A Queueing Model for Sleep as a Vacation

TL;DR

This paper models sleep as a vacation in queueing systems, comparing systems with working and regular vacations to standard models using matrix-analytic methods to analyze service rates and customer numbers.

Contribution

It introduces a queueing model incorporating sleep as a vacation, extending classical queueing theory with analytical comparisons between different vacation types.

Findings

Comparison of mean service rates between vacation and non-vacation systems

Analysis of expected customer numbers in systems with sleep vacations

Application of matrix-analytic methods to evaluate system performance

Abstract

Vacation queueing systems are widely used as an extension of the classical queueing theory. We consider both working vacations and regular vacations in this paper, and compare systems with vacations to the regular $M/M/1$ system via mean service rates and expected numbers of customers, using matrix-analytic methods.