Queueing Times in Geom(N)/G/1 Queue with Relative Priorities

This paper considers the mean queueing times for a multi-class discrete-time Geom/G/1 queueing model with relative priorities. We have derived the mean remaining queueing times for a job given its class, starting from the service commencement of an arbitrary job and conditioning on the numbers of other jobs from all classes. Based on this result, we obtain the unconditional mean queueing times upon arrival, which are functions of traffic intensities and priority parameters of all classes. Finally, we also give some numerical analysis in order to observe the effects of traffic intensities and priority parameters on the mean queueing times of each class on condition that there are two classes of jobs in the queue.