The Study Of Two Types Of Processors-sharing Queuing System

Systems in which the service rates of stations change at the moments that one of stations becomes empty, are known in the literature as systems with coupled processors. In this dissertation, we discuss two types of processors sharing queuing system. One is two parallel queues with coupled processors;The other is the joining the shortest queue model with processor sharing.The dissertation contains three parts: In Chapter 1, the basic application background, advanced studies and the main idea of this paper are introduced. In Chapter 2,I consider a queuing system in which there are two exponential servers, each having his own queue, and arriving customers will join the two queues separately, and analyze the two-dimensional Markov process representing the numbers of jobs in the two stations. A functional equation for the generating function of the stationary distribution of this two-dimensional process is derived and solved through the theory of Riemann-Hilbert boundary value problems. In Chapter 3, I consider the system with two parallel queues, in which arrivals join the shorter queue.I describe the problem of coupling and show that the generating function F(x,y)can be continued as a meromorphic function to the whole complex plane. I consider a particular problem but the results offer a computationally reasonable solution which applies to very general two-dimensional random walks. It is a difficult work using the analytical functional theory of boundary value problems to study JSQ-PS model.