Response Time Analysis of a Multi-Server Processor Sharing Model

In this paper, we investigate the response time of a multi-server processor sharing (PS) model. A multi-server PS model is a PS queue but the number of requests which can be processed simultaneously is limited by a threshold. An arriving request has to wait in the queue if the number of requests exceeds the threshold. Assuming Markovian arrival input of requests and general processing time distribution, we investigate how mean response time is affected by the threshold. Through numerical experiments for various instances, it turns out that the mean response time geometrically converges as the threshold increases. This property is used to derive a useful formula for capacity planning of multi-threaded server systems. We also develop a numerical procedure for computing the response time distribution. We found from numerical experiments that the processing time distribution has a strong impact on the response time distribution.