Preliminary Results on a Simple Approach to G/G/c-Like Queues

In this paper we consider a multi-server queue with a near general arrival process (represented as an arbitrary state-dependent Coxian distribution), a near general state-dependent Coxian service time distribution and a possibly finite queueing room. In addition to the dependence on the current number of customers in the system, the rate of arrivals and the progress of the service may depend on each other. We propose a semi-numerical method based on the use of conditional probabilities to compute the steady-state queue length distribution in such a queueing system. Our approach is conceptually simple, easy to implement and can be applied to both infinite and finite Cm/Ck/c-like queues. The proposed method uses a simple fixed-point iteration. In the case of infinite queues, it avoids the need for arbitrary truncation through the use of asymptotic conditional probabilities. This preliminary study examines the computational behavior of the proposed method with a Cox-2 service distrib...

• Type: Conference
• Year: 2009
• Where: ASMTA
• Authors: Alexandre Brandwajn, Thomas Begin
• Keywords: ASMTA 2009, Queue Length Distribution, Service Times, Steady-state Queue Length, Stochastic Modeling