Heavy Traffic and Singular Control Problems: Examples and Markov Chain Approximations

Abstract

Many of the process models which are used for purposes of analysis or control are approximations to the true physical model. Perhaps the dimension of the actual physical model is very high, or it might be difficult to define a manageable controlled dynamical (Markov) system model which describes well the quantities of basic interest. Sometimes the sheer size of the problem and the nature of the interactions of the component effects allows a good approximation to be made, in the sense that some form of the central limit theorem might be used to “summarize” or “aggregate” many of the random influences and provide a good description of the quantities of interest. Because these simpler or aggregate models will be used in an optimization problem, we need to be sure that optimal or nearly optimal controls (and the minimum value function, resp.) for the aggregated problem will also be nearly optimal for the actual physical problem (and a good approximation to the associated minimum value function, resp.).