Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function

Details Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function

2007-02-14

arxiv.org/abs/math/0702402v1

Annals of Applied Probability 2006, Vol. 16, No. 4, 1962-2006

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000457 in the Annals of Applied Probability (available at http://www.imstat

Scientific paper

10.1214/105051606000000457

We consider the scheduling control problem for a family of unitary networks under heavy traffic, with general interarrival and service times, probabilistic routing and infinite horizon discounted linear holding cost. A natural nonanticipativity condition for admissibility of control policies is introduced. The condition is seen to hold for a broad class of problems. Using this formulation of admissible controls and a time-transformation technique, we establish that the infimum of the cost for the network control problem over all admissible sequencing control policies is asymptotically bounded below by the value function of an associated diffusion control problem (the Brownian control problem). This result provides a useful bound on the best achievable performance for any admissible control policy for a wide class of networks.

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