The M/G/∞ queue busy period distribution exponentiality

Abstract

Infinite servers queuing systems are often used to solve a large number of practical problems, namely in Engineering, Biology, Management, Finance and Sociology. The study of the M/G/∞ systems busy period is very important. Yet it is a very difficult task. This paper presents a service time distributions collection for which the length of the busy period is almost exponential. It is also shown that in heavy-traffic conditions, for a certain class of service time distributions, the length of the busy period of the M/G/∞ systems is approximately exponentially distributed. Thus, in all these cases, the study of this busy period is much simpler.It is also exemplified, with the power function and the Pareto service distributions, that it is possible to have in some particular situations an approximately exponential behaviour for the M/G/∞ queue busy period length.