A recursive equations based representation for the $G/G/m$ queue

TL;DR

This paper introduces recursive equations for the G/G/m queue that model customer arrival and departure times using simple operations, providing a new mathematical framework for analyzing such queues.

Contribution

It presents a novel recursive representation for G/G/m queues based solely on maximum, minimum, and addition operations, enhancing analytical tools for queue modeling.

Findings

Recursive equations accurately model G/G/m queue dynamics.

The approach simplifies analysis by using only basic operations.

Potential for improved computational methods in queue analysis.

Abstract

New recursive equations designed for the G/G/m queue are presented. These equations describe the queue in terms of recursions for the arrival and departure times of customers, and involve only the operations of maximum, minimum and addition.