Heavy-traffic extreme value limits for Erlang delay models

Guodong Pang, Ward Whitt

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider the maximum queue length and the maximum number of idle servers in the classical Erlang delay model and the generalization allowing customer abandonment-the M/M/n+M queue. We use strong approximations to show, under regularity conditions, that properly scaled versions of the maximum queue length and maximum number of idle servers over subintervals [0,t] in the delay models converge jointly to independent random variables with the Gumbel extreme value distribution in the quality-and-efficiency-driven (QED) and ED many-server heavy-traffic limiting regimes as n and t increase to infinity together appropriately; we require that tn→∞ and tn=o(n1/2-ε) as n→∞ for some ε>0.

Original languageEnglish (US)
Pages (from-to)13-32
Number of pages20
JournalQueueing Systems
Volume63
Issue number1
DOIs
StatePublished - Jan 1 2009

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Servers
Random variables
Extreme values
Heavy traffic
Queue
Abandonment
Regularity
Approximation

All Science Journal Classification (ASJC) codes

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

Cite this

Pang, Guodong ; Whitt, Ward. / Heavy-traffic extreme value limits for Erlang delay models. In: Queueing Systems. 2009 ; Vol. 63, No. 1. pp. 13-32.
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Heavy-traffic extreme value limits for Erlang delay models. / Pang, Guodong; Whitt, Ward.

In: Queueing Systems, Vol. 63, No. 1, 01.01.2009, p. 13-32.

Research output: Contribution to journalArticle

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