Second-Order Stochastic Properties in Queueing Systems

Second-order stochastic properties such as convexity and concavity are often indispensable in the optimal design and control of queueing systems. These properties are, however, notoriously difficult to establish, even in the simplest cases where closed-form results are available. Traditional algebraic and analytical machineries are often not effective in identifying these properties. On the other hand, we have been quite successful in developing and applying probabilistic tools in this area. Specifically, these are approaches based on constructing and comparing the dynamical sample paths of the stochastic processes under study. We present here a tutorial on those new notions and results in stochastic convexity/concavity that we have recently developed. Many examples are discussed to illustrate the application of the results in parametric optimization of queues and queueing networks. © 1989 IEEE