Exact asymptotics for the stationary distribution of a Markov chain: A production model

I.J.B.F. Adan, R.D. Foley, D.R. McDonald

Research output: Contribution to journalArticleAcademicpeer-review

23 Citations (Scopus)

Abstract

We derive rough and exact asymptotic expressions for the stationary distribution p of a Markov chain arising in a queueing/production context. The approach we develop can also handle "cascades," which are situations where the fluid limit of the large deviation path from the origin to the increasingly rare event is nonlinear. Our approach considers a process that starts at the rare event. In our production example, we can have two sequences of states that asymptotically lie on the same line, yet p has different asymptotics on the two sequences.
Original languageEnglish
Pages (from-to)311-344
JournalQueueing Systems
Volume62
Issue number4
DOIs
Publication statusPublished - 2009

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