Heavy traffic analysis of open processing networks with complete resource pooling: asymptotic optimality of discrete review policies

2005/03/23 by Baris Ata, Sunil Kumar · 1 citation
Mathematics · #math.PR #msc:60K25 #msc:60F17 #msc:68M20 #msc:90F35.

paper · pdf · doi:10.1214/105051604000000495

published as Annals of Applied Probability 2005, Vol. 15, No. 1A, 331-391 · Published at http://dx.doi.org/10.1214/105051604000000495 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

arxiv created 2005/03/23 · arxiv updated 2009/12/01

Abstract

We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks we consider satisfy the so-called complete resource pooling condition and therefore have one-dimensional approximating Brownian control problems. We propose a simple discrete review policy for controlling such networks. Assuming 2+εmoments on the interarrival times and processing times, we provide a conceptually simple proof of asymptotic optimality of the proposed policy.

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