Paper Info
Title
Properties of the Process of Level Crossings During a Busy Cycle of the M/G/1 Queueing System
Abstract
The variables dv, v ∈ 0, ∞ with dv the number of downcrossings of level v of the virtual waiting time process during a busy cycle of a queueing system constitute a stochastic process {dv, v > 0}. For a stable M/G/1 queueing system this process is investigated in the present paper. Under certain conditions on the density of the service time distribution it is shown that this process is a birth and death process with constant birth rate and time-dependent death rate; however, for the M/M/1 system this process {dv, v > 0} has also constant death rate. A number of properties of the dv-process are studied, yielding also some new results for the M/G/1 queueing system. In particular an explicit expression is found for the variance of the area underneath the sample function of the virtual waiting time process during a busy cycle, thus solving a question posed by Iglehart.
Year
DOI
Venue
1978
10.1287/moor.3.2.133
Math. Oper. Res.
DocType
Volume
Issue
Journal
3
2
Citations 
PageRank 
References 
3
1.21
0
Authors
1
Name
Order
Citations
PageRank
J. W. Cohen1406.76