TABLE OF CONTENTS Customers are intolerant of long response times to their service requests. Typically, if they have to wait more than a few seconds, customers are very likely to abandon their service requests and make repeat requests (reattempts). This is also true of, for example, personal computers executing Internet dial-up scripts, and of TV set-top boxes, both of which have built-in time outs.
Customer impatience, combined with an excessively delayed response to service requests from a network resource, can cause the effective throughput of the resource to collapse to a low level see Rumsewicz [5] for examples of this phenomenon in Signalling System No 7 signalling networks. This behaviour has been seen in simulations of traffic routes between two telephone switches that do not have effective overload controls. If the switch at one end of the route acts as a bottle-neck limiting the rate at which it can return responses to service requests, then it can be driven into a self-sustaining state in which it has such a large backlog of requests and responses waiting to be processed, that all new requests are abandoned by customers, because the delays exceed what customers will tolerate.
The repeat attempt behaviour of a customer is characterised by specifying:
the persistence probability, denoted by p k, that, if the kth service request attempt is rejected, a ( k+1)th attempt will be made;
the distribution of the time interval between the
