  In this paper, we introduce a model of dynamical queue, in which the service
time depends on the server utilization history. The proposed queueing model is
motivated by widely accepted empirical laws describing human performance as a
function of mental arousal. The objective of this paper is to design task
release control policies that can stabilize the queue for the maximum possible
arrival rate, assuming deterministic arrivals. First, we prove an upper bound
on the maximum possible stabilizable arrival rate for any task release control
policy. Then, we propose a simple threshold policy that releases a task to the
server only if its state is below a certain fixed value. Finally, we prove that
this task release control policy ensures stability of the queue for the maximum
possible arrival rate.
