Stability of multi-class queueing networks with infinite virtual queues

Authors:
Yongjiang Guo;Erjen Lefeber;Yoni Nazarathy;Gideon Weiss;Hanqin Zhang
Affiliations:
School of Science, Beijing University of Posts and Telecommunications, Beijing, China;Eindhoven University of Technology, Eindhoven, The Netherlands;The School of Mathematics and Physics, The University of Queensland, Brisbane, Australia;The University of Haifa, Haifa, Israel;Business School, National University of Singapore, Singapore, Singapore
Venue:
Queueing Systems: Theory and Applications
Year:
2014

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Abstract

We generalize the standard multi-class queueing network model by allowing both standard queues and infinite virtual queues which have an infinite supply of work. We pose the general problem of finding policies which allow some of the nodes of the network to work with full utilization, and yet keep all the standard queues in the system stable. Toward this end we show that re-entrant lines, systems of two re-entrant lines through two service stations, and rings of service stations can be stabilized with priority policies under certain parameter restrictions. The analysis throughout the paper depends on model and policy and illustrates the difficulty in solving the general problem.