Performance and power consumption of computers using batch service with event and time counter

In this paper we propose a queueing model with a batch service with both event and time counter. Its lower power consumption is an improvement over the batch service with only an event counter which probably causes a longer mean response time. If there are few events in the queue, the event counter cannot reach the lower boundary of the number of events, and thus the computer system will require a longer waiting time to reach the threshold number of events to start servicing. So we propose a new mechanism by combining a time counter with the event counter, thereby reducing both mean response time and power consumption. We derive the system probabilities of running and waiting from the system state transition diagram. These probabilities help us learn the relationship between power consumption, system response time and batch size under the batch service. Moreover, we can adjust the batch size to estimate an acceptable response time and find the trade-off between both the amount of power saving and the mean response time in computer systems.