|Martínez Sánchez, Joaquín
|Matos, Ana Rita
|Turunen, Anu W.
|Antunes, Carlos Henggeler
|Krasnov, Oleg A.
|Lopes, Joao P.
in Cooperation with on an Cooperation-Score of 37%
Publications (6/6 displayed)
- 2022Performance analysis of a continuous-time two-class global first-come-first-served queue with two servers and presortingcitations
- 2016Discrete-time queues with variable service capacity: a basic model and its analysiscitations
- 2015Public vs. personal transportation: a rational choice based on queueing theory
- 2014Rush hour roulette and the public transport choice
- 2014A continuous-time queueing model with class clustering and global FCFS service disciplinecitations
- 2011Road splits: smooth or rough passage?
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Rush hour roulette and the public transport choice
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.
- public transport
- Markov chain
- travel time
- game theory
- waiting time