The Covariance Function of the Virtual Waiting-Time Process in an M/G/1 Queue

Authors

Teunis J. Ott

Document Type

Report

Publication Date

7-1-1975

Abstract

Let R(t) be the covariance function of the stationary virtual waiting-time process of a stable M|G|1 queue. It is proven that if R(t) exists, i.e., if the service-times have a finite third movement, then R(t) is positive and convex on [0,∞), with an absolutely continuous derivative R' and a bounded, non-negative second derivative R". Also, lim R(t) = 0 and R" can not be chosen monotone. Contrary to a finding by Beneš (1957) it is proven that ∫₀^∞ R(t) dt < ∞ if and only if the service-times have a finite fourth moment.

Keywords

Operations research, Queuing theory, Stochastic processes, Analysis of covariance, Time-series analysis, Mathematical statistics

Publication Title

Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University

Issue

Technical memorandum no. 379

Rights

This work is in the public domain and may be freely downloaded for personal or academic use

Recommended Citation

Ott, Teunis J., "The Covariance Function of the Virtual Waiting-Time Process in an M/G/1 Queue" (1975). Research Reports from the Department of Operations. 117.
https://commons.case.edu/wsom-ops-reports/117