The impact of dependent service times on large-scale service systems

Guodong Pang, Ward Whitt

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

This paper investigates the impact of dependence among successive service times on the transient and steady-state performance of a large-scale service system. This is done by studying an infinite-server queueing model with time-varying arrival rate, exploiting a recently established heavy-traffic limit, allowing dependence among the service times. This limit shows that the number of customers in the system at any time is approximately Gaussian, where the time-varying mean is unaffected by the dependence, but the time-varying variance is affected by the dependence. As a consequence, required staffing to meet customary quality-of-service targets in a large-scale service system with finitely many servers based on a normal approximation is primarily affected by dependence among the service times through this time-varying variance. This paper develops formulas and algorithms to quantify the impact of the dependence among the service times on that variance. The approximation applies directly to infinite-server models but also indirectly to associated finite-server models, exploiting approximations based on the peakedness (the ratio of the variance to the mean in the infinite-server model). Comparisons with simulations confirm that the approximations can be useful to assess the impact of the dependence.

Original languageEnglish (US)
Pages (from-to)262-278
Number of pages17
JournalManufacturing and Service Operations Management
Volume14
Issue number2
DOIs
StatePublished - Mar 1 2012

All Science Journal Classification (ASJC) codes

  • Strategy and Management
  • Management Science and Operations Research

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