Closed Networks of Exponential Queues

Moshe Haviv
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Moshe Haviv: The Hebrew University

Chapter Chapter 10 in Queues, 2013, pp 151-163 from Springer

Abstract: 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.

Keywords: Queue Length; Service Rate; Limit Probability; Close Network; Queue Model (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-1-4614-6765-6_10

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DOI: 10.1007/978-1-4614-6765-6_10

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