M/G/1-FIFO Queue with Uniform Service Times

TL;DR

This paper derives an exact formula for the equilibrium waiting time density in an M/U/1 queue with uniform service times, using inverse Laplace transforms and delay differential equations, and discusses tail asymptotics and queue lengths.

Contribution

It provides a novel exact analytical expression for the waiting time distribution in M/U/1 queues, advancing theoretical understanding.

Findings

Exact waiting time density formula derived

Analysis of tail probability asymptotics conducted

Insights into queue length distributions obtained

Abstract

An exact formula for the equilibrium M/U/1 waiting time density is now effectively known. What began as a numeric exploration became a symbolic banquet. Inverse Laplace transforms provided breadcrumbs in the trail; delay differential equations subsequently gave clear-cut precision. We also remark on tail probability asymptotics and on queue lengths.