Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich. mehr Informationen...
The remaining service time upon reaching a high level in M/G/1 queues
Ist Teil von
Queueing systems, 2001-01, Vol.39 (1), p.55-78
Ort / Verlag
Dordrecht: Kluwer
Erscheinungsjahr
2001
Link zum Volltext
Quelle
SpringerLink Journals
Beschreibungen/Notizen
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[Right arrow][infinity]. 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. [PUBLICATION ABSTRACT]