The M/G/1 Queue in Heavy Traffic and its Covariance Function

Authors

Teunis J. Ott

Document Type

Report

Publication Date

8-1-1975

Abstract

Let X(t) be the virtual waiting-time process of a stable M|G|1 queue. Let R(t) be the covariance function of the stationary process X(t), B(t) the busy-period distribution of X(t); and let E(t) = P{X(t) = 0|X(0) = 0}. For X(t) some heavy-traffic results are given, among which limiting expressions for R(t) and its derivatives and for B(t) and E(t). These results are used to find the covariance function of stationary Brownian Motion on [0,∞).

Keywords

Operations research, Queuing theory, Stochastic processes, Brownian motion processes, Time-series analysis

Publication Title

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

Issue

Technical memorandum no. 387

Rights

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

Recommended Citation

Ott, Teunis J., "The M/G/1 Queue in Heavy Traffic and its Covariance Function" (1975). Research Reports from the Department of Operations. 275.
https://commons.case.edu/wsom-ops-reports/275