The Annals of Applied Probability

Exponential penalty function control of loss networks

Garud Iyengar and Karl Sigman

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We introduce penalty-function-based admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is that it avoids solving the associated dynamic program. However, a disadvantage of this approach is that it requires the capacity requested by individual requests to be sufficiently small compared to total available capacity. We first solve a related deterministic linear program (LP) and then translate an optimal solution of the LP into an admission control policy for the loss network via an exponential penalty function. We show that the penalty policy is a target-tracking policy—it performs well because the optimal solution of the LP is a good target. We demonstrate that the penalty approach can be extended to track arbitrarily defined target sets. Results from preliminary simulation studies are included.

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Ann. Appl. Probab. Volume 14, Number 4 (2004), 1698-1740.

First available: 5 November 2004

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Zentralblatt MATH identifier

Primary: 93E03: Stochastic systems, general 93E35: Stochastic learning and adaptive control 90C59: Approximation methods and heuristics

Exponential penalty loss networks mathematical programming bounds stochastic control


Iyengar, Garud; Sigman, Karl. Exponential penalty function control of loss networks. The Annals of Applied Probability 14 (2004), no. 4, 1698--1740. doi:10.1214/105051604000000936.

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