Bus travel time prediction using support vector machines for high variance conditions
Abstract
Real-time bus travel time prediction has been an interesting problem since past decade, especially in India. Popular methods for travel time prediction include time series analysis, regression methods, Kalman filter method and Artificial Neural Network (ANN) method. Reported studies using these methods did not consider the high variance situations arising from the varying traffic and weather conditions, which is very common under heterogeneous and lane-less traffic conditions such as the one in India. The aim of the present study is to analyse the variance in bus travel time and predict the travel time accurately under such conditions. Literature shows that Support Vector Machines (SVM) technique is capable of performing well under such conditions and hence is used in this study. In the present study, nu-Support Vector Regression (SVR) using linear kernel function was selected. Two models were developed, namely spatial SVM and temporal SVM, to predict bus travel time. It was observed that in high mean and variance sections, temporal models are performing better than spatial. An algorithm to dynamically choose between the spatial and temporal SVM models, based on the current travel time, was also developed. The unique features of the present study are the traffic system under consideration having high variability and the variables used as input for prediction being obtained from Global Positioning System (GPS) units alone. The adopted scheme was implemented using data collected from GPS fitted public transport buses in Chennai (India). The performance of the proposed method was compared with available methods that were reported under similar traffic conditions and the results showed a clear improvement.
Keyword : support vector machines, bus travel time prediction, approximate entropy, high variability, heterogeneous traffic
How to Cite
Bachu, A. K., Reddy, K. K., & Vanajakshi, L. (2021). Bus travel time prediction using support vector machines for high variance conditions. Transport, 36(3), 221-234. https://doi.org/10.3846/transport.2021.15220
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Chu, L.; Oh, J.-S.; Recker, W. 2005. Adaptive Kalman filter based freeway travel time estimation, in Transportation Research Board 84th Annual Meeting Compendium of Papers CD-ROM, 9–13 January 2005, Washington, DC, US, 1–21.
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Fan, W.; Gurmu, Z. 2015. Dynamic travel time prediction models for buses using only GPS data, International Journal of Transportation Science and Technology 4(4): 353–366. https://doi.org/10.1016/S2046-0430(16)30168-X
Fatima, E.; Kumar, R. 2014. Introduction of public bus transit in Indian cities, International Journal of Sustainable Built Environment 3(1): 27–34. https://doi.org/10.1016/j.ijsbe.2014.06.001
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Kumar, S. V.; Vanajakshi, L. 2014. Pattern identification based bus arrival time prediction, Proceedings of the Institution of Civil Engineers – Transport 167(3): 194–203. https://doi.org/10.1680/tran.12.00001
Kumar, B. A.; Vanajakshi, L.; Subramanian, S. C. 2014a. Patternbased bus travel time prediction under heterogeneous traffic conditions, in TRB 93rd Annual Meeting Compendium of Papers, 12–16 January 2014, Washington, DC, US, 1–16.
Kumar, V.; Kumar, B. A.; Vanajakshi, L.; Subramanian, S. C. 2014b. Comparison of model based and machine learning approaches for bus arrival time prediction, in TRB 93rd Annual Meeting Compendium of Papers, 12–16 January 2014, Washington, DC, US, 1–14.
Kwon, J.; Coifman, B.; Bickel, P. 2000. Day-to-day travel-time trends and travel-time prediction from loop-detector data, Transportation Research Record: Journal of the Transportation Research Board 1717: 120–129. https://doi.org/10.3141/1717-15
Lewis, C. D. 1982. Industrial and Business Forecasting Methods: a Practical Guide to Exponential Smoothing and Curve Fitting. Butterworth Scientific. 143 p.
Li, R. 2006. Enhancing Motorway Travel Time Prediction Models through Explicit Incorporation of Travel Time Variability. PhD Thesis. Monash University, Melbourne, Australia. 264 p.
Liu, H.; Van Zuylen, H. J.; Van Lint, H.; Chen, Y.; Zhang, K. 2005. Prediction of urban travel times with intersection delays, in Proceedings: 2005 IEEE Intelligent Transportation Systems, 13–16 September 2005, Vienna, Austria, 402–407. https://doi.org/10.1109/ITSC.2005.1520198
Liu, X.; Chien, S. I.; Chen, M. 2014. An adaptive model for highway travel time prediction, Journal of Advanced Transportation 48(6): 642–654. https://doi.org/10.1002/atr.1216
Makridakis, S. 1993. Accuracy measures: theoretical and practical concerns, International Journal of Forecasting 9(4): 527–529. https://doi.org/10.1016/0169-2070(93)90079-3
Mazloumi, E.; Rose, G.; Currie, G.; Sarvi, M. 2011. An integrated framework to predict bus travel time and its variability using traffic flow data, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 15(2): 75–90. https://doi.org/10.1080/15472450.2011.570109
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 1855: 49–59. https://doi.org/10.3141/1855-06
Padmanaban, R. P. S.; Divakar, K.; Vanajakshi, L.; Subramanian, S. C. 2010. Development of a real-time bus arrival prediction system for Indian traffic conditions, IET Intelligent Transport Systems 4(3): 189–200. https://doi.org/10.1049/iet-its.2009.0079
Patnaik, J.; Chien, S.; Bladikas, A. 2004. Estimation of bus arrival times using APC data, Journal of Public Transportation 7(1): 1–20. https://doi.org/10.5038/2375-0901.7.1.1
Pattanamekar, P.; Park, D.; Rilett, L. R.; Lee, J.; Lee, C. 2003. Dynamic and stochastic shortest path in transportation networks with two components of travel time uncertainty, Transportation Research Part C: Emerging Technologies 11(5): 331–354. https://doi.org/10.1016/s0968-090x(03)00029-9
Pincus, S. M. 1991. Approximate entropy as a measure of system complexity, Proceedings of the National Academy of Sciences of the United States of America 88(6): 2297–2301. https://doi.org/10.1073/pnas.88.6.2297
Rajbhandari, R. 2005. Bus Arrival Time Prediction Using Stochastic Time Series and Markov Chains. PhD Dissertation. New Jersey Institute of Technology, Newark, NJ, US. 157 p. Available from Internet: http://archives.njit.edu/vol01/etd/2000s/2005/njit-etd2005-038/njit-etd2005-038.pdf
Ramakrishna, Y.; Ramakrishna, P.; Lakshmanan, V.; Sivanandan, R. 2006. Bus travel time prediction using GPS data, in Map India 2006: 9th Annual International Conference and Exhibition, 30 January – 1 February 2006, Delhi, India.
Russo, R. 2021. Statistics for the Behavioural Sciences: an Introduction to Frequentist and Bayesian Approaches. Routledge. 330 p.
Schölkopf, B.; Smola, A. J.; Williamson, R. C.; Bartlett, P. L. 2006. New support vector algorithms, Neural Computation 12(5): 1207–1245. https://doi.org/10.1162/089976600300015565
Shalaby, A.; Farhan, A. 2004. Prediction model of bus arrival and departure times using AVL and APC data, Journal of Public Transportation 7(1): 41–61. https://doi.org/10.5038/2375-0901.7.1.3
Suwardo; Napiah, M.; Kamaruddin, I. 2010. ARIMA models for bus travel time prediction, Journal of the Institution of Engineers, Malaysia 71(2): 49–58.
Vanajakshi, L.; Rilett, L. R. 2004. A comparison of the performance of artificial neural networks and support vector machines for the prediction of traffic speed, in IEEE Intelligent Vehicles Symposium, 2004, 14–17 June 2004, Parma, Italy, 194–199. https://doi.org/10.1109/ivs.2004.1336380
Vanajakshi, L.; Rilett, L. R. 2007. Support vector machine technique for the short term prediction of travel time, 2007 IEEE Intelligent Vehicles Symposium, 13–15 June 2007, Istanbul, Turkey, 600–605. https://doi.org/10.1109/ivs.2007.4290181
Vanajakshi, L.; Subramanian, S. C.; Sivanandan, R. 2009. Travel time prediction under heterogeneous traffic conditions using global positioning system data from buses, IET Intelligent Transport Systems 3(1): 1–9. https://doi.org/10.1049/iet-its:20080013
Vapnik, V. N. 1999. An overview of statistical learning theory, IEEE Transactions on Neural Networks 10(5): 988–999. https://doi.org/10.1109/72.788640
Wall, Z.; Dailey, D. J. 1999. An algorithm for predicting the arrival time of mass transit vehicles using automatic vehicle location data, in Transportation Research Board 78th Annual Meeting, 10–14 January 1999, Washington DC, US, 1–10.
Wu, C.-H.; Su, D.-C.; Chang, J.; Wei, C.-C.; Ho, J.-M.; Lin, K.-J.; Lee, D. T. 2003. An advanced traveler information system with emerging network technologies, in Proceedings of 6th Asia-Pacific Intelligent Transportation Systems Forum, 4–9 October 2003, Taipei, Taiwan, 1–8.
Xu, H., Ying, J. 2017. Bus arrival time prediction with real-time and historic data, Cluster Computing 20(4): 3099–3106. https://doi.org/10.1007/s10586-017-1006-1
Yang, M.; Chen, C.; Wang, L.; Yan, X.; Zhou, L. 2016. Bus arrival time prediction using support vector machine with genetic algorithm, Neural Network World 26(3): 205–217. https://doi.org/10.14311/nnw.2016.26.011
Yu, B.; Lam, W. H. K.; Tam, M. L. 2011. Bus arrival time prediction at bus stop with multiple routes, Transportation Research Part C: Emerging Technologies 19(6): 1157–1170. https://doi.org/10.1016/j.trc.2011.01.003
Yu, B.; Song, X.; Guan, F.; Yang, Z.; Yao, B. 2016. k-nearest neighbor model for multiple-time-step prediction of shortterm traffic condition, Journal of Transportation Engineering 142(6): 04016018. https://doi.org/10.1061/(asce)te.1943-5436.0000816
Yu, B.; Yang, Z.; Yao, B. 2006. Bus arrival time prediction using support vector machines, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 10(4): 151–158. https://doi.org/10.1080/15472450600981009
Yu, Bin; Yang, Z.-Z.; Chen, K.; Yu, Bo. 2010a. Hybrid model for prediction of bus arrival times at next station, Journal of Advanced Transportation 44(3): 193–204. https://doi.org/10.1002/atr.136
Yu, Bo; Lu, J.; Yu, Bin; Yang, Z. 2010b. An adaptive bus arrival time prediction model, Journal of the Eastern Asia Society for Transportation Studies 8: 1126–1136.
Yu, Z.; Wood, J. S; Gayah, V. V. 2017. Using survival models to estimate bus travel times and associated uncertainties, Transportation Research Part C: Emerging Technologies 74: 366–382. https://doi.org/10.1016/j.trc.2016.11.013
Zhou, Y.; Yao, L.; Chen, Y.; Gong, Y.; Lai, J. 2017. Bus arrival time calculation model based on smart card data, Transportation Research Part C: Emerging Technologies 74: 81–96. https://doi.org/10.1016/j.trc.2016.11.014
Bian, B.; Zhu, N.; Ling, S.; Ma, S. 2015. Bus service time estimation model for a curbside bus stop, Transportation Research Part C: Emerging Technologies 57: 103–121. https://doi.org/10.1016/j.trc.2015.06.011
Cathey, F. W.; Dailey, D. J. 2003. A prescription for transit arrival/departure prediction using automatic vehicle location data, Transportation Research Part C: Emerging Technologies 11(3–4): 241–264. https://doi.org/10.1016/s0968-090x(03)00023-8
Chamberlain, R. G. 1996. GIS FAQ Q5.1: Great Circle Distance between 2 Points. Available from Internet: https://www.movable-type.co.uk/scripts/gis-faq-5.1.html
Chang, C.-C.; Lin, C.-J. 2011. LIBSVM: a library for support vector machines, ACM Transactions on Intelligent Systems and Technology 2(3): 27. https://doi.org/10.1145/1961189.1961199
Chen, M.; Liu, X.; Xia, J.; Chien, S. I. 2004. A dynamic bus-arrival time prediction model based on APC data, Computer-Aided Civil and Infrastructure Engineering 19(5): 364–376. https://doi.org/10.1111/j.1467-8667.2004.00363.x
Chen, S.-K.; Zhan, C.-C.; Chen, L.-G. 2007. Prediction method of bus arrival time based on link travel time, Computer Engineering 33(21): 281–282. (in Chinese). https://doi.org/10.3969/j.issn.1000-3428.2007.21.100
Cheng, S.; Liu, B.; Zhai, B. 2010. Bus arrival time prediction model based on APC data, in 6th Advanced Forum on Transportation of China (AFTC 2010), 16 October 2010, Beijing, China, 165–169. https://doi.org/10.1049/cp.2010.1123
Chu, L.; Oh, J.-S.; Recker, W. 2005. Adaptive Kalman filter based freeway travel time estimation, in Transportation Research Board 84th Annual Meeting Compendium of Papers CD-ROM, 9–13 January 2005, Washington, DC, US, 1–21.
Cohen, J. 1988. Statistical Power Analysis for the Behavioral Sciences. Routledge. 400 p.
Dailey, D. J.; Maclean, S. D.; Cathey, F. W.; Wall, Z. R. 2001. Transit vehicle arrival prediction: algorithm and large-scale implementation, Transportation Research Record: Journal of the Transportation Research Board 1771: 46–51. https://doi.org/10.3141/1771-06
Evans, J. D. 1995. Straightforward Statistics for the Behavioral Sciences. Brooks/Cole Pub Co. 634 p.
Fan, W.; Gurmu, Z. 2015. Dynamic travel time prediction models for buses using only GPS data, International Journal of Transportation Science and Technology 4(4): 353–366. https://doi.org/10.1016/S2046-0430(16)30168-X
Fatima, E.; Kumar, R. 2014. Introduction of public bus transit in Indian cities, International Journal of Sustainable Built Environment 3(1): 27–34. https://doi.org/10.1016/j.ijsbe.2014.06.001
Fu, L.; Rilett, L. R. 1998. Expected shortest paths in dynamic and stochastic traffic networks, Transportation Research Part B: Methodological 32(7): 499–516. https://doi.org/10.1016/s0191-2615(98)00016-2
Hans, E.; Chiabaut, N.; Leclercq, L.; Bertini, R. L. 2015. Real-time bus route state forecasting using particle filter and mesoscopic modeling, Transportation Research Part C: Emerging Technologies 61: 121–140. https://doi.org/10.1016/j.trc.2015.10.017
Jeong, R.; Rilett, L. R. 2004. Bus arrival time prediction using artificial neural network model, in Proceedings: the 7th International IEEE Conference on Intelligent Transportation Systems, 3–6 October 2004, Washington, DC, US, 988–993. https://doi.org/10.1109/itsc.2004.1399041
Kumar, S. V.; Dogiparthi K. C.; Vanajakshi, L.; Subramanian, S. C. 2017. Integration of exponential smoothing with state space formulation for bus travel time and arrival time prediction, Transport 32(4): 358–367. https://doi.org/10.3846/16484142.2015.1100676
Kumar, S. V.; Vanajakshi, L. 2012. Application of multiplicative decomposition and exponential smoothing techniques for bus arrival time prediction, in TRB 91st Annual Meeting Compendium of Papers DVD, 22–26 January 2012, Washington, DC, US, 1–12.
Kumar, S. V.; Vanajakshi, L. 2014. Pattern identification based bus arrival time prediction, Proceedings of the Institution of Civil Engineers – Transport 167(3): 194–203. https://doi.org/10.1680/tran.12.00001
Kumar, B. A.; Vanajakshi, L.; Subramanian, S. C. 2014a. Patternbased bus travel time prediction under heterogeneous traffic conditions, in TRB 93rd Annual Meeting Compendium of Papers, 12–16 January 2014, Washington, DC, US, 1–16.
Kumar, V.; Kumar, B. A.; Vanajakshi, L.; Subramanian, S. C. 2014b. Comparison of model based and machine learning approaches for bus arrival time prediction, in TRB 93rd Annual Meeting Compendium of Papers, 12–16 January 2014, Washington, DC, US, 1–14.
Kwon, J.; Coifman, B.; Bickel, P. 2000. Day-to-day travel-time trends and travel-time prediction from loop-detector data, Transportation Research Record: Journal of the Transportation Research Board 1717: 120–129. https://doi.org/10.3141/1717-15
Lewis, C. D. 1982. Industrial and Business Forecasting Methods: a Practical Guide to Exponential Smoothing and Curve Fitting. Butterworth Scientific. 143 p.
Li, R. 2006. Enhancing Motorway Travel Time Prediction Models through Explicit Incorporation of Travel Time Variability. PhD Thesis. Monash University, Melbourne, Australia. 264 p.
Liu, H.; Van Zuylen, H. J.; Van Lint, H.; Chen, Y.; Zhang, K. 2005. Prediction of urban travel times with intersection delays, in Proceedings: 2005 IEEE Intelligent Transportation Systems, 13–16 September 2005, Vienna, Austria, 402–407. https://doi.org/10.1109/ITSC.2005.1520198
Liu, X.; Chien, S. I.; Chen, M. 2014. An adaptive model for highway travel time prediction, Journal of Advanced Transportation 48(6): 642–654. https://doi.org/10.1002/atr.1216
Makridakis, S. 1993. Accuracy measures: theoretical and practical concerns, International Journal of Forecasting 9(4): 527–529. https://doi.org/10.1016/0169-2070(93)90079-3
Mazloumi, E.; Rose, G.; Currie, G.; Sarvi, M. 2011. An integrated framework to predict bus travel time and its variability using traffic flow data, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 15(2): 75–90. https://doi.org/10.1080/15472450.2011.570109
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 1855: 49–59. https://doi.org/10.3141/1855-06
Padmanaban, R. P. S.; Divakar, K.; Vanajakshi, L.; Subramanian, S. C. 2010. Development of a real-time bus arrival prediction system for Indian traffic conditions, IET Intelligent Transport Systems 4(3): 189–200. https://doi.org/10.1049/iet-its.2009.0079
Patnaik, J.; Chien, S.; Bladikas, A. 2004. Estimation of bus arrival times using APC data, Journal of Public Transportation 7(1): 1–20. https://doi.org/10.5038/2375-0901.7.1.1
Pattanamekar, P.; Park, D.; Rilett, L. R.; Lee, J.; Lee, C. 2003. Dynamic and stochastic shortest path in transportation networks with two components of travel time uncertainty, Transportation Research Part C: Emerging Technologies 11(5): 331–354. https://doi.org/10.1016/s0968-090x(03)00029-9
Pincus, S. M. 1991. Approximate entropy as a measure of system complexity, Proceedings of the National Academy of Sciences of the United States of America 88(6): 2297–2301. https://doi.org/10.1073/pnas.88.6.2297
Rajbhandari, R. 2005. Bus Arrival Time Prediction Using Stochastic Time Series and Markov Chains. PhD Dissertation. New Jersey Institute of Technology, Newark, NJ, US. 157 p. Available from Internet: http://archives.njit.edu/vol01/etd/2000s/2005/njit-etd2005-038/njit-etd2005-038.pdf
Ramakrishna, Y.; Ramakrishna, P.; Lakshmanan, V.; Sivanandan, R. 2006. Bus travel time prediction using GPS data, in Map India 2006: 9th Annual International Conference and Exhibition, 30 January – 1 February 2006, Delhi, India.
Russo, R. 2021. Statistics for the Behavioural Sciences: an Introduction to Frequentist and Bayesian Approaches. Routledge. 330 p.
Schölkopf, B.; Smola, A. J.; Williamson, R. C.; Bartlett, P. L. 2006. New support vector algorithms, Neural Computation 12(5): 1207–1245. https://doi.org/10.1162/089976600300015565
Shalaby, A.; Farhan, A. 2004. Prediction model of bus arrival and departure times using AVL and APC data, Journal of Public Transportation 7(1): 41–61. https://doi.org/10.5038/2375-0901.7.1.3
Suwardo; Napiah, M.; Kamaruddin, I. 2010. ARIMA models for bus travel time prediction, Journal of the Institution of Engineers, Malaysia 71(2): 49–58.
Vanajakshi, L.; Rilett, L. R. 2004. A comparison of the performance of artificial neural networks and support vector machines for the prediction of traffic speed, in IEEE Intelligent Vehicles Symposium, 2004, 14–17 June 2004, Parma, Italy, 194–199. https://doi.org/10.1109/ivs.2004.1336380
Vanajakshi, L.; Rilett, L. R. 2007. Support vector machine technique for the short term prediction of travel time, 2007 IEEE Intelligent Vehicles Symposium, 13–15 June 2007, Istanbul, Turkey, 600–605. https://doi.org/10.1109/ivs.2007.4290181
Vanajakshi, L.; Subramanian, S. C.; Sivanandan, R. 2009. Travel time prediction under heterogeneous traffic conditions using global positioning system data from buses, IET Intelligent Transport Systems 3(1): 1–9. https://doi.org/10.1049/iet-its:20080013
Vapnik, V. N. 1999. An overview of statistical learning theory, IEEE Transactions on Neural Networks 10(5): 988–999. https://doi.org/10.1109/72.788640
Wall, Z.; Dailey, D. J. 1999. An algorithm for predicting the arrival time of mass transit vehicles using automatic vehicle location data, in Transportation Research Board 78th Annual Meeting, 10–14 January 1999, Washington DC, US, 1–10.
Wu, C.-H.; Su, D.-C.; Chang, J.; Wei, C.-C.; Ho, J.-M.; Lin, K.-J.; Lee, D. T. 2003. An advanced traveler information system with emerging network technologies, in Proceedings of 6th Asia-Pacific Intelligent Transportation Systems Forum, 4–9 October 2003, Taipei, Taiwan, 1–8.
Xu, H., Ying, J. 2017. Bus arrival time prediction with real-time and historic data, Cluster Computing 20(4): 3099–3106. https://doi.org/10.1007/s10586-017-1006-1
Yang, M.; Chen, C.; Wang, L.; Yan, X.; Zhou, L. 2016. Bus arrival time prediction using support vector machine with genetic algorithm, Neural Network World 26(3): 205–217. https://doi.org/10.14311/nnw.2016.26.011
Yu, B.; Lam, W. H. K.; Tam, M. L. 2011. Bus arrival time prediction at bus stop with multiple routes, Transportation Research Part C: Emerging Technologies 19(6): 1157–1170. https://doi.org/10.1016/j.trc.2011.01.003
Yu, B.; Song, X.; Guan, F.; Yang, Z.; Yao, B. 2016. k-nearest neighbor model for multiple-time-step prediction of shortterm traffic condition, Journal of Transportation Engineering 142(6): 04016018. https://doi.org/10.1061/(asce)te.1943-5436.0000816
Yu, B.; Yang, Z.; Yao, B. 2006. Bus arrival time prediction using support vector machines, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 10(4): 151–158. https://doi.org/10.1080/15472450600981009
Yu, Bin; Yang, Z.-Z.; Chen, K.; Yu, Bo. 2010a. Hybrid model for prediction of bus arrival times at next station, Journal of Advanced Transportation 44(3): 193–204. https://doi.org/10.1002/atr.136
Yu, Bo; Lu, J.; Yu, Bin; Yang, Z. 2010b. An adaptive bus arrival time prediction model, Journal of the Eastern Asia Society for Transportation Studies 8: 1126–1136.
Yu, Z.; Wood, J. S; Gayah, V. V. 2017. Using survival models to estimate bus travel times and associated uncertainties, Transportation Research Part C: Emerging Technologies 74: 366–382. https://doi.org/10.1016/j.trc.2016.11.013
Zhou, Y.; Yao, L.; Chen, Y.; Gong, Y.; Lai, J. 2017. Bus arrival time calculation model based on smart card data, Transportation Research Part C: Emerging Technologies 74: 81–96. https://doi.org/10.1016/j.trc.2016.11.014