A note on the stability of multiclass Markovian queueing networks

2010/06/22 by Sayee C. Kompalli, Kompalli, Sayee C., Ravi R. Mazumdar +1
Business, Management and Accounting · Engineering · #Advanced Queuing Theory Analysis #Advanced Wireless Network Optimization #Advanced Battery Technologies Research

paper · pdf · doi:10.48550/arxiv.1006.4387

Abstract

In this paper we show that in a multiclass Markovian network with unit rate servers, the condition that the average load ρ at every server is less than unity is indeed sufficient for the stability or positive recurrence for any work conserving scheduling policy and class-independent routing. We use a variation of the positive recurrence criterion for multidimensional discrete-time Markov chains over countable state spaces due to Rosberg (JAP, Vol.~17, No.~3, 1980) and a monotonicity argument to establish this assertion.

Citations

• Applying a New Device in the Optimization of Exponential Queuing Systems

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