M/D/1 Queues with LIFO and SIRO Policies

TL;DR

This paper compares M/D/1 queues with LIFO and SIRO policies, highlighting the known symbolic results for LIFO and the numerical challenges for SIRO, emphasizing the need for alternative approaches.

Contribution

It provides a detailed analysis of the equilibrium waiting time densities for M/D/1-LIFO and M/D/1-SIRO queues, identifying computational limitations for SIRO.

Findings

Symbolic solutions are available for M/D/1-LIFO waiting times.

Numerical methods for M/D/1-SIRO are limited due to inverse Laplace transform issues.

Implementing Burke's recursions for SIRO remains challenging.

Abstract

While symbolics for the equilibrium M/D/1-LIFO waiting time density are completely known, corresponding numerics for M/D/1-SIRO are derived from recursions due to Burke (1959). Implementing an inverse Laplace transform-based approach for the latter remains unworkable.