Continuity of a queueing integral representation in the M1 topology

Guodong Pang, Ward Whitt

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We establish continuity of the integral representation y(t) = x(t) + f 0th(y(s)) ds, t ≥ 0, mapping a function x into a function y when the underlying function space D is endowed with the Skorohod M1 topology. We apply this integral representation with the continuous mapping theorem to establish heavy-traffic stochastic-process limits for many-server queueing models when the limit process has jumps unmatched in the converging processes as can occur with bursty arrival processes or service interruptions. The proof of M1-continuity is based on a new characterization of the M1 convergence, in which the time portions of the parametric representations are absolutely continuous with respect to Lebesgue measure, and the derivatives are uniformly bounded and converge in L1.

Original languageEnglish (US)
Pages (from-to)214-237
Number of pages24
JournalAnnals of Applied Probability
Volume20
Issue number1
DOIs
StatePublished - Feb 1 2010

Fingerprint

Queueing
Integral Representation
Topology
Skorohod Topology
Parametric Representation
Heavy Traffic
Jump Process
Queueing Model
Lebesgue Measure
Absolutely Continuous
Function Space
Stochastic Processes
Converge
Derivative
Theorem
Integral
Continuity

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Continuity of a queueing integral representation in the M1 topology. / Pang, Guodong; Whitt, Ward.

In: Annals of Applied Probability, Vol. 20, No. 1, 01.02.2010, p. 214-237.

Research output: Contribution to journalArticle

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