Queueing Systems

, Volume 47, Issue 1–2, pp 81–106 | Cite as

On Stochastic Bounds for Monotonic Processor Sharing Networks

  • T. Bonald
  • A. Proutière


We consider a network of processor sharing nodes with independent Poisson arrival processes. Nodes are coupled through their service capacity in that the speed of each node depends on the number of customers present at this and any other node. We assume the network is monotonic in the sense that removing a customer from any node increases the service rate of all customers. Under this assumption, we give stochastic bounds on the number of customers present at any node. We also identify limiting regimes that allow to test the tightness of these bounds. The bounds and the limiting regimes are insensitive to the service time distribution. We apply these results to a number of practically interesting systems, including the discriminatory processor sharing queue, the generalized processor sharing queue, and data networks whose resources are shared according to max–min fairness.

processor sharing networks stochastic bounds balance monotonicity insensitivity 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • T. Bonald
    • 1
  • A. Proutière
    • 1
  1. 1.France Telecom R&DFrance

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