Delay Distributions for Simple Trunk Groups with Recurrent Input and Exponential Service Times†

At a telephone exchange, calls appear before a simple trunk group of m lines in accordance with a recurrent process. If every line is busy, calls are delayed. The call holding times are mutually independent random variables with common exponential distribution. In this paper, methods are given for the determination of the distribution of the delay for a stationary process and various orders of service. Three orders of service are considered: (1) order of arrival, (2) random order, and (3) inverse order of arrival.