The performance of the M/G/1 queue under the dyadic Min(N,D)-policy and its cost optimization

In this paper, we consider the M/G/1 queueing system under the Min(N,D)-policy in which the idle server resumes its service if either NN customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds DD, whichever occurs first.We first analyze the queue length, the workload and the waiting time. Then, we consider two linear cost models (one based on the mean workload and the other based on the mean queue length) and compare the optimal Min(N,D)-policy with the optimal NN-policy and the optimal DD-policy.