Asymptotic evaluation of closed queueing networks with many stations

Alexander Birman · Yaakov Kogan

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Advanced Queuing Theory Analysis Interconnection Networks and Systems Petri Nets in System Modeling

Abstract

Asymptotic formulas are derived for the partition function of multichain closed product form networks with groups of stations, each group consisting of many identical stations. The derivation of the asymptotic expansion is based on an integral representation of the partition function in a multidimensional complex space and its evaluation using the saddle point method. The saddle point method is also used to derive an iterative algorithm which reduces the problem of solving the multichain network to a set of single chain problems. The accuracy of the approximations is evaluated in two case studies: a memory interference model in a multiprocessing system and a model of a multiprogramming system.

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References

1975Queuing Networks with Multiple Closed Chains: Theory and Computational Algorithms 1979Closed Exponential Networks of Queues with Saturation: The Jackson-Type Stationary Distribution and Its Asymptotic Analysis 1982Integral Representations and Asymptotic Expansions for Closed Markovian Queueing Networks: Normal Usage 1981A Class of Closed Markovian Queuing Networks: Integral Representations, Asymptotic Expansions, and Generalizations*1986Asymptotic expansions for closed Markovian networks with state-dependent service rates

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