transportation Researh Board Annual Meeting, Washington, D (D-ROM) REFERENES [] J. W.. Van Lint, Reliable Real-Time Framework for Short-Term Freeway Travel Time Predition. J. Transp. Eng., vol. 32, no. 2, pp , Deember, [2] J. Rie and E. V. Zwet A simple and effetive method for prediting travel time on freeway, IEEE Trans. Intell. Transp. Syst., vol. 5, no. 3, pp , Sep [3] D. Billings and J. S. Yang Appliation of the ARIMA Models to Urban Roadway Travel Time Predition - A ase Study, In Pro. of IEEE International onferene on Systems, Man, and ybernetis, pp , Taipei, Taiwan, 2006 [4] M. hen and I. J. hien, Dynami freeway travel time predition using probe vehile data: Link-based vs. path-base, Transportation