On Characterizing the Extrema of a Function of Two Variables, One of Which is Discrete

This research was motivated by design problems in queueing theory where the objective function is composed of a discrete variable and a continuous variable. Sufficient conditions are developed such that any local minimum of such an objective function is also a global minimum. A two-parameter design problem associated with an M/E_k/1 system is used as an example to show how the conditions are utilized.