On a Retrial Single-Server Queueing System with Finite Buffer and Multivariate Poisson Flow

On a Retrial Single-Server Queueing System with Finite Buffer and Multivariate Poisson Flow We consider a single-server queueing system with a finite buffer, K input Poisson flows of intensities λ i , and distribution functions B i (x) of service times for calls of the ith type, $$i = \overline {1,K}$$ . If the buffer is overflowed, an arriving call is sent to the orbit and becomes a repeat call. In a random time, which has exponential distribution, the call makes an attempt to reenter the buffer or server, if the latter is free. The maximum number of calls in the orbit is limited; if the orbit is overflowed, an arriving call is lost. We find the relation between steady-state distributions of this system and a system with one Poisson flow of intensity $${\lambda } = \sum\limits_{i = 1}^K {{\lambda }_i }$$ where type i of a call is chosen with probability λ i /λ at the beginning of its service. A numerical example is given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

On a Retrial Single-Server Queueing System with Finite Buffer and Multivariate Poisson Flow

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Publisher
Springer Journals
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/A:1013883603388
Publisher site
See Article on Publisher Site

Abstract

We consider a single-server queueing system with a finite buffer, K input Poisson flows of intensities λ i , and distribution functions B i (x) of service times for calls of the ith type, $$i = \overline {1,K}$$ . If the buffer is overflowed, an arriving call is sent to the orbit and becomes a repeat call. In a random time, which has exponential distribution, the call makes an attempt to reenter the buffer or server, if the latter is free. The maximum number of calls in the orbit is limited; if the orbit is overflowed, an arriving call is lost. We find the relation between steady-state distributions of this system and a system with one Poisson flow of intensity $${\lambda } = \sum\limits_{i = 1}^K {{\lambda }_i }$$ where type i of a call is chosen with probability λ i /λ at the beginning of its service. A numerical example is given.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 9, 2004

References

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