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A BMAP/SM/1 queueing system with Markovian arrival input of disasters

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Alexander Dudin  and
Shoichi Nishimura
Alexander Dudin*
Affiliation:
Belarus State University
Shoichi Nishimura*
Affiliation:
Science University of Tokyo
*
∗Postal address: Department of Applied Mathematics and Informatics, Belarus State University, 4, F.Skorina Ave, Minsk-50, 220050 Belarus.
∗∗Postal address: Department of Applied Mathematics, Science University of Tokyo, 1–3, Kagurazaka, Shinjuku-ku, Tokyo, 162–8601 Japan. Email address: nishimur@kagu.sut.ac.jp.
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Abstract

Disaster arrival in a queuing system with negative arrivals causes all customers to leave the system instantaneously. Here we obtain a queue-length and virtual waiting (sojourn) time distribution for the more complicated system BMAP/SM/1 with MAP input of disasters.

Keywords

Negative arrivalsBMAP/SM/1-type queuemodified multidimensional quasi-Toeplitz Markov chain

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 868 - 881
Copyright
Copyright © Applied Probability Trust 1999 

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