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Insensitivity of Queueing Networks

  • Muhammad El-Taha
  • Shaler StidhamJr.
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 11)

Abstract

A queueing process is said to be insensitive if the distribution of the number of jobs in the system depends on the service-time distribution only through its mean. In Chapter 4 we give a sample-path proof of the insensitivity of a batch- arrival G/G/1-LCFS-PR queue, in which the batch sizes and service times are allowed to be state dependent (see also Stidham and El-Taha [182]). In this chapter we present a unified approach to proving insensitivity of symmetric queues in discrete-time using the method of time reversal. We use discrete- time sample-path analysis to show that the asymptotic frequency distribution of the number of jobs in infinite-server, Erlang loss, and round-robin models, is insensitive to the asymptotic distribution of service times under weak assumptions. For the infinite-server model, our assumptions allow batch arrivals and permit batch sizes and service times to be dependent. We show that insensitivity holds if the frequency distribution of batch sizes solves a system of equations. A solution to this set of equations occurs if the batch size of arrivals at each time unit follows a Poisson distribution. Similar results hold for the Loss model with constant batch sizes and deterministic service requirements, and for the round-robin queue.

Keywords

Service Time Batch Size Service Requirement Round Robin Batch Arrival 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Muhammad El-Taha
    • 1
  • Shaler StidhamJr.
    • 2
  1. 1.University of Southern MaineUSA
  2. 2.University of North Carolina at Chapel HillUSA

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