Diffusion Approximations for Complex Repair Systems.

摘要

A wide variety of complex repair systems can be modeled as continuous time Markov chains. These systems are closed networks of queues with a total of n jobs circulating in the network. The process of interest is the number of jobs, X sub n (t), at the various repair centers at time t. After appropriate translation and scaling, we show that the processes (X sub n (t) : t > or = 0) converge weakly to a limiting multivariate Ornstein-Uhlenbeck process. This limit process is then used to obtain computable approximations for X sub n (t). Numerical results are presented for three specific repairman models and the approximations are compared with exact results obtained through product form formulae. In most cases the approximation is quite accurate.