Product-Form Solutions for a Class of Structured Multidimensional Markov Processes

Autor:	Jori Selen, Ijbf Ivo Adan, Jsh Johan van Leeuwaarden
Přispěvatelé:	Stochastic Operations Research
Rok vydání:	2014
Předmět:	Queueing theory Class (set theory) Computer science Applied Mathematics Boundary (topology) Markov process Algebra symbols.namesake Mathematics - Analysis of PDEs Product (mathematics) symbols State space Linear combination 60J27 60J28 60K25 Finite set Mathematics - Probability
Zdroj:	SIAM Journal on Applied Mathematics, 74(3), 844-863. Society for Industrial and Applied Mathematics (SIAM)
ISSN:	1095-712X 0036-1399
DOI:	10.1137/130943297
Popis:	Motivated by queueing systems with heterogeneous parallel servers, we consider a class of structured multi-dimensional Markov processes whose state space can be partitioned into two parts: a finite set of boundary states and a structured multi-dimensional set of states, exactly one dimension of which is infinite. Using separation of variables, we show that the equilibrium distribution, typically of the queue length, can be represented as a linear combination of product forms. For an important subclass of queueing systems, we characterize explicitly the waiting time distribution in terms of mixtures of exponentials. Comment: 21 pages, 2 figures -- version 3 incorporates minor textual and layout changes
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::660e5249991db90e2cc3f578941f3090 https://doi.org/10.1137/130943297 Zobrazit plný text záznamu