Delay Distributions for One Line with Poisson Input, General Holding Times, and Various Orders of Service

At a telephone exchange, calls appear before a single trunk line in accordance with a Poisson process of density λ. If the trunk line is busy, calls are delayed. The call holding times are identically distributed, mutually independent, positive random variables with distribution function H(x). In this paper the distribution function of the delay and its moments are given for a stationary process and for three orders of service: (i) order of arrival, (ii) random order, and (iii) reverse order of arrival.