Queues with Levy input and hysteretic control
We consider a (doubly) reflected L,vy process where the L,vy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion.
hysteretic control m/g/1 queue storage process levy process levy exponent double reflection workload distribution two-state strategy