A Mixed Integer Convexity Result with an Application to an M/M/s Queueing System

Many optimization problems in queueing theory have functions with integer and real variables. Convexity results for these func- tions can be obtained by flxing either the integer or the real vari- able where bounds of the considered function play an important role. Tokgoz, Maalouf and Kumin (11) introduces the concept of mixed convexity for functions with real and integer variables and obtain convexity results without flxing any variables. The motiva- tion for this paper is based on a conjecture of Kumin (6) in regard to the convexity of an objective function corresponding to an M=M=s queueing system. In addition, generalized convexity results for a set of functionals with domain Z n £R m are obtained and the condi- tions for a local minimum point to be the unique global minimum are stated.