Large deviations approach to asymptotically optimal control of crisscross network in heavy traffic

• 成果类型: Article
• 署名作者: Budhiraja, A; Ghosh, AP
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000250
• 发表日期: 2005
• 页码: 1887-1935
• 关键词: parallel servers; SYSTEM; CONVERGENCE; workload; QUEUE

摘要

In this work we study the problem of asymptotically optimal control of a well-known multi-class queuing network, referred to as the crisscross network, in heavy traffic. We consider exponential inter-arrival and service times, linear holding cost and an infinite horizon discounted cost criterion. In a suitable parameter regime, this problem has been studied in detail by Martins, Shreve and Soner [SIAM J. Control Optim. 34 (1996) 21332171] using viscosity solution methods. In this work, using the pathwise solution of the Brownian control problem, we present an elementary and transparent treatment of the problem (with the identical parameter regime as in [SIAM J. Control Optim. 34 (1996) 2133-2171]) using large deviation ideas introduced in [Ann. Appl. Probab. 10 (2000) 75-103, Ann. Appl. Probab. 11 (2001) 608-649]. We obtain an asymptotically optimal scheduling policy which is of threshold type. The proof is of independent interest since it is one of the few results which gives the asymptotic optimality of a control policy for a network with a more than one-dimensional workload process.