On generalized networks of queues with positive and negative arrivals

Document Type

Article

Publication Date

1-1-1993

Abstract

Consider a generalized queueing network model that is subject to two types of arrivals. The first type represents the regular customers; the second type rep-, resents signals. A signal induces a regular customer already present at a node • to leave. Gelenbe [5] showed that such a network possesses a product form solution when each node consists of a single exponential server. In this paper we study a number of issues concerning this class of networks. First, we explain why such networks have a product form solution. Second, we generalize existing results to include different service disciplines, state-dependent service rates, multiple job classes, and batch servicing. Finally, we establish the relationship between these networks and networks of quasi-reversible queues. We show that the product form solution of the generalized networks is a consequence of a property of the individual nodes viewed in isolation. This property is similar to the quasi-reversibility property of the nodes of a Jackson network: if the arrivals of the regular customers and of the signals at a node in isolation are independent Poisson, the departure processes of the regular customers and the signals are also independent Poisson, and the current state of the system is independent of the past departure processes. © 1993, Cambridge University Press. All rights reserved.

Identifier

84976137499 (Scopus)

Publication Title

Probability in the Engineering and Informational Sciences

External Full Text Location

https://doi.org/10.1017/S0269964800002941

e-ISSN

14698951

ISSN

02699648

First Page

301

Last Page

334

Issue

3

Volume

7

Grant

421900

Fund Ref

National Science Foundation

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