Journal article

Networks of of infinite-server queues with multiplicative transitions

Dieter Fiems, Michel Mandjes, Brendan Patch



This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a ‘multiplicative transition’). For this model we characterize the joint probability generating function in terms of a system of partial differential equations; this system enables the evaluation of (transient as well as stationary) moments. We show that several relevant systems fit in the framework developed, such as networks of retrial queues, networks in which jobs can be rerouted when links fail, and storage systems. Numerical examples illustrate how our results can be used to support design problems.

University of Melbourne Researchers


Awarded by NWO Gravitation Programme Networks

Awarded by NWO Top Grant

Awarded by ARC Centre of Excellence for Mathematical and Statistical Frontiers

Funding Acknowledgements

The authors wish to thank Peter Taylor (The University of Melbourne) and Ross McVinish (The University of Queensland) for useful remarks. The research for this paper is partly funded by the NWO Gravitation Programme Networks, Grant Number 024.002.003 (Mandjes, Patch), an NWO Top Grant, Grant Number 613.001.352 (Mandjes), the ARC Centre of Excellence for Mathematical and Statistical Frontiers under grant number CE140100049 (Patch), and an Australian Government Research Training Program (RTP) scholarship (Patch).