Single-server queues under overdispersion in the heavy-traffic regime

O. Boxma, M. Heemskerk (Corresponding author), M. Mandjes

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

This paper addresses the analysis of the queue-length process of single-server queues under overdispersion, i.e., queues fed by an arrival process for which the variance of the number of arrivals in a given time window exceeds the corresponding mean. Several variants are considered, using concepts as mixing and Markov modulation, resulting in different models with either endogenously triggered or exogenously triggered random environments. Only in special cases explicit expressions can be obtained, e.g., when the random arrival and/or service rate can attain just finitely many values. While for more general model variants exact analysis is challenging, one can derive limit theorems in the heavy-traffic regime. In some of our derivations we rely on evaluating the relevant Laplace transform in the heavy-traffic scaling using Taylor expansions, whereas other results are obtained by applying the continuous mapping theorem.

Original languageEnglish
Pages (from-to)197-230
Number of pages34
JournalStochastic Models
Volume37
Issue number1
DOIs
Publication statusPublished - 2021

Keywords

  • 90B22
  • Heavy traffic
  • Markov modulation
  • overdispersion
  • Primary: 60K25
  • random environment
  • Secondary: 60J60
  • single-server queues

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