Moments Of Queue Length In M/M[k]/1 Queue using Recursive Formula

Knowledge of the moments of production and queue lengths are sufficient to carry out a great number of performance evaluation, optimization, and decision support tasks. With the multiple points of view that exist in any queuing system, several measures are necessary in order to specify overall system Quality of service. An application of the higher moments of queue length distribution is related to optimization problem. Starting from the basic state transition equations of the queue, we get the recursive formula for the moments of queue length distribution. This method provides an alternative approach to derive the higher moments of queue length, instead of taking the derivatives of Moment Generating Function.