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A Single Server Queueing Loss Model with Heterogeneous Arrival and Service

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  • Shun-Chen Niu

    (Cleveland State University, Cleveland, Ohio)

Abstract

A heterogeneous arrival and service single server queueing loss model is analyzed. The arrival process of customers is assumed to be a nonstationary Poisson process with an intensity function whose evolution is governed by a two-state continuous time Markov chain. Different service distributions for different types of customers are allowed. The explicit loss formula for the model considered is obtained. In a special case, it is shown that as the arrival process becomes more regular the loss decreases. For single server loss systems with renewal arrivals, counterexamples are given to show that regularity of arrival and service distributions do not work to good effect in general. Two sufficient conditions for it to be true are given.

Suggested Citation

  • Shun-Chen Niu, 1980. "A Single Server Queueing Loss Model with Heterogeneous Arrival and Service," Operations Research, INFORMS, vol. 28(3-part-i), pages 584-593, June.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:3-part-i:p:584-593
    DOI: 10.1287/opre.28.3.584
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    Cited by:

    1. Antony Svoronos & Linda Green, 1987. "The N‐seasons S‐servers loss system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(4), pages 579-591, August.

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