Controlled stochastic networks in heavy traffic: convergence of value functions
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.
scientific article; zbMATH DE number 6034169
scientific article