Stochastic Processes in Queueing Theory pp 202-234 | Cite as

# Systems with Refusals

## Abstract

A natural characterization of such systems is the number of occupied channels at either the time of arrival of the *n*-th customer (*q*_{ n }), or at time *t* (*q*(*t*)). The variables *q*_{ n } and *q*(*t*) will be called, as before, the *queue lengths*. As already explained in the introduction, the operation of the (systems ‹*G/m*›_{ R }) is analogous to that of ‹G/m› but with the essential difference that here, *q*(0) ≤ *m*, and if *q*_{ n } = *m* at the moment of arrival of the *n*-th group of requests, then all requests of this group are refused and leave the system. If, however, *q*_{ n } < *m*, then those requests of the group are refused which remain after the idle channels have been filled. Thus, we have q_{n} ≤ *m* and *q*(*t*) ≤ *m* here and the important parameters of the systems are the probabilities that a customer is refused.

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