484 research outputs found
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
DYNAMICS OF RANDOM EARLY DETECTION GATEWAY UNDER A LARGE NUMBER OF TCP FLOWS
While active queue management (AQM) mechanisms such as Random Early Detection (RED) are widely deployed in the Internet, they are rarely utilized or otherwise poorly configured. The problem stems from a lack of a tractable analytical framework which captures the interaction between the TCP congestion-control and AQM mechanisms. Traditional TCP traffic modeling has focused on "micro-scale" modeling of TCP, i.e., detailed modeling of a single TCP flow. While micro-scale models of TCP are suitable for understanding the precise behavior of an individual flow, they are not well suited to the situation where a large number of TCP flows interact with each other as is the case in realistic networks.
In this dissertation, an innovative approach to TCP traffic modeling is proposed by considering the regime where the number of TCP flows competing for the bandwidth in the bottleneck RED gateway is large. In the limit, the queue size and the aggregate TCP traffic can be approximated by simple recursions which are independent of the number of flows. The limiting model is therefore scalable as it does not suffer from the state space explosion. The steady-state queue length and window distribution can be evaluated from well-known TCP models.
We also extend the analysis to a more realistic model which incorporates session-level dynamics and heterogeneous round-trip delays. Typically, ad-hoc assumptions are required to make the analysis for models with session-level dynamics tractable under a certain regime. In contrast, our limiting model derived here is compatible with other previously proposed models in their respective regime without having to rely on ad-hoc assumptions. The contributions from these additional layers of dynamics to the asymptotic queue are now crisply revealed through the limit theorems. Under mild assumptions, we show that the steady-state queue size depends on the file size and round-trip delay only through their mean values.
We obtain more accurate description of the queue dynamics by means of a Central Limit analysis which identifies an interesting relationship between the queue fluctuations and the random packet marking mechanism in AQM. The analysis also reveals the dependency of the magnitude of the queue fluctuations on the variability of the file size and round-trip delay. Simulation results supporting conclusions drawn from the limit theorems are also presented
Distributed optimization in transportation and logistics networks
Many important problems in communication networks, transportation networks, and logistics networks are solved by the minimization of cost functions. In general, these can be complex optimization problems involving many variables. However, physicists noted that in a network, a node variable (such as the amount of resources of the nodes) is connected to a set of link variables (such as the flow connecting the node), and similarly each link variable is connected to a number of (usually two) node variables. This enables one to break the problem into local components, often arriving at distributive algorithms to solve the problems. Compared with centralized algorithms, distributed algorithms have the advantages of lower computational complexity, and lower communication overhead. Since they have a faster response to local changes of the environment, they are especially useful for networks with evolving conditions. This review will cover message-passing algorithms in applications such as resource allocation, transportation networks, facility location, traffic routing, and stability of power grids
On the Integration of Unmanned Aerial Vehicles into Public Airspace
Unmanned Aerial Vehicles will soon be integrated in the airspace and start serving us in various capacities such as package delivery, surveillance, search and rescue missions, inspection of infrastructure, precision agriculture, and cinematography.
In this thesis, motivated by the challenges this new era brings about, we design a layered architecture called Internet of Drones (IoD). In this architecture, we propose a structure for the traffic in the airspace as well as the interaction between the components of our system such as unmanned aerial vehicles and service providers. We envision the minimal features that need to be implemented in various layers of the architecture, both on the Unmanned Aerial Vehicle (UAV)'s side and on the service providers' side. We compare and contrast various approaches in three existing networks, namely the Internet, the cellular network, and the air traffic control network and discuss how they relate to IoD.
As a tool to aid in enabling integration of drones in the airspace, we create a traffic flow model. This model will assign velocities to drones according to the traffic conditions in a stable way as well as help to study the formation of congestion in the airspace. We take the novel problem posed by the 3D nature of UAV flights as opposed to the 2D nature of road vehicles movements and create a fitting traffic flow model. In this model, instead of structuring our model in terms of roads and lanes as is customary for ground vehicles, we structure it in terms of channels, density and capacities. The congestion is formulated as the perceived density given the capacity and the velocity of vehicles will be set accordingly. This view removes the need for a lane changing model and its complexity which we believe should be abstracted away even for the ground vehicles as it is not fundamentally related to the longitudinal movements of vehicles. Our model uses a scalar capacity parameter and can exhibit both passing and blocking behaviors. Furthermore, our model can be solved analytically in the blocking regime and piece-wise analytically solved when in the passing regime.
Finally, it is not possible to integrate UAVs into the airspace without some mechanism for coordination or in other words scheduling. We define a new scheduling problem in this regard that we call Vehicle Scheduling Problem (VSP). We prove NP-hardness for all the commonly used objective functions in the context of Job Shop Scheduling Problem (JSP). Then for the number of missed deadlines as our objective function, we give a Mixed Integer Programming (MIP) formulation of VSP. We design a heuristic algorithm and compare the quality of the schedules created for small instances with the exact solution to the MIP instance. For larger instances, these comparisons are made with a baseline algorithm
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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
Router-based algorithms for improving internet quality of service.
We begin this thesis by generalizing some results related to a recently proposed positive system model of TCP congestion control algorithms. Then, motivated by a mean ¯eld analysis of the positive system model, a novel, stateless, queue management scheme is designed: Multi-Level Comparisons with index l (MLC(l)). In the limit, MLC(l) enforces max-min fairness in a network of TCP flows.
We go further, showing that counting past drops at a congested link provides su±cient information to enforce max-min fairness among long-lived flows and to reduce the flow completion times of short-lived flows. Analytical models are presented, and the accuracy of predictions are validated by packet level ns2 simulations.
We then move our attention to e±cient measurement and monitoring techniques. A small active counter architecture is presented that addresses the problem of accurate approximation of statistics counter values at very-high speeds that can be both updated and estimated on a per-packet basis. These algorithms are necessary in the design of router-based flow control algorithms since on-chip
Static RAM (SRAM) currently is a scarce resource, and being economical with its usage is an important task. A highly scalable method for heavy-hitter identifcation that uses our small active counters architecture is developed based on heuristic argument. Its performance is compared to several state-of-the-art algorithms and shown to out-perform them.
In the last part of the thesis we discuss the delay-utilization tradeoff in the congested Internet links.
While several groups of authors have recently analyzed this tradeoff, the lack of realistic assumption in their models and the extreme complexity in estimation of model parameters, reduces their applicability at real Internet links. We propose an adaptive scheme that regulates the available queue space to keep utilization at desired, high, level. As a consequence, in large-number-of-users regimes, sacrifcing 1-2% of bandwidth can result in queueing delays that are an order of magnitude smaller than in the standard BDP-bu®ering case. We go further and introduce an optimization framework for describing the problem of interest and propose an online algorithm for solving it
Router-based algorithms for improving internet quality of service.
We begin this thesis by generalizing some results related to a recently proposed positive system model of TCP congestion control algorithms. Then, motivated by a mean ¯eld analysis of the positive system model, a novel, stateless, queue management scheme is designed: Multi-Level Comparisons with index l (MLC(l)). In the limit, MLC(l) enforces max-min fairness in a network of TCP flows.
We go further, showing that counting past drops at a congested link provides su±cient information to enforce max-min fairness among long-lived flows and to reduce the flow completion times of short-lived flows. Analytical models are presented, and the accuracy of predictions are validated by packet level ns2 simulations.
We then move our attention to e±cient measurement and monitoring techniques. A small active counter architecture is presented that addresses the problem of accurate approximation of statistics counter values at very-high speeds that can be both updated and estimated on a per-packet basis. These algorithms are necessary in the design of router-based flow control algorithms since on-chip
Static RAM (SRAM) currently is a scarce resource, and being economical with its usage is an important task. A highly scalable method for heavy-hitter identifcation that uses our small active counters architecture is developed based on heuristic argument. Its performance is compared to several state-of-the-art algorithms and shown to out-perform them.
In the last part of the thesis we discuss the delay-utilization tradeoff in the congested Internet links.
While several groups of authors have recently analyzed this tradeoff, the lack of realistic assumption in their models and the extreme complexity in estimation of model parameters, reduces their applicability at real Internet links. We propose an adaptive scheme that regulates the available queue space to keep utilization at desired, high, level. As a consequence, in large-number-of-users regimes, sacrifcing 1-2% of bandwidth can result in queueing delays that are an order of magnitude smaller than in the standard BDP-bu®ering case. We go further and introduce an optimization framework for describing the problem of interest and propose an online algorithm for solving it
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
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