Analysis of bulk arrival queuing model for quality of service based traffic scheduling

Method of Moments defines a recursion on higher-order moments of queue-lengths that is solved at each step by a linear system of equations. This method provides an alternative approach to derive the higher moments of queue length instead of taking the derivatives of Moment Generating Function. The presented results are in continuation of previous research on M/M/1 and M/M/1/B queues. The moment recursive formulas of the queue length distribution for the various Markovian queues is presented along with the consideration of bulk queue represented as M/M^[k]/1. The recursive formula for M/M^[k]/1 queue is derived along with graphical analysis of Markovian queues. The moments of queue length distribution are analysed with respect to utilization factor. The higher utilization of system reduces the mean waiting time of service hence increases the quality of service.