The Annals of Applied Probability

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

Amarjit Budhiraja and Arka Prasanna Ghosh

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Abstract

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) 2133–2171] 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.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 3 (2005), 1887-1935.

Dates
First available in Project Euclid: 15 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1121433772

Digital Object Identifier
doi:10.1214/105051605000000250

Mathematical Reviews number (MathSciNet)
MR2152248

Zentralblatt MATH identifier
1080.60084

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B22: Queues and service [See also 60K25, 68M20] 90B35: Scheduling theory, deterministic [See also 68M20]
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]

Keywords
Control of queuing networks heavy traffic Brownian control problem crisscross network large deviations asymptotic optimality

Citation

Budhiraja, Amarjit; Ghosh, Arka Prasanna. A large deviations approach to asymptotically optimal control of crisscross network in heavy traffic. Ann. Appl. Probab. 15 (2005), no. 3, 1887--1935. doi:10.1214/105051605000000250. https://projecteuclid.org/euclid.aoap/1121433772


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References

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