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Title

A large closed queueing network containing two types of node and multiple customer classes: one bottleneck station

Author(s)

Abramov, Vyacheslav M.

Abstract

The paper studies a closed queueing network containing two types of node. The first type (server station) is an infinite server queueing system, and the second type (client station) is a single server queueing system with autonomous service, i.e. every client station serves customers (units) only at random instants generated by strictly stationary and ergodic sequence of random variables. It is assumed that there are r server stations. At the initial time moment all units are distributed in the server stations, and the ith server station contains N i units, i=1,2,...,r, where all the values N i are large numbers of the same order. The total number of client stations is equal to k. The expected times between departures in the client stations are small values of the order O(N -1) (N=N 1+N 2+...+N r). After service completion in the ith server station a unit is transmitted to the jth client station with probability p i,j (j=1,2,...,k), and being served in the jth client station the unit returns to the ith server station. Under the assumption that only one of the client stations is a bottleneck node, i.e. the expected number of arrivals per time unit to the node is greater than the expected number of departures from that node, the paper derives the representation for non-stationary queue-length distributions in non-bottleneck client stations.

Publication type

Journal article

Source

Queueing Systems, Vol. 48, no. 1-2 (Sep 2004), pp. 45-73

Publication year

2004

FOR Code(s)

0102 Applied Mathematics;  0103 Numerical and Computational Mathematics;  0104 Statistics

Keyword(s)

Autonomous service;  Bottleneck;  Closed queueing network;  Martingales;  Multiple customer classes;  Semimartingales;  Stochastic calculus

Publisher

Springer

ISSN

0257-0130

Publisher URL

http://dx.doi.org/10.1023/B:QUES.0000039887.30622.ef

Copyright

Copyright © 2004 Kluwer Academic Publishers. The accepted manuscript is reproduced in accordance with the copyright policy of the publisher. The definitive version is available at www.springer.com.

Full text

Peer reviewed