Controlled stochastic networks in heavy traffic: convergence of value functions
type: Item
instance of: scholarly article
title: Controlled stochastic networks in heavy traffic: convergence of value functions
zbMATH Open document ID: 1244.60091
DOI: 10.1214/11-AAP784
author: Amarjit Budhiraja
author: Arka P. Ghosh
published in: The Annals of Applied Probability
publication date: 2012-05-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1205.0925
full work available at URL: https://projecteuclid.org/euclid.aoap/1333372012
review text: Scheduling control problems for a family of unitary networks under heavy traffic with general inter-arrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control problems, which have been proposed as approximate models for the study of these critically loaded controlled stochastic networks, can be regarded as formal scaling limits of such stochastic systems. It is shown that, under broad conditions, the value function of the suitably scaled network control problem converges to that of the associated diffusion control problem. This scaling limit result, in addition to giving a precise mathematical basis for the above approximation approach, suggests a general strategy for constructing near optimal controls for the physical stochastic networks by solving the associated diffusion control problem.
reviewed by: Tiit Riismaa
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 68M20
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 90B36
Mathematics Subject Classification ID: 90B15
zbMATH DE Number: 6034169
zbMATH Keywords: stochastic control
zbMATH Keywords: scaling limits
zbMATH Keywords: diffusion approximation
zbMATH Keywords: unitary network
zbMATH Keywords: asymptotic optimality
zbMATH Keywords: singular control with state constraints
MaRDI profile type: Publication
arXiv ID: 1205.0925
cites work: Heavy traffic analysis of open processing networks with complete resource pooling: asymptotic optimality of discrete review policies
cites work: Singular control with state constraints on unbounded domain
cites work: Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy
cites work: Dynamic scheduling of a parallel server system in heavy traffic with complete resource pooling: asymptotic optimality of a threshold policy
cites work: On the Continuity of the Optimal Policy Set for Linear Programs
cites work: Two workload properties for Brownian networks
cites work: A large deviations approach to asymptotically optimal control of crisscross network in heavy traffic
cites work: Diffusion approximations for controlled stochastic networks: an asymptotic bound for the value function
cites work: Existence of optimal controls for singular control problems with state constraints
cites work: Q2730382
cites work: Asymptotic optimality of maximum pressure policies in stochastic processing networks
cites work: On lipschitz continuity of the solution mapping to the skorokhod problem, with applications
cites work: Convex duality and the Skorokhod problem. II
cites work: Q3721531
cites work: Q3806523
cites work: Q4894801
cites work: Brownian models of open processing networks: Canonical representation of workload.
cites work: Reflected Brownian motion on an orthant
cites work: Dynamic control of Brownian networks: State space collapse and equivalent workload formulations
cites work: Diffusion approximation for \(GI/G/1\) controlled queues
cites work: Q2730383
cites work: Q4004190
cites work: Heavy Traffic Analysis of a Controlled Multiclass Queueing Network via Weak Convergence Methods
cites work: Sequencing and Routing in Multiclass Queueing Networks Part II: Workload Relaxations
cites work: Control Techniques for Complex Networks
cites work: Asymptotically Optimal Admission Control of a Queue with Impatient Customers
cites work: An invariance principle for semimartingale reflecting Brownian motions in an orthant
description: scientific article; zbMATH DE number 6034169