Applications of Singular Perturbation Methods in Queueing

A survey is presented describing the application of singular perturbation techniques to queueing systems. The goal is to compute performance measures by constructing approximate solutions to specific problems involving either the Kolmogorov forward or backward equation which contain a small parameter. These techniques are particularly useful on problems for which exact solutions are not available. Four different classes of problems are surveyed: (i) state-dependent queues; (ii) systems with a processor-sharing server; (iii) queueing networks; (iv) time dependent behavior. For each class, an illustrative example is presented along with the direction of current research.