This paper gives a simple, accurate first order asymptotic analysis of the transient and steady state behavior of a network which is closed, not product-form and has multiple classes. One of the two nodes of the network is an infinite server and the discipline in the other node is discriminatory processor-sharing. Specifically, if there are n j jobs of class j at the latter node, then each class j job receives a fraction w j / (ऱ w i n i ) of the processor capacity. This work has applications to data networks. For the asymptotic regime of high loading of the processor and high processing capacity, we derive the explicit first order transient behavior of the means of queue lengths. We also give explicit expressions for the steady state mean values and a simple procedure for finding the time constants (eigenvalues) that govern the approach to steady state. The results are based on an extension of Kurtz's theorem concerning the fluid limit of Markov processes. Some numerical experiments show that the analysis is quite accurate.
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A closed network with a discriminatory processor-sharing server
Mitra, D.; Weiss, A.
Follow ACM SIGMETRICS Performance Evaluation Review
, Volume 17 (1)
Association for Computing Machinery – Apr 1, 1989
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