Chapter 4 Diffusion approximations

Publisher Summary This chapter presents an overview of the basic applications of the theory of diffusion approximations to operations research. A diffusion approximation is a technique in which a complicated and analytically intractable stochastic process is replaced by an appropriate diffusion process. A diffusion process is a Markov process having continuous sample paths. Diffusion processes have a great deal of analytical structure and are, therefore, more mathematically tractable than the original process with which the user starts. The approach underlying the application of diffusion approximations is, therefore, comparable to that underlying normal approximation for sums of random variables. In the latter setting, the central limit theorem permits to replace the analytically intractable sum of random variables by an appropriately chosen normal random variable. The chapter also describes the basic theory of weak convergence that underlies the method of diffusion approximation. It highlights various applications of this methodology to the approximation of complex queueing systems. Because the focus is on developing approximations for the distribution of a process, the basic elements of the theory of weak convergence in a function space are described in the chapter.