We consider the problem of admission control in resource sharing systems, such as web servers and transaction processing systems, when the job size distribution has high variability, with the aim of minimizing the mean response time. It is well known that in such resource sharing systems, as the number of tasks concurrently sharing the resource is increased, the server throughput initially increases, due to more efficient utilization of resources, but starts falling beyond a certain point, due to resource contention and thrashing. Most admission control mechanisms solve this problem by imposing a fixed upper bound on the number of concurrent transactions allowed into the system, called the MultiProgramming-Limit (MPL), and making the arrivals which find the server full queue up. Almost always, the MPL is chosen to be the point that maximizes server efficiency. paper we abstract such resource sharing systems as a Processor Sharing (PS) server with state-dependent service rate and a F...