Heavy traffic analysis of maximum pressure policies for stochastic processing networks with multiple bottlenecks

Authors:
Barış Ata;Wuqin Lin
Affiliations:
Kellogg School of Management, Northwestern University, Evanston, USA 60208;Kellogg School of Management, Northwestern University, Evanston, USA 60208
Venue:
Queueing Systems: Theory and Applications
Year:
2008

Citing 11
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Abstract

A class of open processing networks operating under a maximum pressure policy is considered in the heavy traffic regime. We prove that the diffusion-scaled workload process for a network with several bottleneck resources converges to a semimartingale reflecting Brownian motion (SRBM) living in a polyhedral cone. We also establish a state space collapse result that the queue length process can be lifted from the lower-dimensional workload process.