In the Search for the Infinite Servers Queue with Poisson Arrivals Busy Period Distribution Exponential Behavior

TL;DR

This paper investigates conditions under which the busy period length in an infinite servers queue with Poisson arrivals exhibits exponential behavior, providing theoretical insights and practical implications for managing server resources.

Contribution

It presents a general theoretical result characterizing exponential behavior in the busy period distribution of infinite servers queues with Poisson arrivals.

Findings

Derived conditions for exponential busy period distribution

Computed moments of busy period length

Implications for server management in practical applications

Abstract

This paper purpose is to investigate exponential behavior conditions for the infinite servers queue with Poisson arrivals busy period length distribution. It is presented a general theoretical result that is the basis of this work. The complementary analysis rely on the infinite servers queue with Poisson arrivals busy period length distribution moments computation. In infinite servers queue with Poisson arrivals practical applications, in economic, management, and business areas, the management of the effective number of servers is essential since the physical presence of infinite servers is not viable and so it is necessary to create that condition through an adequate management of the number of servers during the busy period.