The transient M/G/1/0 queue: some bounds and approximations for light traffic with application to reliability. (1995) - Atkinson, J. Ben
Abstract : We consider the transient analysis of the M / G / 1 / 0 queue, for which P n ( t ) denotes the probability that there are no customers in the system at time t, given that there are n ( n = 0, 1 ) customers in the system at time 0 . The analysis, which is based upon coupling theory, leads to simple bounds on P n ( t ) for the M / G / 1 / 0 and M / PH / 1 / 0 queues and improved bounds for the special case M / E r / 1 / 0 . Numerical results are presented for various values of the mean arrival rate λ to demonstrate the increasing accuracy of approximations based upon the above bounds in light traffic, i.e., as λ → 0 . An important area of application for the M / G / 1 / 0 queue is as a reliability model for a single repairable component. Since most practical reliability problems have λ values that are small relative to the mean service rate, the approximations are potentially useful in that context. A duality relation between the M / G / 1 / 0 and GI / M / 1 / 0 queues is also described.