The Effect of Increasing Routing Choice on Resource Pooling

Stephen R. E. Turner

70 citations0/0 files storedProbability in the Engineering and Informational Sciences

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Optimization and Search Problems

Abstract

We consider a network of N identical /M/l or /M/∞ queues. There are two types of arriving customers, those that have no routing choice, and those that first pick r queues at random, and are then routed to the least busy of those queues. We derive the limiting distribution of queue lengths as N→∞, and investigate how this distribution varies with r. We show that even a small amount of routing choice can lead to substantial gains in performance through resource pooling. We corroborate these conclusions by carrying out some simulations of a related model, from which the previous model can be derived by an exchangeable queue simplification. We also observe that the exchangeable queue simplification results in a performance gain for some parameters, in contrast to earlier work.

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References

1987Brownian Motion and Stochastic Flow Systems.1986Comparison Methods for Queues and Other Stochastic Models.1984Comparison Methods for Queues and Other Stochastic Models 1991Loss Networks 1985Blocking When Service Is Required From Several Facilities Simultaneously 1993Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling 1997Dynamic control of Brownian networks: state space collapse and\n\t\t equivalent workload formulations

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