A Jackson network consists of J nodes (or stations), each with one or several servers. The processing times of jobs at each node are i.i.d., following an exponential distribution with unit mean. The service rate, i.e., the rate by which work is depleted, at each node i can be both node-dependent and state-dependent. Specifically, whenever there are x i jobs at node i, the processing rate is μ i (x i ),where μ i (·)is a function Z + ↦ ℜ+, with μ i (0)= 0 and μ i (x) > 0 for all x > 0. Jobs travel among the nodes following a routing matrix P:= (p ij ), where, for i, j = 1,..., J,p ij is the probability that a job leaving node i will go to node j.
KeywordsConvolution Kelly Rium Summing
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- Buzacott, J.A. and Shanthikumar, J.G. 1993. Stochastic Models of Manufacturing Systems, Prentice Hall, Englewood Cliffs, NJ.Google Scholar
- Buzacott, J.A., Shanthikumar, J.G., and Yao, D.D. 1994. Stochastic Modeling and Analysis of Manufacturing Systems, Chapter 1, D.D. Yao (ed.), Springer-Verlag, New York.Google Scholar
- Gordon, W.J. and Newell, G. F. 1967. Closed Queueing Networks with Exponential Servers. Operations Research, 15, 252–267.Google Scholar