Abstract
In this paper, we consider a queueing system under the D-policy in which there are two classes of customers. Class-1 customers have a non-preemptive priority over class-2 customers. The idle server begins to serve the customers only when the total workload of the waiting customers (regardless of their classes) exceeds D. We derive the Laplace-Stieltjes transform of the waiting time of each class of customers. We then derive the mean waiting times. Lastly, we compare our analytical results with the simulation estimates for verification purposes.
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