Heavy-traffic limits for many-server queues with service interruptions

Guodong Pang, Ward Whitt

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

We establish many-server heavy-traffic limits for G/M/n+M queueing models, allowing customer abandonment (the +M), subject to exogenous regenerative service interruptions. With unscaled service interruption times, we obtain a FWLLN for the queue-length process, where the limit is an ordinary differential equation in a two-state random environment. With asymptotically negligible service interruptions, we obtain a FCLT for the queue-length process, where the limit is characterized as the pathwise unique solution to a stochastic integral equation with jumps. When the arrivals are renewal and the interruption cycle time is exponential, the limit is a Markov process, being a jump-diffusion process in the QED regime and an O-U process driven by a Levy process in the ED regime (and for infinite-server queues). A stochastic-decomposition property of the steady-state distribution of the limit process in the ED regime (and for infinite-server queues) is obtained.

Original languageEnglish (US)
Pages (from-to)167-202
Number of pages36
JournalQueueing Systems
Volume61
Issue number2-3
DOIs
StatePublished - Mar 1 2009

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Servers
Ordinary differential equations
Markov processes
Integral equations
Decomposition
Interruption
Multi-server queues
Heavy traffic
Queue

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics

Cite this

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Heavy-traffic limits for many-server queues with service interruptions. / Pang, Guodong; Whitt, Ward.

In: Queueing Systems, Vol. 61, No. 2-3, 01.03.2009, p. 167-202.

Research output: Contribution to journalArticle

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