User optimal policies for a stochastic transportation network

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dc.contributor.advisor Ziedins, I en
dc.contributor.advisor Solomon, W en
dc.contributor.author Afimeimounga, Heti en
dc.date.accessioned 2019-10-15T02:02:29Z en
dc.date.issued 2011 en
dc.identifier.uri http://hdl.handle.net/2292/48535 en
dc.description.abstract This thesis studies user optimal policies (or user equilibria) for routing in queueing networks, with particular emphasis on networks where the Downs- Thomson paradox appears. We consider here a queueing network with two modes of transport private (road) transportation and public (train) transportation – which are modelled as a single server first-in-first-out ·|M|1 queue and infinite server batch-service ·|G(N)|∞ queue respectively, where N is the size of the batch. The waiting time at the single server queue increases as traffic increases while the service frequency at the batch-service queue increases with demand, and hence waiting time there decreases. User equilibria or user optimal policies may occur when users in a network individually choose the best (shortest) route for themselves. The Downs-Thomson paradox occurs when improvements in service produce an overall decline in performance as user equilibria adjust. We study this network system in the setting of both state-dependent routing and probabilistic routing. We use coupling arguments to show that under state-dependent routing a unique user optimal policy exists and is monotone. We also analyze the user equilibria (user optimal policies) in the setting of probabilistic routing when the road is modelled as an M|G|1 queue instead of an M|M|1 queue. This analysis shows that for some parameter values there exist multiple equilibria (not all stable) for N ≥ 2. Furthermore, we analyze the properties of the user optimal policies for the same network with M|M|1 queue versus M|M(N)|1 queue in the settings of both state-dependent routing and probabilistic routing. en
dc.publisher ResearchSpace@Auckland en
dc.relation.ispartof PhD Thesis - University of Auckland en
dc.relation.isreferencedby UoA99220733314002091 en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title User optimal policies for a stochastic transportation network en
dc.type Thesis en
thesis.degree.discipline Statistics en
thesis.degree.grantor The University of Auckland en
thesis.degree.level Doctoral en
thesis.degree.name PhD en
dc.rights.holder Copyright: The author en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.elements-id 784114 en
pubs.org-id Science en
pubs.org-id Statistics en
pubs.record-created-at-source-date 2019-10-15 en


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