The Annals of Applied Probability

Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function

Amarjit Budhiraja and Arka Prasanna Ghosh

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Abstract

We consider the scheduling control problem for a family of unitary networks under heavy traffic, with general interarrival and service times, probabilistic routing and infinite horizon discounted linear holding cost. A natural nonanticipativity condition for admissibility of control policies is introduced. The condition is seen to hold for a broad class of problems. Using this formulation of admissible controls and a time-transformation technique, we establish that the infimum of the cost for the network control problem over all admissible sequencing control policies is asymptotically bounded below by the value function of an associated diffusion control problem (the Brownian control problem). This result provides a useful bound on the best achievable performance for any admissible control policy for a wide class of networks.

Article information

Source
Ann. Appl. Probab., Volume 16, Number 4 (2006), 1962-2006.

Dates
First available in Project Euclid: 17 January 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1169065213

Digital Object Identifier
doi:10.1214/105051606000000457

Mathematical Reviews number (MathSciNet)
MR2288710

Zentralblatt MATH identifier
1125.60096

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 equivalent workload formulation unitary networks asymptotic optimality

Citation

Budhiraja, Amarjit; Ghosh, Arka Prasanna. Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function. Ann. Appl. Probab. 16 (2006), no. 4, 1962--2006. doi:10.1214/105051606000000457. https://projecteuclid.org/euclid.aoap/1169065213


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