Product forms for queueing networks with state-dependent multiple job transitions

Richard J. Boucherie · Nico M. Van DIJK

98 citations0/0 files storedAdvances in Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Petri Nets in System Modeling

Abstract

A general framework of continuous-time queueing networks is studied with simultaneous state dependent service completions such as due to concurrent servicing or discrete-time slotting and with state dependent batch routings such as most typically modelling blocking. By using a key notion of group-local-balance, necessary and sufficient conditions are given for the stationary distribution to be of product form. These conditions and a constructive computation of the product form are based upon merely local solutions of the group-local-balance equations which can usually be solved explicitly for concrete networks. Moreover, a decomposition theorem is presented to separate service and routing conditions. General batch service and batch routing examples yielding a product form are hereby concluded. As illustrated by various examples, known results on both discrete- and continuous-time queueing networks are unified and extended.

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References

1975Open, Closed, and Mixed Networks of Queues with Different Classes of Customers 1957Networks of Waiting Lines 1963Jobshop-Like Queueing Systems 2004Jobshop-Like Queueing Systems 1987Introduction to Queueing Networks 1990An Introduction to Queueing Networks 1977Product Form and Local Balance in Queueing Networks 1984Insensitivity of blocking probabilities in a circuit-switching network

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2017Balanced fair resource sharing in computer clusters 2000Product Form Queueing Networks 1997A Geometric Product-Form Distribution for a Queueing Network by Non-Standard Batch Arrivals and Batch Transfers 2000On Numerical Computations of Some Discrete-Time Queues 1993A generalization of Norton's theorem for queueing networks 2006Insensitive queueing models for communication networks 1997

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