The Interrupted Poisson as an Overflow Process

A Poisson process which is alternately turned on for an exponentially distributed time and then turned off for another (independent) exponentially distributed time will be called an interrupted Poisson process-it can be viewed as a Poisson process modulated by a random switch. It was suggested by W. S. Hayward of Bell Laboratories that such a process be used to simulate overflow traffic. We will show t h a t the interrupted Poisson process provides a simple and accurate method of simulating overflow traffic. The objective is to reduce the cost of computer simulations of traffic systems by using the interrupted Poisson process to model the overflow traffic. Generation of actual overflow traffic by simulating the behavior of the trunk group from which it overflows is time consuming since a record must be kept of all calls which are offered to the subtending trunk group, whether they contribute to the overflow traffic or not. This is especially true when the traffic is overflowing a large trunk group. Moreover, the interrupted Poisson process provides a simple, approximate description of the overflow traffic and consequently facilitates analytical studies. 437