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 |
dc.identifier.wikidata |
Q112885476 |
|