Queues with workload-dependent arrival and service rates

R. Bekker*, S. C. Borst, O. J. Boxma, O. Kella

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Scopus citations

Abstract

We consider two types of queues with workload-dependent arrival rate and service speed. Our study is motivated by queueing scenarios where the arrival rate and/or speed of the server depends on the amount of work present, like production systems and the Internet. First, in the M/G/1 case, we compare the steady-state distribution of the workload (both at arbitrary epochs and at arrival instants) in two models, in which the ratio of arrival rate and service speed is equal. Applying level crossing arguments, we show that the steady-state distributions are proportional. Second, we consider a G/G/1-type queue with workload-dependent interarrival times and service speed. Using a stochastic mean-value approach, several well-known relations for the workload at various epochs in the ordinary G/G/1 queue are generalized.

Original languageAmerican English
Pages (from-to)537-556
Number of pages20
JournalQueueing Systems
Volume46
Issue number3-4
DOIs
StatePublished - 2004

Keywords

  • Level crossings
  • Stochastic mean-value approach
  • Workload
  • Workload-dependent arrival and service rates

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