QUEUE, with Poisson arrivals, constant service time and infinite servers, BUSY PERIOD DISTRIBUTION

TL;DR

This paper derives exact parameters and interprets the probability density function of the busy period in an infinite-server queue with Poisson arrivals and constant service time, providing an algorithm for distribution computation.

Contribution

It provides exact calculations and a computational algorithm for the busy period distribution in an infinite-server queue with Poisson arrivals and constant service time.

Findings

Exact parameters of the busy period distribution are computed.

An algorithm for computing the distribution function is developed and demonstrated.

The probability density function is interpreted and explained in detail.

Abstract

The queue system,with Poisson arrivals,constant service time and infinite servers, busy period distribution is intensively studied because, due to its probability density function quite easy interpretation, it may serve as a clue to interpret the queue systems, with Poisson arrivals, infinite servers, and other service time distributions, busy period distributions. In this work the queue system, with Poisson arrivals,constant service time and infinite servers, busy period distribution parameters are exactly computed and its probability density function is interpreted and explained. The only problem is how to compute the distribution function, for which an algorithm is presented and exemplified its application.