Light-traffic analysis for queues with spatially distributed arrivals

Dirk Kroese, Volker Schmidt

Research output: Contribution to journalArticleAcademicpeer-review

19 Citations (Scopus)
70 Downloads (Pure)

Abstract

We consider the following continuous polling system: Customers arrive according to a homogeneous Poisson process (or a more general stationary point process) and wait on a circle in order to be served by a single server. The server is "greedy," in the sense that he always moves (with constant speed) towards the nearest customer. The customers are served according to an arbitrary service time distribution, in the order in which they are encountered by the server. First-order and second-order Taylor-expansions are found for the expected configuration of customers, for the mean queue length, and for expectation and distribution function of the workload. It is shown that under light traffic conditions the greedy server works more efficiently than the cyclically polling server.
Original languageUndefined
Pages (from-to)135-157
Number of pages23
JournalMathematics of operations research
Volume21
Issue number1
DOIs
Publication statusPublished - 1996

Keywords

  • Queue length
  • Queueing Theory
  • Workload
  • Taylor-expansion
  • general stationary input
  • IR-98527
  • continuous polling system
  • greedy server
  • light-traffic derivative
  • METIS-140765
  • Poisson arrivals

Cite this

Kroese, Dirk ; Schmidt, Volker. / Light-traffic analysis for queues with spatially distributed arrivals. In: Mathematics of operations research. 1996 ; Vol. 21, No. 1. pp. 135-157.
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Light-traffic analysis for queues with spatially distributed arrivals. / Kroese, Dirk; Schmidt, Volker.

In: Mathematics of operations research, Vol. 21, No. 1, 1996, p. 135-157.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Light-traffic analysis for queues with spatially distributed arrivals

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AU - Schmidt, Volker

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N2 - We consider the following continuous polling system: Customers arrive according to a homogeneous Poisson process (or a more general stationary point process) and wait on a circle in order to be served by a single server. The server is "greedy," in the sense that he always moves (with constant speed) towards the nearest customer. The customers are served according to an arbitrary service time distribution, in the order in which they are encountered by the server. First-order and second-order Taylor-expansions are found for the expected configuration of customers, for the mean queue length, and for expectation and distribution function of the workload. It is shown that under light traffic conditions the greedy server works more efficiently than the cyclically polling server.

AB - We consider the following continuous polling system: Customers arrive according to a homogeneous Poisson process (or a more general stationary point process) and wait on a circle in order to be served by a single server. The server is "greedy," in the sense that he always moves (with constant speed) towards the nearest customer. The customers are served according to an arbitrary service time distribution, in the order in which they are encountered by the server. First-order and second-order Taylor-expansions are found for the expected configuration of customers, for the mean queue length, and for expectation and distribution function of the workload. It is shown that under light traffic conditions the greedy server works more efficiently than the cyclically polling server.

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KW - Taylor-expansion

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KW - continuous polling system

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KW - light-traffic derivative

KW - METIS-140765

KW - Poisson arrivals

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