| Two examples are presented in this thesis that demonstrate how for a network with two queues, the queue length distribution can be characterized and performance measures calculated using complex analysis. The two models analyzed are (1) A symmetric "join the shortest queue" model with two, parallel, coupled processors, and (2) A two-node Jackson network with coupled processing.;For each model, a functional equation is found that provides a relationship through which the characteristic function can be derived as the solution to a complex boundary value problem. A concise form for the average queue lengths is also presented. |
