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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