Asymptotic expansions for large closed queueing networks with multiple job classes

Charles Knessl · Charles Tier

18 citations0/0 files storedIEEE Transactions on Computers

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

Abstract

A closed BCMP queuing network consisting of R job classes (chains), K+1 single-server, fixed-rate nodes, and M/sub j/ class j jobs (j=1, 2, . . ., R) is considered. Asymptotic expansions are constructed for the partition function under assumptions (1) K>>1, (2) M/sub j/>>1 for each j, and (3) K/M/sub j/=O(1). Analytic expressions for performance measures such as the mean queue length are also given. The approach employs the ray method and the method of matched asymptotic expansions. Numerical comparisons illustrate the accuracy of the approximations.>

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1975Open, Closed, and Mixed Networks of Queues with Different Classes of Customers 1963Jobshop-Like Queueing Systems 1973Computational algorithms for closed queueing networks with exponential servers 2004Jobshop-Like Queueing Systems 1967Closed Queuing Systems with Exponential Servers 1975Queuing Networks with Multiple Closed Chains: Theory and Computational Algorithms 1984Open and Closed Models for Networks of Queues 1980Queueing network models of multiprogramming

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2016A Bayesian Approach to Parameter Inference in Queueing Networks 1998Asymptotic approximations and bottleneck analysis in product form queueing networks with large populations 2017Accelerating Performance Inference over Closed Systems by Asymptotic Methods

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