The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 15, Number 3 (2005), 1887-1935.
A large deviations approach to asymptotically optimal control of crisscross network in heavy traffic
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.
Ann. Appl. Probab., Volume 15, Number 3 (2005), 1887-1935.
First available in Project Euclid: 15 July 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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