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 Multi-Programming-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 serve efficiency.

In this paper we abstract such resource sharing systems as a Processor Sharing (PS) server with state-dependent service rate and a First-Come-First-Served (FCFS) queue, and we analyze the performance of this model from a queueing theoretic perspective. We start by showing that, counter to the common wisdom, the peak efficiency point is not always optimal for minimizing the mean response time. Instead, significant performance gains can be obtained by running the system at less than the peak efficiency. We provide a simple expression for the static MPL that achieves near-optimal mean response time for general distributions.

Next we present two traffic-oblivious dynamic admission control policies that adjust the MPL based on the instantaneous queue length while also taking into account the variability of the job size distribution. The structure of our admission control policies is a mixture of fluid control when the number of jobs in the system is high, with a stochastic component when the system is near-empty. We show via simulations that our dynamic policies are much more robust to unknown traffic intensities and burstiness in the arrival process than imposing a static MPL.

47 pages

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