Average waiting time of customers in a priority M/D/k queue with finite buffers

Analysis of priority multiserver queues is known to be a difficult problem. In this paper, a priority M/D/k queue with finite buffers is analyzed and an approximate closed-form expression for the average waiting time of customers belonging to different priority classes is obtained. The key assumption is the presence of heavy traffic in the network leading to loss of customers from the service stations. Several interesting numerical results are reported that show the interplay between arrival and service rate of customers, capacity of the buffer, proportion of traffic belonging to each class and probability of loss as experienced by incoming customers.