Strong stochastic convexity and its applications in parametric optimization of queueing systems

Abstract

The authors establish the notion of strong stochastic convexity (SSCX), which implies stochastic convexity. They demonstrate that SSCX is a property exhibited by a wide range of random variables. They also show that SSCX is preserved under random mixture, random summation, and any increasing and convex operations that are applied to a set of independent random variables. Making use of the closure property of SSCX, the authors study GI/G/1 queues and tandem queues with general interarrival and service times and finite intermediate buffers. Applications of the SSCX property in the parametric optimization of such systems are also discussed.<>