APPROXIMATE TRANSIENT ANALYSIS OF SOME QUEUING SYSTEMS

Approximations for the time-dependent queue size distribution P//n(t) and the mean queue size E left bracket X(t) right bracket of an M/M/1 queue are proposed. With a Laplace transform-generating function technique, the exact analysis involves the complex root u*** inside the unit circle of a certain quadratic. The exact value of u*** leads to transforms that, when inverted, yield rather complicated expressions for P//n(t) and E left bracket X(t) right bracket . Three iterative procedures that give successive rational approximations for u*** are discussed. The methods can be applied to approximate the behavior of more complicated queues. Applications to the M/M/2 queue and the M/E//p/1 queue are discussed.