Monotonicity in the limited processor sharing queue

We study a processor sharing queue with a limited number of service positions and an infinite buffer. The occupied service positions share an underlying resource. We prove that for service times with a decreasing failure rate, the queue length is stochastically decreasing in the number of service positions, and that for service times with an increasing failure rate, the queue length is stochastically increasing. The result is illustrated with simulations, and the queue length is compared to that in other queueing models with and without restrictions on the number of service positions.