The Annals of Applied Probability

Asymptotic optimality of maximum pressure policies in stochastic processing networks

J. G. Dai and Wuqin Lin

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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.

Article information

Ann. Appl. Probab. Volume 18, Number 6 (2008), 2239-2299.

First available in Project Euclid: 26 November 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90B15: Network models, stochastic 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 90B18: Communication networks [See also 68M10, 94A05] 90B22: Queues and service [See also 60K25, 68M20] 68M10: Network design and communication [See also 68R10, 90B18] 60J60: Diffusion processes [See also 58J65]

Stochastic processing networks maximum pressure policies backpressure policies heavy traffic Brownian models diffusion limits state space collapse asymptotic optimality


Dai, J. G.; Lin, Wuqin. Asymptotic optimality of maximum pressure policies in stochastic processing networks. Ann. Appl. Probab. 18 (2008), no. 6, 2239--2299. doi:10.1214/08-AAP522.

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