ON THE DIFFUSION-APPROXIMATION TO 2 PARALLEL QUEUES WITH PROCESSOR SHARING

We consider a two-dimensional queueing model in which the server in the second queue helps the server in the first queue during periods when the second queue is empty. We analyze the system in the heavy traffic limit and obtain explicit approximate solutions to the resulting diffusion equations using singular perturbation methods. Approximate asymptotic formulas are obtained for the stationary distribution of the number of customers as well as for some first passage time problems associated with the busy period. We show our formulas reduce to the asymptotic expansions of the exact solutions, when the latter are available.