Abstract
This paper provides an explicit solution to the problem of regulating the stream of customers arriving at a facility so that they do not overload or under-utilize the facility. To do this, a rule by which some arriving customers are sent elsewhere must be decided upon. Although techniques based on optimal control of piecewise deterministic processes can be applied and necessary conditions of optimality such as the dynamic programming verification theorem exists, explicit solutions are difficult, if not impossible, to obtain. In this paper, we first give certain characterizations of the optimal solution and then use the backward method to obtain explicit solution for certain cases. Numerical comparisons with certain intuitive control policies are also made.