Networks of queues with customers of different types

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Abstract
The behaviour in equilibrium of networks of queues in which customers may be of different types is studied. The type of a customer is allowed to influence his choice of path through the network and, under certain conditions, his service time distribution at each queue. The model assumed will usually cause each service time distribution to be of a form related to the negative exponential distribution. Theorems 1 and 2 establish the equilibrium distribution for the basic model in the closed and open cases; in the open case the individual queues are independent in equilibrium. In Section 4 similar results are obtained for other models, models which include processes better described as networks of colonies or as networks of stacks. In Section 5 the effect of time reversal upon certain processes is used to obtain further information about the equilibrium behaviour of those processes.

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