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Performance Evaluation of Classical and Quantum Communication Systems

03 May
Friday, 05/03/2019 9:30am to 11:30am
A310 LGRC
Ph.D. Dissertation Proposal Defense
Speaker: Gayane Vardoyan

Abstract:

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 mathematical analysis. Moreover, some of the more popular variants were not 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 or 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 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, quantum communication technology is rapidly advancing. In view of this, it is prudent to model and analyze quantum networks, whose applications range from cryptography to sensing. Certain types of quantum distributed applications, such as the E91 protocol for quantum key distribution, make use of entanglements to meet their objectives. 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 entanglement switching networks and introduce methods to model the process of entanglement generation, a set of switching policies, memory constraints, link heterogeneity, and decoherence for a switch that can serve bipartite (and in a specific case, tripartite) entanglements. 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 switch, they quickly become intractable when one introduces link heterogeneity or 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 entanglements. Through analysis,  we discover that randomized policies allow the switch to achieve a better capacity than time-division multiplexing, but the advantage decreases as the number of links grows.

In ongoing work, we expand our analysis from a single quantum switch to a network of switches. The goal is to derive expressions for the entanglement capacity that can be achieved between two nodes in the network. The first objective is to obtain an exact formula, as well as bounds for the capacity. Secondly, we plan to explore approximation algorithms for quicker computation. A thorough understanding of this problem may allow us to design distributed switching algorithms that efficiently utilize resources (e.g. entanglements) in a quantum network.

Advisor: Don Towsley