A closed network with a discriminatory processor-sharing server

Authors:
D. Mitra;A. Weiss
Affiliations:
AT&T Bell Laboratories, Murray Hill, New Jersey;AT&T Bell Laboratories, Murray Hill, New Jersey
Venue:
SIGMETRICS '89 Proceedings of the 1989 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Year:
1989

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Abstract

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 nj jobs of class j at the latter node, then each class j job receives a fraction wj/(&Sgr;wini) 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.