In systems with finite queue length, the service rate does not have to exceed the arrival rate.

Question

Quizplus · Accepted Answer

In systems with finite queue length, as long as the arrival rate does not exceed the total capacity of the system (including the queue), the service rate does not have to exceed the arrival rate. This is because even if some customers have to wait in the queue, eventually they will be served and the system will reach a steady state. However, if the arrival rate exceeds the system's capacity, the queue will grow infinitely and the system will not reach a steady state. In this case, the service rate must exceed the arrival rate in order to prevent an infinite queue.

In Systems with Finite Queue Length, the Service Rate Does