An exponential semi-markov process, with applications to queueing theory.

A class of semi-Markov processes is introduced, for which the intervals of time between events are dependent, identically and exponentially distributed random variables. The sequence of correlation coefficients for pairs of intervals is examined, to determine the types of processes which can be so modeled. As an application, such processes are used as input to an exponential server, in order to measure the effect of correlations in the arrival process on the behaviour of the queue.