A Mixed Integer Convexity Result with an Application to an M/M/s Queueing System
نویسندگان
چکیده
Many optimization problems in queueing theory have functions with integer and real variables. Convexity results for these functions can be obtained by fixing either the integer or the real variable where bounds of the considered function play an important role. Tokgöz, Maalouf and Kumin [11] introduces the concept of mixed convexity for functions with real and integer variables and obtain convexity results without fixing any variables. The motivation 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 Zn×Rm are obtained and the conditions for a local minimum point to be the unique global minimum are stated.
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