A Bound on the Variance of the Waiting Time in a Queueing System

TL;DR

This paper establishes that under weak conditions, FCFS minimizes and LCFS maximizes the variance of waiting times in queueing systems, providing bounds on variability across service disciplines.

Contribution

It proves that LCFS maximizes the waiting time variance under conditions similar to those for FCFS minimization, extending understanding of variability bounds.

Findings

FCFS minimizes waiting time variance

LCFS maximizes waiting time variance

Provides bounds on variance for all disciplines

Abstract

Kingman has shown, under very weak conditions on the interarrival- and sevice-time distributions, that First-Come-First-Served minimizes the variance of the waiting time among possible service disciplines. We show, under the same conditions, that Last-Come-First-Served maximizes the variance of the waiting time, thereby giving an upper bound on the variance among all disciplines.