Rush hour roulette and the public transport choice
- Author
- Hannah Van den Bossche (UGent) , Koen De Turck (UGent) , Balakrishna Prabhu, Dieter Fiems (UGent) and Herwig Bruneel (UGent)
- Organization
- Abstract
- We focus on rush hour congestion on a macroscopic scale. When there is limited traffic, travel times are hardly influenced by the presence of traffic. In contrast, when there is a lot of traffic, the presence of other users has a severe impact on travel times through the finite capacity of the road infrastructure. Therefore we propose to model congestion at a macroscopic scale by a Markovian level-dependent queueing system, service rates being sub-linear in terms of the queue content. We assess the choice between private and public transport in two cases. Assuming that the arrival rate is constant over time and that the cost of public transport is expressed in terms of waiting time, we determine the proportion of users taking public transport at the Wardrop equilibrium and compare with the socially optimal proportion. Moreover, for a particular choice of level-dependent rates we show equivalence of the queueing system at hand with a discriminatory processor sharing system with permanent customers. We then relax the assumption of having constant arrival rates. In particular, we study the fluid limit of the time-dependent (and level-dependent) system and again focus on the proportion of users that take public transport.
- Keywords
- Markov chain, game theory, rush hour, Queueing, traffic
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-5757344
- MLA
- Van den Bossche, Hannah, et al. “Rush Hour Roulette and the Public Transport Choice.” Booklet of Abstracts of the First European Conference on Queueing Theory, edited by Herwig Bruneel et al., University Press, 2014, pp. 55–55.
- APA
- Van den Bossche, H., De Turck, K., Prabhu, B., Fiems, D., & Bruneel, H. (2014). Rush hour roulette and the public transport choice. In H. Bruneel, O. Boxma, J. Walraevens, & S. Wittevrongel (Eds.), Booklet of Abstracts of the First European Conference on Queueing Theory (pp. 55–55). Ghent, Belgium: University Press.
- Chicago author-date
- Van den Bossche, Hannah, Koen De Turck, Balakrishna Prabhu, Dieter Fiems, and Herwig Bruneel. 2014. “Rush Hour Roulette and the Public Transport Choice.” In Booklet of Abstracts of the First European Conference on Queueing Theory, edited by Herwig Bruneel, Onno Boxma, Joris Walraevens, and Sabine Wittevrongel, 55–55. Ghent, Belgium: University Press.
- Chicago author-date (all authors)
- Van den Bossche, Hannah, Koen De Turck, Balakrishna Prabhu, Dieter Fiems, and Herwig Bruneel. 2014. “Rush Hour Roulette and the Public Transport Choice.” In Booklet of Abstracts of the First European Conference on Queueing Theory, ed by. Herwig Bruneel, Onno Boxma, Joris Walraevens, and Sabine Wittevrongel, 55–55. Ghent, Belgium: University Press.
- Vancouver
- 1.Van den Bossche H, De Turck K, Prabhu B, Fiems D, Bruneel H. Rush hour roulette and the public transport choice. In: Bruneel H, Boxma O, Walraevens J, Wittevrongel S, editors. Booklet of Abstracts of the First European Conference on Queueing Theory. Ghent, Belgium: University Press; 2014. p. 55–55.
- IEEE
- [1]H. Van den Bossche, K. De Turck, B. Prabhu, D. Fiems, and H. Bruneel, “Rush hour roulette and the public transport choice,” in Booklet of Abstracts of the First European Conference on Queueing Theory, Ghent, Belgium, 2014, pp. 55–55.
@inproceedings{5757344, abstract = {{We focus on rush hour congestion on a macroscopic scale. When there is limited traffic, travel times are hardly influenced by the presence of traffic. In contrast, when there is a lot of traffic, the presence of other users has a severe impact on travel times through the finite capacity of the road infrastructure. Therefore we propose to model congestion at a macroscopic scale by a Markovian level-dependent queueing system, service rates being sub-linear in terms of the queue content. We assess the choice between private and public transport in two cases. Assuming that the arrival rate is constant over time and that the cost of public transport is expressed in terms of waiting time, we determine the proportion of users taking public transport at the Wardrop equilibrium and compare with the socially optimal proportion. Moreover, for a particular choice of level-dependent rates we show equivalence of the queueing system at hand with a discriminatory processor sharing system with permanent customers. We then relax the assumption of having constant arrival rates. In particular, we study the fluid limit of the time-dependent (and level-dependent) system and again focus on the proportion of users that take public transport.}}, author = {{Van den Bossche, Hannah and De Turck, Koen and Prabhu, Balakrishna and Fiems, Dieter and Bruneel, Herwig}}, booktitle = {{Booklet of Abstracts of the First European Conference on Queueing Theory}}, editor = {{Bruneel, Herwig and Boxma, Onno and Walraevens, Joris and Wittevrongel, Sabine}}, isbn = {{9789461972095}}, keywords = {{Markov chain,game theory,rush hour,Queueing,traffic}}, language = {{eng}}, location = {{Ghent, Belgium}}, pages = {{55--55}}, publisher = {{University Press}}, title = {{Rush hour roulette and the public transport choice}}, year = {{2014}}, }