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Closed Networks of Exponential Queues

In: Queues

Author

Listed:
  • Moshe Haviv

    (The Hebrew University)

Abstract

Suppose M single-server service stations are located in a network. Service times in station i follow an exponential distribution with parameter μ i , 1 ≤ i ≤ M. There are N customers (or jobs) who are “trapped” in the network and move from one station to another as soon as service ends at the former station. These dynamics are governed by a transition (stochastic) matrix P. Specifically, once a job ends its service in station i, it hops to the queue in front of server j with probability P ij . Of course, P ij ≥ 0, 1 ≤ i, j≤ M, and $$\Sigma _{j=1}^{M}P_{ij} = 1$$ . There is no need to assume that P ii = 0, 1 ≤ i ≤ M. However, we assume that P (or more precisely, a Markov chain whose transition probabilities are given in P) is irreducible.

Suggested Citation

  • Moshe Haviv, 2013. "Closed Networks of Exponential Queues," International Series in Operations Research & Management Science, in: Queues, edition 127, chapter 0, pages 151-163, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-6765-6_10
    DOI: 10.1007/978-1-4614-6765-6_10
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