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Heterogeneous multitrunking queueing systems with thresholds

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  • Martin J. Fischer
  • Carl M. Harris

Abstract

Queueing systems with multiple servers are commonly used to model telecommunications systems. But, in general, the service rate of each of the servers is not the same. This fact is indeed true in a communication network where one path (server) may be a terrestrial link and the other (server) a satellite link with its inherent propagation delay. In this article we consider a two‐server system where arriving customers are first placed in the queue for the faster server until that queue size reaches a certain threshold, whereupon they are diverted to the slower server. Additional arriving customers are assigned to the slower server until the faster server's queue drops to another lower threshold, at which point arrivals are reassigned to the faster server. We develop an exact mathematical model of the steady‐state behavior of each queueing system and a simple analytic approximation.

Suggested Citation

  • Martin J. Fischer & Carl M. Harris, 1991. "Heterogeneous multitrunking queueing systems with thresholds," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 579-597, August.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:4:p:579-597
    DOI: 10.1002/1520-6750(199108)38:43.0.CO;2-L
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    References listed on IDEAS

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    1. B. Krishnamoorthi, 1963. "On Poisson Queue with Two Heterogeneous Servers," Operations Research, INFORMS, vol. 11(3), pages 321-330, June.
    2. John H. Rath & Diane Sheng, 1979. "Technical Note—Approximations for Overflows from Queues with a Finite Waiting Room," Operations Research, INFORMS, vol. 27(6), pages 1208-1216, December.
    3. Vijendra P. Singh, 1970. "Two-Server Markovian Queues with Balking: Heterogeneous vs. Homogeneous Servers," Operations Research, INFORMS, vol. 18(1), pages 145-159, February.
    4. U. Narayan Bhat & Martin J. Fischer, 1976. "Multichannel queueing systems with heterogeneous classes of arrivals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(2), pages 271-282, June.
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