Tail asymptotics of a Markov-modulated infinite-server queue

J. Blom*, K. De Turck, O. Kella, M. Mandjes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

This paper analyzes large deviation probabilities related to the number of customers in a Markov-modulated infinite-server queue, with state-dependent arrival and service rates. Two specific scalings are studied: in the first, just the arrival rates are linearly scaled by N (for large N), whereas in the second in addition the Markovian background process is sped up by a factor N1+ε, for some ε > 0. In both regimes (transient and stationary) tail probabilities decay essentially exponentially, where the associated decay rate corresponds to that of the probability that the sample mean of i.i.d. Poisson random variables attains an atypical value.

Original languageAmerican English
Pages (from-to)337-357
Number of pages21
JournalQueueing Systems
Volume78
Issue number4
DOIs
StatePublished - 16 Oct 2014

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Keywords

  • Infinite-server systems
  • Large deviations
  • Markov modulation
  • Queues

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