The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 16, Number 4 (2006), 1962-2006.
Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function
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.
Ann. Appl. Probab., Volume 16, Number 4 (2006), 1962-2006.
First available in Project Euclid: 17 January 2007
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. 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