**ABSTRACT**

We propose an alternative approach for studying queueing systems by employing robust optimization as opposed to stochastic analysis. While traditional queueing theory relies on Kolmogorov's axioms of probability and models arrivals and services as renewal processes, we use the limit laws of probability as the axioms of our methodology and model the queueing systemsprimitives by uncertainty sets. In this framework, we obtain closed form expressions for the waiting times in multi-server queues with heavy-tailed arrival and service processes. These expressions are not available under traditional queueing theory for heavy-tailed processes, while they lead to the same qualitative insights for independent and identically distributed arrival and service times. We also develop an exact calculus for analyzing a network ofqueues with multiple servers 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. We show that our approach, which we call the Robust Queueing Network Analyzer (RQNA) a) yields results with error percentages in single digits (for all experiments we performed) relative to simulation, b) performs significantly better than the Queueing Network Analyzer (QNA) proposed in Whitt (1983), and c) is to a large extent insensitive to the number of servers per queue, thenetwork 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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