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We propose an alternative approach for studying queues based on robust optimization. We model the uncertainty in the arrivals and services via polyhedral uncertainty sets which are inspired from the limit laws of probability. Using the generalized central limit theorem, this framework allows to model heavy-tailed behavior characterized by bursts of rapidly occurring arrivals and long service times. We take a worst-case approach and obtain closed form upper bounds on the system time in a multi-server queue. These expressions provide qualitative insights which mirror the conclusions obtained in the probabilistic setting for light-tailed arrivals and services and generalize them to the case of heavy-tailed behavior. We also develop a calculus for analyzing a network of queues based on the following key principle: (a) the departure from a queue, (b) the superposition, and (c) the thinning of arrival processes have the same uncertainty set representation as the original arrival processes. The proposed approach (a) yields results with error percentages in single digits relative to simulation, and (b) is to a large extent insensitive to the number of servers per queue, network size, degree of feedback, traffic intensity, and somewhat sensitive to the degree of diversity of external arrival distributions in the network.

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Complexity ranking can be used as a measure of the degree of difficulty in understanding, operating, and managing systems. Categorization of systems according to their level of complexity provides guidance for system management, optimization, and cost reduction. With the fundamental role of clinical engineers in medical equipment selection, equipment performance programs, education programs, and risk analysis, development of a medical device complexity model provides a useful tool for managing medical technology.

We propose a novel robust optimization approach to analyze and optimize the expected performance of supply chain networks. We model uncertainty in the demand at the sink nodes via polyhedral sets which are inspired from the limit laws of probability. We characterize the uncertainty sets by variability parameters which control the degree of conservatism of the model, and thus the level of probabilistic protection. At each level, and following the steps of the traditional robust optimization approach, we obtain worst case values which directly depend on the values of the variability parameters. We go beyond the traditional robust approach and treat the variability parameters as random variables. This allows us to devise a methodology to approximate and optimize the expected behavior via averaging the worst case values over the possible realizations of the variability parameters. Unlike stochastic analysis and optimization, our approach replaces the high-dimensional problem of evaluating expectations with a low-dimensional approximation that is inspired by probabilistic limit laws. We illustrate our approach by finding optimal base-stock and affine policies for fairly complex supply chain networks. Our computations suggest that our methodology (a) generates optimal base-stock levels that match the optimal solutions obtained via stochastic optimization within no more than 4 iterations, (b) yields optimal affine policies which often times exhibit better results compared to optimal base-stock policies, and (c) provides optimal policies that consistently outperform the solutions obtained via the traditional robust optimization approach.