Size-limited batch movement in product-form closed discrete-time queueing networks

Abstract

Existing models for product-form closed discrete-time queueing networks with batch movement of customers implicitly assume that batch sizes are unrestricted. In many practical modelling situations however, it is necessary to impose restrictions on the batch sizes, and this paper examines the repercushions of such restrictions on the product-form properties of the networks. It is shown that when batch sizes are restricted independently then, in general, the resulting networks cannot have a product-form equilibrium distribution. Sufficient conditions to retain a product-form are derived in the cases when batch sizes are either correlated or depend on the state of the network. Examples of applying the results to obtain product-form networks with both correlated and state dependent batch movement are given.