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The computation of steady-state distribution of parallel systems with two servers

This paper considers a queuing system that may be applied to specific networking systems and calculates the steady-state probabilities of the number of electronic signals waiting in this parallel queuing system to be transmitted. There are two identical servers, each has its own queue. Upon the arrival time, the new arrival goes into the shortest queue, and stays in that queue until it is served, i.e., no jockeying is allowed in this model. This is a well-known model. Using complex analysis and linear algebra, we are able to find the steady-state probabilities of the queue length. Numerical results are presented and the convergence rate is discussed.