Queuing Network Models with State-Dependent Routing

Don Towsley

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Interconnection Networks and Systems

Abstract

A model of a closed queuing network within which customer routing between queues may depend on the state of the network is presented. The routing functions allowed may be rational functions of the queue lengths of various downstream queues which reside within special subnetworks called p-subnetworks. If a network with no state-dependent routing has a product-form joint equilibrium distribution of the queue lengths, then the introduction of these routing functions will preserve the product form of the equilibrium distribution. An example to illustrate the applicability of the model to the problem of analyzing a load balancing strategy is presented. It is also indicated how the parametric analysis of a network with routing functions can be simplified through the analysis of a simpler “equivalent” network.

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References

1975Open, Closed, and Mixed Networks of Queues with Different Classes of Customers 1975Theory, Volume 1, Queueing Systems 1973Computational algorithms for closed queueing networks with exponential servers 1976Networks of queues 1979Models for Dynamic Load Balancing in a Heterogeneous Multiple Processor System 1975Approximate Analysis of General Queuing Networks 1977Product Form and Local Balance in Queueing Networks 1976Networks of queues and the method of stages

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1998State-dependent stochastic networks. Part I. Approximations and applications with continuous diffusion limits 1985Modeling a class of state-dependent routing in flexible manufacturing systems 1989Approximate Analysis of Queues in Series with Phase-Type Service Times and Blocking 1982Twenty Five Years of Cyclic Queues and Closed Queue Networks: A Review 2003Queueing networks with blocking 1987Modeling a Class of Flexible Manufacturing Systems with Reversible Routing

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