The authors have developed and applied probabilistic tools to establish second-order stochastic properties such as convexity and concavity in the optimal design and control of queueing systems. Their approaches are based on constructing and comparing the dynamical sample paths of the stochastic processes under study. They present a tutorial on these notions and results in stochastic convexity/concavity. Many examples are discussed to illustrate the application of the results in parametric optimization of queues and queueing networks.>
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Shanthikumar et al. (1989) studied this question.
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