Waiting time dynamics of priority-queue networks

Details Waiting time dynamics of priority-queue networks Waiting time dynamics of priority-queue networks

2009-03-04

arxiv.org/abs/0903.0704v2

Phys. Rev. E 79, 056110 (2009)

Physics

Data Analysis, Statistics and Probability

5 pages, 3 figures, minor changes, final published version

Scientific paper

10.1103/PhysRevE.79.056110

We study the dynamics of priority-queue networks, generalizations of the binary interacting priority queue model introduced by Oliveira and Vazquez [Physica A {\bf 388}, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.

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