Mathematics – Probability
Scientific paper
2009-01-16
Annals of Applied Probability 2008, Vol. 18, No. 6, 2239-2299
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/08-AAP522 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/08-AAP522
We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each quadratic holding cost structure, there is a maximum pressure policy that asymptotically minimizes the holding cost. A key to the optimality proofs is to prove a state space collapse result and a heavy traffic limit theorem for the network processes under a maximum pressure policy. We extend a framework of Bramson [Queueing Systems Theory Appl. 30 (1998) 89--148] and Williams [Queueing Systems Theory Appl. 30 (1998b) 5--25] from the multiclass queueing network setting to the stochastic processing network setting to prove the state space collapse result and the heavy traffic limit theorem. The extension can be adapted to other studies of stochastic processing networks.
Dai Jim G.
Lin Wuqin
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