dc.rights.license | CC-BY-NC-ND | |
dc.contributor.advisor | Leskela, Lasse | |
dc.contributor.advisor | Dajani, Karma | |
dc.contributor.advisor | Bhulai, Sandjai | |
dc.contributor.author | Berg, L. van den | |
dc.date.accessioned | 2011-03-29T17:00:47Z | |
dc.date.available | 2011-03-29 | |
dc.date.available | 2011-03-29T17:00:47Z | |
dc.date.issued | 2011 | |
dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/6819 | |
dc.description.abstract | Stochastic comparison is a method to prove bounds on performance metrics of stochastic
models. Here, coupling can be used to define two processes on a common probability
space, which makes it possible to compare the steady-state distributions of the processes.
Two processes are stochastically related if their steady-state distributions satisfy a certain
comparison relation. Such a stochastic relation can be more general than a stochastic order.
In this thesis, a thorough description of stochastic comparison using coupling for
the probability kernels of Markov processes is presented. Necessary and sufficient conditions
for the stochastic comparison of stochastically related Markov queueing networks
are given, in particular for the coordinate-wise and the summation relation. Also, an example
of a Jackson network with breakdowns is studied, and an explicit coupling which
preserves a subrelation of the coordinate-wise order relation is constructed. This allows to
conclude that the steady-state distributions of the breakdown models are coordinate-wise
comparable.
Keywords: coupling, stochastic comparison, stochastic order, stochastic relation, Strassen’s
theorem, Markov queueing network, Jackson network, probability kernel | |
dc.description.sponsorship | Utrecht University | |
dc.format.extent | 474419 bytes | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.title | Stochastic comparison of Markov queueing networks using coupling. | |
dc.type.content | Master Thesis | |
dc.rights.accessrights | Open Access | |
dc.subject.keywords | coupling, stochastic comparison, stochastic order, stochastic relation, Strassen’s
theorem, Markov queueing network, Jackson network, probability kernel | |
dc.subject.courseuu | Stochastics and Financial Mathematics | |