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Level crossing analysis of priority queues and a conservation identity for vacation models

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  • J. George Shanthikumar

Abstract

The two purposes of this article are to illustrate the power and simplicity of level crossing analysis and to present a conservation identity for M/G/1 priority queues with server vacations. To illustrate the use of level crossing analysis we apply it to preemptive (resume) priority M/G/1 queues with single‐ and multiple‐server vacations considered by Kella and Yechiali (1986) and to non‐preemptive priority M/M/c queues considered by Kella and Yechiali (1985). The conservation identity presented here states that the ratios of mean waiting times in an M/G/1 queue with and without server vacation policies are independent of the service discipline for first come first served, shortest processing time, shortest processing time within generations and non‐preemptive priority service disciplines.

Suggested Citation

  • J. George Shanthikumar, 1989. "Level crossing analysis of priority queues and a conservation identity for vacation models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(6), pages 797-806, December.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:6:p:797-806
    DOI: 10.1002/1520-6750(198912)36:63.0.CO;2-W
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    References listed on IDEAS

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    1. 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.
    2. P. H. Brill & M. J. M. Posner, 1977. "Level Crossings in Point Processes Applied to Queues: Single-Server Case," Operations Research, INFORMS, vol. 25(4), pages 662-674, August.
    3. J. G. Shanthikumar & M. Jeya Chandra, 1982. "Application of level crossing analysis to discrete state processes in queueing systems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(4), pages 593-608, December.
    4. Charles E. Skinner, 1967. "A Priority Queuing System with Server-Walking Time," Operations Research, INFORMS, vol. 15(2), pages 278-285, April.
    5. P. H. Brill & M. J. M. Posner, 1981. "The System Point Method in Exponential Queues: A Level Crossing Approach," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 31-49, February.
    6. Teghem, J., 1986. "Control of the service process in a queueing system," European Journal of Operational Research, Elsevier, vol. 23(2), pages 141-158, February.
    7. J. G. Shanthikumar, 1981. "M / G /1 Queues with Scheduling within Generations and Removable Server," Operations Research, INFORMS, vol. 29(5), pages 1010-1018, October.
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