Steady-state distributions of parallel queues

This paper is concerned with the steady-state probability distributions for a well-known parallel queue with two identical servers, each having its ow n queue. Upon the arrival time, the new arrival joins the shortest queue, a nd stays in that queue until being served. Jockeying between queues is not allowed. To make the problem solvable, the states of the resulting Markov c hain are truncated into a banded array. Two steady-state distributions will be derived by using probability generating function and matrix-geometric m ethod: the probability of queue length and the customer sojourn time. Under certain conditions, the sojourn time has a phase-type distribution. Numeri cal results are presented and the convergence of the truncated model is dis cussed.