On a telephone traffic system with several kinds of service distributions

Abstract

Let us suppose that telephone calls arrive at a telephone exchange according to a recurrent process. We shall assume that there are infinitely many lines available and that, therefore, no call is ever lost. Ordinarily, it is assumed that the holding times (the durations of the connections) are identically distributed, independent, random variables with an exponential distribution. The American folklore, however, assumes that women talk more than men. In this paper, we shall consider the possibility of calls requiring one of several (s) different exponential holding times.