A conditional probability approach to M/G/1-like queues

Following up on a recently renewed interest in computational methods for M/G/1-type processes, this paper considers an M/G/1-like system in which the service time distribution is represented by a Coxian series of memoryless stages. We present a novel approach to the solution of such systems. Our method is based on conditional probabilities, and provides a simple, computationally efficient and stable approach to the evaluation of the steady-state queue length distribution. We provide a proof of the numerical stability of our method. Without explicit use of matrix-geometric techniques or stochastic complementation, we are able to handle systems with state-dependent service and arrival rates. The proposed approach can be used to compute the queue length distribution for both finite and infinite M/G/1-like queues. In the case of an infinite, state-independent queue, our method allows us to show using elementary tools that the queue length distribution is asymptotically geometric. The para...

• Type: Journal
• Year: 2008
• Where: PE
• Authors: Alexandre Brandwajn, Hongyun Wang
• Keywords: Optimization, PE 2008, Queue Length Distribution, Service Time Distribution, Steady-state Queue Length