Asymptotic optimality of maximum pressure policies in stochastic processing networks

Simple item page
dc.creatorDai, J. G.
dc.creatorLin, Wuqin
dc.date2009-01-16
dc.date.accessioned2026-07-07T12:31:03Z
dc.date.available2026-07-07T12:31:03Z
dc.descriptionWe 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/08-AAP522 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0901.2451
dc.identifierhttp://arxiv.org/abs/0901.2451
dc.identifierAnnals of Applied Probability 2008, Vol. 18, No. 6, 2239-2299
dc.identifierdoi:10.1214/08-AAP522
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216325
dc.subjectProbability
dc.subject90B15, 60K25 (Primary) 90B18, 90B22, 68M10, 60J60 (Secondary)
dc.titleAsymptotic optimality of maximum pressure policies in stochastic processing networks
dc.typetext

Files

Collections

arXiv