Optimal control of a class of linear hybrid systems with saturation

We consider a class of queueing systems that can operate in several modes; in each mode the queue lengths exhibit a linear growth until a specified upper or lower level is reached, after which the queue length stays at that level until the end of the mode. We present some methods to determine the optimal switching time instants that minimize a criterion such as average queue length, worst case queue length, average waiting time, and so on. We show that if there is no upper saturation then for some objective functions the optimal switching scheme can be computed very efficiently.