Minimising average passenger waiting time in personal rapid transit systems
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Personal Rapid Transit (PRT) is an emerging urban transport mode. A PRT system operates much like a conventional hackney taxi system, except that the vehicles are driven by computer (no human driver) between stations in a dedicated network of guideways. The world’s first two PRT systems began operating in 2010 and 2011. In both PRT and taxi systems, passengers request immediate service; they do not book ahead. Perfect information about future requests is therefore not available, but statistical information about future requests is available from historical data. If the system does not use this statistical information to position empty vehicles in anticipation of future requests, long passenger waiting times result, which makes the system less attractive to passengers, but using it gives rise to a difficult stochastic optimisation problem. This paper develops three lower bounds on achievable mean passenger waiting time, one based on queuing theory, one based on the static problem, in which it is assumed that perfect information is available, and one based on a Markov Decision Process model. An evaluation of these lower bounds, together with a practical heuristic developed previously, in simulation shows that these lower bounds can often be nearly attained, particularly when the fleet size is large. The results also show that low waiting times and high utilisation can be simultaneously obtained when the fleet size is large, which suggests important economies of scale.
KeywordsPersonal rapid transit Empty vehicle redistribution Taxi Queuing model Markov decision process Waiting time
- 2getthere (2011). Masdar operations. Accessed 11 May, 2011, URL http://www.2getthere.eu/?p=128.
- Adan, I., & Resing, J. (2002). Queueing theory. Course Notes, Eindhoven University of Technology. Google Scholar
- Anderson, J. E. (1978). Transit systems theory. Totowa: Lexington Books. Google Scholar
- Bell, M. G. H., & Wong, K. I. (2005). A rolling horizon approach to the optimal dispatching of taxis. In H. S. Mahmassani (Ed.), Transportation and traffic theory: flow, dynamics and human interaction: proceedings of the 16th international symposium on transportation and traffic theory (pp. 629–648). Amsterdam: Elsevier. Google Scholar
- Bertsekas, D. P., & Tsitsiklis, J. N. (1996). Neuro-dynamic programming. Cambridge: Athena Scientific. Google Scholar
- Bertsimas, D., & Tsitsiklis, J. (1997). Introduction to linear optimization. Cambridge: Athena Scientific. Google Scholar
- Bly, P. H., & Teychenne, P. (2005). Three financial and socio-economic assessments of a personal rapid transit system. In Proceedings of the tenth international conference on automated people movers (p 39). Reston: American Society of Civil Engineers. http://link.aip.org/link/?ASC/174/39. Google Scholar
- Boxma, O. J., Cohen, J. W., & Huffels, N. (1979). Approximations of the mean waiting time in an M/G/s queueing system. Operations Research, 27(6). Google Scholar
- van Eijl, C. A. (1995). A polyhedral approach to the delivery man problem. Tech. Rep. COSOR 95-19, Eindhoven University of Technology. Google Scholar
- Lees-Miller, J. D. (2011). Empty vehicle redistribution for personal rapid transit. PhD thesis, University of Bristol. Google Scholar
- Lees-Miller, J. D., & Wilson, R. E. (2011). Sampling for personal rapid transit empty vehicle redistribution. Transportation Research Record: Journal of the Transportation Research Board Google Scholar
- Lees-Miller, J. D., & Wilson, R. E. (2012). Proactive empty vehicle redistribution for personal rapid transit and taxis. Transportation Planning and Technology. Google Scholar
- Li, S. (2006). Multi-attribute taxi logistics optimization. Master’s thesis, Massachusetts Institute of Technology. Google Scholar
- Nagarajan, V., & Ravi, R. (2008). The directed minimum latency problem. In A. Goel, K. Jansen, J. D. P. Rolim, & R. Rubinfeld (Eds.), Lecture notes in computer science: Vol. 5171. Approximation, randomization and combinatorial optimization. Algorithms and techniques (pp. 193–206). Berlin: Springer. CrossRefGoogle Scholar
- Puterman, M. L. (2005). Markov decision processes: discrete stochastic dynamic programming. New York: Wiley-Interscience. Google Scholar
- Sutton, R. S., & Barto, A. G. (1999). Reinforcement learning: an introduction. Cambridge: MIT Press. Google Scholar
- ULTra PRT (2010). ULTra at London Heathrow airport. Accessed July 31, URL http://www.ultraprt.com/applications/existing-systems/heathrow/.
- Wang, H., Lee, D. H., & Cheu, R. (2009). PDPTW based taxi dispatch modeling for booking service. In Fifth international conference on natural computation (pp. 242–247). New York: IEEE Press. Google Scholar
- Wesselowski, K., & Cassandras, C. G. (2006). The elevator dispatching problem: hybrid system modeling and receding horizon control. In C. Cassandras, A. Giua, C. Seatzu, & J. Zaytoon (Eds.), Analysis and design of hybrid systems 2006: a proceedings volume from the 2nd IFAC conference (pp. 136–141). Amsterdam: Elsevier. CrossRefGoogle Scholar