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Busy period, virtual waiting time and number of customers in G δ|M ϰ|1|B system.
- Source :
- Queueing Systems; Jun2010, Vol. 65 Issue 2, p175-209, 35p
- Publication Year :
- 2010
-
Abstract
- In this article, we determine the integral transforms of several two-boundary functionals for a difference of a compound Poisson process and a compound renewal process. Another part of the article is devoted to studying the above-mentioned process reflected at its infimum. We use the results obtained to study a G<superscript> δ</superscript>|M<superscript> ϰ</superscript>|1|B system with batch arrivals and finite buffer in the case when δ∼ge( λ). We derive the distributions of the main characteristics of the queuing system, such as the busy period, the time of the first loss of a customer, the number of customers in the system, the virtual waiting time in transient and stationary regimes. The advantage is that these results are given in a closed form, namely, in terms of the resolvent sequences of the process. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02570130
- Volume :
- 65
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Queueing Systems
- Publication Type :
- Academic Journal
- Accession number :
- 50035995
- Full Text :
- https://doi.org/10.1007/s11134-010-9170-5