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Distribution of the workload in multiclass queueing systems with server vacations

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  • Hideaki Takagi
  • Tetsuya Takine
  • Onno J. Boxma

Abstract

The steady‐state workload at an arbitrary time is considered for several single‐server queueing systems with nonpreemptive services for multiple classes of customers (arriving according to Poisson processes) and server vacation (switchover) times. The distribution of the workload at an arbitrary point during the vacation period is obtained for systems with setup times, and for polling systems with exhaustive, gated, or globally gated service disciplines. From the stochastic decomposition property, this workload is added to the workload in the corresponding M/G/1 system without vacations to give the workload at an arbitrary time in vacation systems. Dependence of the workload distribution on the vacation parameters is studied.

Suggested Citation

  • Hideaki Takagi & Tetsuya Takine & Onno J. Boxma, 1992. "Distribution of the workload in multiclass queueing systems with server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(1), pages 41-52, February.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:1:p:41-52
    DOI: 10.1002/1520-6750(199202)39:13.0.CO;2-K
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    References listed on IDEAS

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    3. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    4. Hideaki Takagi, 1990. "Priority Queues with Setup Times," Operations Research, INFORMS, vol. 38(4), pages 667-677, August.
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