Effect of the server capacity distribution on the optimal control of a bulk service queueing system

In this paper the optimal control of a single-channel bulk service queueing system with random server capacity is investigated. Given an accumulation level r, the server stops processing new customers whenever the queue falls below r and resumes service when the queue reaches level r again. Server capacity becomes random following an idle period. A quick search procedure is designed to determine the value of r that yields the minimum expected total cost per unit of time. The effect of the server capacity distribution on the optimal control is then studied. Finally, a sensitivity analysis is conducted in order to assess the extent to which our results are valid.