  We consider a single server queueing system with admission control and the
possibility to switch dynamically between a low and a high service rate, and
examine the benefit of this service rate flexibility. We formulate a discounted
Markov Decision Process model for the problem of joint admission and service
control, and show that the optimal policy has a threshold structure for both
controls. Regarding the benefit due to flexibility, we show that it is
increasing in system congestion, and that its effect on the admission policy is
to increase the admission threshold. We also derive a simple approximate
condition between the admission reward and the relative cost of service rate
increase, so that the service rate flexibility is beneficial. We finally show
that the results extend to the expected average reward case.
