Infinite Servers with Poisson Arrivals Queue Busy Period with PME Distribution

TL;DR

This paper demonstrates that in an infinite server queue with Poisson arrivals, a PME-distributed busy period implies the service time has a long tail distribution, using Laplace transform analysis.

Contribution

It establishes a novel link between PME-distributed busy periods and long tail service times in infinite server queues.

Findings

Busy period with PME distribution implies long tail service times.

Laplace transform analysis is used to derive the result.

Provides insight into queue behavior with specific distributional assumptions.

Abstract

In this article it is shown that if the busy period of a MGinf queue system is PME distributed, the service time is a random variable with a long tail distribution. The result is obtained through Laplace transforms analysis.