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Performance Evaluation of Classical and Quantum Communication Systems

The Transmission Control Protocol (TCP) is a robust and reliable method used to transport data across a network. Many variants of TCP exist, e.g., Scalable TCP, CUBIC, and H-TCP. While some of them have been studied from empirical and theoretical perspectives, others have been less amenable to a thorough mathematical analysis. Moreover, some of the more popular variants had not been analyzed in the context of the high-speed environments for which they were designed. To address this issue, we develop a generalized modeling technique for TCP congestion control under the assumption of high bandwidth-delay product. In a separate contribution, we develop a versatile fluid model for congestion-window-based and rate-based congestion controllers that can be used to analyze a protocol’s stability. We apply this model to CUBIC – the default implementation of TCP in Linux systems – and discover that under a certain loss probability model, CUBIC is locally asymptotically stable. The contribution of this work is twofold: (i) the first formal stability analysis of CUBIC, and (ii) the fluid model can be easily adapted to other protocols whose window or rate functions are difficult to model. We demonstrate another application of this model by analyzing the stability of H-TCP, another popular variant used in data science networks. On a different front, a wide range of quantum distributed applications, which either promise to improve on existing classical applications or offer functionality that is entirely unobtainable via classical means, are helping to fuel rapid technological advances in the area of quantum communication. In view of this, it is prudent to model and analyze quantum networks, whose applications range from quantum cryptography to quantum sensing. Several types of quantum distributed applications, such as the E91 protocol for quantum key distribution, make use of entanglement to meet their objectives. Thus, being able to distribute entanglement efficiently is one of the most important and fundamental tasks that must be performed in a quantum network – without this functionality, many quantum distributed applications would be rendered infeasible. Modeling such systems is vital in order to better conceptualize their operation, and more importantly, to discover and address the challenges involved in actualizing them. To this end, we explore the limits of star-topology entanglement switching networks and introduce methods to model the process of entanglement generation, a set of switching policies, memory constraints, link heterogeneity, and quantum state decoherence for a switch that can serve bipartite (and in a specific case, tripartite) entangled states. In one part of this work, we compare two modeling techniques: discrete time Markov chains (DTMCs) and continuous-time Markov chains (CTMCs). We find that while DTMCs are a more accurate way to model the operation of an entanglement distribution switch, they quickly become intractable when one introduces link heterogeneity or state decoherence into the model. In terms of accuracy, we show that not much is lost for the case of homogeneous links, infinite buffer and no decoherence when CTMCs are employed. We then use CTMCs to model more complex systems. In another part of this work, we analyze a switch that can store one or two qubits per link and can serve both bipartite and tripartite entangled states. Through analysis, we discover that randomized policies allow the switch to achieve a better capacity than time-division multiplexing between bipartite and tripartite entangling measurements, but the advantage decreases as the number of links grows.
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