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

An Optimal Medium Access Control with Partial Observations for Sensor Networks

We consider medium access control (MAC) in multihop sensor networks, where only partial information about the shared medium is available to the transmitter. We model our setting as a queuing problem in which the service rate of a queue is a function of a partially observed Markov chain representing the available bandwidth, and in which the arrivals are controlled based on the partial observations so as to keep the system in a desirable mildly unstable regime. The optimal controller for this problem satisfies a separation property: we first compute a probability measure on the state space of the chain, namely the information state, then use this measure as the new state on which the control decisions are based. We give a formal description of the system considered and of its dynamics, we formalize and solve an optimal control problem, and we show numerical simulations to illustrate with concrete examples properties of the optimal control law. We show how the ergodic behavior of our queuing model is characterized by an invariant measure over all possible information states, and we construct that measure. Our results can be specifically applied for designing efficient and stable algorithms for medium access control in multiple-accessed systems, in particular for sensor networks

An Adaptive Virtual Queue (AVQ) Algorithm for Active Queue Management

Virtual queue-based marking schemes have been recently proposed for Active Queue Management (AQM) in Internet routers. We consider a particular scheme, which we call the Adaptive Virtual Queue (AVQ), and study its following properties: its stability in the presence of feedback delays, its ability to maintain small queue lengths, and its robustness in the presence of extremely short flows (the so-called web mice). Using a linearized model of the system dynamics, we present a simple rule to design the parameters of the AVQ algorithm. We then compare its performance through simulation with several well-known AQM schemes such as RED, REM, Proportional Integral (PI) controller, and a nonadaptive virtual queue algorithm. With a view toward implementation, we show that AVQ can be implemented as a simple token bucket using only a few lines of code

Nonlinear continuous feedback controllers

Packet-switched communication networks such as today's Internet are built with several interconnected core and distribution packet forwarding routers and several sender and sink transport agents. In order to maintain stability and avoid congestion collapse in the network, the sources control their rate behavior and voluntarily adjust their sending rates to accommodate other sources in the network. In this thesis, we study one class of sender rate control that is modeled using continuous first-order differential equation of the sending rates. In order to adjust the rates appropriately, the network sends continuous packet-loss feedback to the sources. We study a form of closed-loop feedback congestion controllers whose rate adjustments exhibit a nonlinear form. There are three dimensions to our work in this thesis. First, we study the network optimization problem in which sources choose utilities to maximize their underlying throughput. Each sender maximizes its utility proportional to the throughput achieved. In our model, sources choose a utility function to define their level of satisfaction of the underlying resource usages. The objective of this direction is to establish the properties of source utility functions using inequality constrained bounded sets and study the functional forms of utilities against a chosen rate differential equation. Second, stability of the network and tolerance to perturbation are two essential factors that keep communication networks operational around the equilibrium point. Our objective in this part of the thesis is to analytically understand the existence of local asymptotic stability of delayed-feedback systems under homogeneous network delays. Third, we propose a novel tangential controller for a generic maximization function and study its properties using nonlinear optimization techniques. We develop the necessary theoretical background and the properties of our controller to prove that it is a better rate adaptation algorithm for logarithmic utilities compared to the well-studied proportional controllers. We establish the asymptotic local stability of our controller with upper bounds on the increase / decrease gain parameters

Layering as Optimization Decomposition: Questions and Answers

Network protocols in layered architectures have historically been obtained on an ad-hoc basis, and much of the recent cross-layer designs are conducted through piecemeal approaches. Network protocols may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems in the form of generalized Network Utility Maximization (NUM), providing insight on what they optimize and on the structures of network protocol stacks. In the form of 10 Questions and Answers, this paper presents a short survey of the recent efforts towards a systematic understanding of "layering" as "optimization decomposition". The overall communication network is modeled by a generalized NUM problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. Furthermore, there are many alternative decompositions, each leading to a different layering architecture. Industry adoption of this unifying framework has also started. Here we summarize the current status of horizontal decomposition into distributed computation and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and coding. We also discuss under-explored future research directions in this area. More importantly than proposing any particular crosslayer design, this framework is working towards a mathematical foundation of network architectures and the design process of modularization

End-to-End Congestion Control Schemes: Utility Functions, Random Losses and ECN Marks

We present a framework for designing end-to-end congestion control schemes in a network where each user may have a different utility function and may experience noncongestion-related losses. We first show that there exists an additive-increase-multiplicative-decrease scheme using only end-to-end measurable losses such that a socially optimal solution can be reached. We incorporate round-trip delay in this model, and show that one can generalize observations regarding TCP-type congestion avoidance to more general window flow control schemes. We then consider explicit congestion notification (ECN) as an alternate mechanism (instead of losses) for signaling congestion and show that ECN marking levels can be designed to nearly eliminate losses in the network by choosing the marking level independently for each node in the network. While the ECN marking level at each node may depend on the number of flows through the node, the appropriate marking level can be estimated using only aggregate flow measurements, i.e., per-flow measurements are not required