Stochastic Networks: Admission and Routing Using Penalty Functions

  • Authors:

  • Jan Cosyn;Karl Sigman

  • Affiliations:

  • Nuon Belgium NV, Weggevoerdenstraat 16, 9200 Dendermonde, Belgium jan.cosyn@tiscali.be;Department of Industrial Engineering and Operations Research, Columbia University, 500 West 120th Street, MC:4704, New York, NY 10027, USA karl.sigman@columbia.edu

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2004

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Abstract

We propose an admission and routing control policy for a network of service facilities in a stochastic setting in order to maximize a long run average reward. Queueing and reneging before entering the network is allowed; we introduce orbiting as an approximation to the queueing. Once a customer has entered the network, it incurs no more waiting. Our control policy is easy to implement and we prove that it performs well in steady state as long as the capacity request sizes are relatively small compared to the capacity of the service facilities. The policy is a target tracking policy: a linear program provides a target operating point and an exponential penalty function is used to translate the optimal deterministic point into a feasible admission and routing policy. This translation essentially transforms the admission and routing control problem into a problem of load balancing via the construction of fictitious systems. Simulation studies are included to illustrate that our policy also performs well when request sizes are moderate or large with respect to the capacity.