Analytical distribution of waiting time in the M/{iD}/1 queue
We give an analytical formula for the steady-state distribution of queue-wait in the M/G/1 queue, where the service time for each customer is a positive integer multiple of a constant D > 0. We call this an M/{iD}/1 queue. We give numerical algorithms to calculate the distribution. In addition, in the case that the service distribution is sparse, we give revised algorithms that can compute the distribution more quickly.
waiting time m/discrete/1 queue m/d/1 queue integer partitions numerical queueing methods