Paper Info
Title
The Remaining Service Time upon Reaching a High Level in M/G/1 Queues
Abstract
The distribution of the remaining service time upon reaching some target level in an M/G/1 queue is of theoretical as well as practical interest. In general, this distribution depends on the initial level as well as on the target level, say, B. Two initial levels are of particular interest, namely, level “1” (i.e., upon arrival to an empty system) and level “B−1” (i.e., upon departure at the target level).In this paper, we consider a busy cycle and show that the remaining service time distribution, upon reaching a high level B due to an arrival, converges to a limiting distribution for B→∞. We determine this asymptotic distribution upon the “first hit” (i.e., starting with an arrival to an empty system) and upon “subsequent hits” (i.e., starting with a departure at the target) into a high target level B. The form of the limiting (asymptotic) distribution of the remaining service time depends on whether the system is stable or not. The asymptotic analysis in this paper also enables us to obtain good analytical approximations of interesting quantities associated with rare events, such as overflow probabilities.
Year
DOI
Venue
2001
10.1023/A:1017935616446
Queueing Syst.
Keywords
Field
DocType
remaining service time,asymptotics,M,/,G,/1 queue,level crossing
Applied mathematics,Mathematical optimization,Telecommunications,Level crossing,Queue,M/G/1 queue,Asymptotic analysis,Service time,Mathematics,Limiting,Rare events,Asymptotic distribution
Journal
Volume
Issue
ISSN
39
1
1572-9443
Citations 
PageRank 
References 
10
1.40
0
Authors
3
Name
Order
Citations
PageRank
Pieter-Tjerk de Boer118422.82
Victor F. Nicola246884.45
Jan-kees C. W. Van Ommeren3738.53