Some structural properties of a Markovian storage/production system

Autor(en): Stadje, W 
Stichwörter: Computer Science; Computer Science, Interdisciplinary Applications; content process; independent increments; M/G/1; nonhomogeneous Poisson process; Operations Research & Management Science; peak; storage/production system; virtual waiting time
Erscheinungsdatum: 1997
Herausgeber: BALTZER SCI PUBL BV
Journal: QUEUEING SYSTEMS
Volumen: 25
Ausgabe: 1-4
Startseite: 339
Seitenende: 350
Zusammenfassung: 
We consider a storage/production system with state-dependent production rate and state-dependent demand arrival rate. Every arriving demand gives rise to a `peak' in the trajectory of the content process. We characterize the processes N-0(x) and N-1(x), defined as the number of peaks and the number of record peaks, respectively, before the content reaches the level x. The results are applied to the virtual waiting time process W(t) of a M/G/1 queue. Assuming that W(0) = x(0), M(x) is defined to be the number of arrivals before the virtual waiting time drops from x(0) to x(0-x) (0 less than or equal to x less than or equal to x(0)); in particular, M(x(0)) is the number of customers arriving during the first busy period. It is shown that (M(x))(0 less than or equal to x less than or equal to x0) is a compound Poisson process, and its jump size distribution is derived in closed form.
ISSN: 02570130
DOI: 10.1023/A:1019112703841

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