In Pursuit of Desirable Equilibria in Large Scale Networked Systems

This thesis addresses an interdisciplinary problem in the context of engineering, computer science and economics: In a large scale networked system, how can we achieve a desirable equilibrium that benefits the system as a whole? We approach this question from two perspectives. On the one hand, given a system architecture that imposes certain constraints, a system designer must propose efficient algorithms to optimally allocate resources to the agents that desire them. On the other hand, given algorithms that are used in practice, a performance analyst must come up with tools that can characterize these algorithms and determine when they can be optimally applied. Ideally, the two viewpoints must be integrated to obtain a simple system design with efficient algorithms that apply to it. We study the design of incentives and algorithms in such large scale networked systems under three application settings, referred to herein via the subheadings: Incentivizing Sharing in Realtime D2D Networks: A Mean Field Games Perspective, Energy Coupon: A Mean Field Game Perspective on Demand Response in Smart Grids, Dynamic Adaptability Properties of Caching Algorithms, and Accuracy vs. Learning Rate of Multi-level Caching Algorithms. Our application scenarios all entail an asymptotic system scaling, and an equilibrium is defined in terms of a probability distribution over system states. The question in each case is to determine how to attain a probability distribution that possesses certain desirable properties. For the first two applications, we consider the design of specific mechanisms to steer the system toward a desirable equilibrium under self interested decision making. The environments in these problems are such that there is a set of shared resources, and a mechanism is used during each time step to allocate resources to agents that are selfish and interact via a repeated game. These models are motivated by resource sharing systems in the context of data communication, transportation, and power transmission networks. The objective is to ensure that the achieved equilibria are socially desirable. Formally, we show that a Mean Field Game can be used to accurately approximate these repeated game frameworks, and we describe mechanisms under which socially desirable Mean Field Equilibria exist. For the third application, we focus on performance analysis via new metrics to determine the value of the attained equilibrium distribution of cache contents when using different replacement algorithms in cache networks. The work is motivated by the fact that typical performance analysis of caching algorithms consists of determining hit probability under a fixed arrival process of requests, which does not account for dynamic variability of request arrivals. Our main contribution is to define a function which accounts for both the error due to time lag of learning the items' popularity, as well as error due to the inaccuracy of learning, and to characterize the tradeoff between the two that conventional algorithms achieve. We then use the insights gained in this exercise to design new algorithms that are demonstrably superior

A Low-Complexity Approach to Distributed Cooperative Caching with Geographic Constraints

We consider caching in cellular networks in which each base station is equipped with a cache that can store a limited number of files. The popularity of the files is known and the goal is to place files in the caches such that the probability that a user at an arbitrary location in the plane will find the file that she requires in one of the covering caches is maximized. We develop distributed asynchronous algorithms for deciding which contents to store in which cache. Such cooperative algorithms require communication only between caches with overlapping coverage areas and can operate in asynchronous manner. The development of the algorithms is principally based on an observation that the problem can be viewed as a potential game. Our basic algorithm is derived from the best response dynamics. We demonstrate that the complexity of each best response step is independent of the number of files, linear in the cache capacity and linear in the maximum number of base stations that cover a certain area. Then, we show that the overall algorithm complexity for a discrete cache placement is polynomial in both network size and catalog size. In practical examples, the algorithm converges in just a few iterations. Also, in most cases of interest, the basic algorithm finds the best Nash equilibrium corresponding to the global optimum. We provide two extensions of our basic algorithm based on stochastic and deterministic simulated annealing which find the global optimum. Finally, we demonstrate the hit probability evolution on real and synthetic networks numerically and show that our distributed caching algorithm performs significantly better than storing the most popular content, probabilistic content placement policy and Multi-LRU caching policies.Comment: 24 pages, 9 figures, presented at SIGMETRICS'1

An approximate analysis of heterogeneous and general cache networks

In this paper, we propose approximate models to assess the performance of a cache network with arbitrary topology where nodes run the Least Recently Used (LRU), First-In First-Out (FIFO), or Random (RND) replacement policies on arbitrary size caches. Our model takes advantage of the notions of cache characteristic time and Time-To-Live (TTL)-based cache to develop a unified framework for approximating metrics of interest of interconnected caches. Our approach is validated through event-driven simulations; and when possible, compared to the existing a-NET model [23].Dans ce travail, nous proposons des modèles approximatifs pour évaluer les performances d'un réseau de caches ayant une topologie arbitraire où les noeuds exécutent les politiques Least Recently Used (LRU), First In First Out (FIFO), ou Random replacement (RND) sur des caches de taille quelconque. Notre modèle tire parti des notions de temps caractéristique d'un cache et des modèles Time-To-Live (TTL) de cache pour développer une approche unifiée pour l'approximation des métriques de performance sur des caches interconnectés. Notre approche est validée par des simulations événementielles; et, si possible, comparée au modèle existant a-NET [23]

In Pursuit of Desirable Equilibria in Large Scale Networked Systems

This thesis addresses an interdisciplinary problem in the context of engineering, computer science and economics: In a large scale networked system, how can we achieve a desirable equilibrium that benefits the system as a whole? We approach this question from two perspectives. On the one hand, given a system architecture that imposes certain constraints, a system designer must propose efficient algorithms to optimally allocate resources to the agents that desire them. On the other hand, given algorithms that are used in practice, a performance analyst must come up with tools that can characterize these algorithms and determine when they can be optimally applied. Ideally, the two viewpoints must be integrated to obtain a simple system design with efficient algorithms that apply to it. We study the design of incentives and algorithms in such large scale networked systems under three application settings, referred to herein via the subheadings: Incentivizing Sharing in Realtime D2D Networks: A Mean Field Games Perspective, Energy Coupon: A Mean Field Game Perspective on Demand Response in Smart Grids, Dynamic Adaptability Properties of Caching Algorithms, and Accuracy vs. Learning Rate of Multi-level Caching Algorithms. Our application scenarios all entail an asymptotic system scaling, and an equilibrium is defined in terms of a probability distribution over system states. The question in each case is to determine how to attain a probability distribution that possesses certain desirable properties. For the first two applications, we consider the design of specific mechanisms to steer the system toward a desirable equilibrium under self interested decision making. The environments in these problems are such that there is a set of shared resources, and a mechanism is used during each time step to allocate resources to agents that are selfish and interact via a repeated game. These models are motivated by resource sharing systems in the context of data communication, transportation, and power transmission networks. The objective is to ensure that the achieved equilibria are socially desirable. Formally, we show that a Mean Field Game can be used to accurately approximate these repeated game frameworks, and we describe mechanisms under which socially desirable Mean Field Equilibria exist. For the third application, we focus on performance analysis via new metrics to determine the value of the attained equilibrium distribution of cache contents when using different replacement algorithms in cache networks. The work is motivated by the fact that typical performance analysis of caching algorithms consists of determining hit probability under a fixed arrival process of requests, which does not account for dynamic variability of request arrivals. Our main contribution is to define a function which accounts for both the error due to time lag of learning the items' popularity, as well as error due to the inaccuracy of learning, and to characterize the tradeoff between the two that conventional algorithms achieve. We then use the insights gained in this exercise to design new algorithms that are demonstrably superior

Resource Allocation in Distributed Service Networks

The past few years have witnessed significant growth in the use of distributed network analytics involving agile code, data and computational resources. In many such networked systems, for example, Internet of Things (IoT), a large number of smart devices, sensors, processing and storage resources are widely distributed in a geographic region. These devices and resources distributed over a physical space are collectively called a distributed service network. Efficient resource allocation in such high performance service networks remains one of the most critical problems. In this thesis, we model and optimize the allocation of resources in a distributed service network. This thesis contributes to two different types of service networks: caching, and spatial networks; and develops new techniques that optimize the overall performance of these services. First, we propose a new method to compute an upper bound on hit probability for all non-anticipative caching policies in a distributed caching system. We find our bound to be tighter than state-of-the-art upper bounds for a variety of content request arrival processes. We then develop a utility based framework for content placement in a cache network for efficient and fair allocation of caching resources. We develop provably optimal distributed algorithms that operate at each network cache to maximize the overall network utility. Next, we develop and evaluate assignment policies that allocate resources to users with a goal to minimize the expected distance traveled by a user request, where both resources and users are located on a line. Lastly, we design and evaluate resource proximity aware user-request allocation policies with a goal to reduce the implementation cost associated with moving a request/job to/from its allocated resource while balancing the number of requests allocated to a resource. Depending on the topology, our proposed policies achieve a 8% - 99% decrease in implementation cost as compared to the state-of-the-art

Topics in access, storage, and sensor networks

In the first part of this dissertation, Data Over Cable Service Interface Specification (DOCSIS) and IEEE 802.3ah Ethernet Passive Optical Network (ETON), two access networking standards, are studied. We study the impact of two parameters of the DOCSIS protocol and derive the probability of message collision in the 802.3ah device discovery scheme. We survey existing bandwidth allocation schemes for EPONs, derive the average grant size in one such scheme, and study the performance of the shortest-job-first heuristic. In the second part of this dissertation, we study networks of mobile sensors. We make progress towards an architecture for disconnected collections of mobile sensors. We propose a new design abstraction called tours which facilitates the combination of mobility and communication into a single design primitive and enables the system of sensors to reorganize into desirable topologies alter failures. We also initiate a study of computation in mobile sensor networks. We study the relationship between two distributed computational models of mobile sensor networks: population protocols and self-similar functions. We define the notion of a self-similar predicate and show when it is computable by a population protocol. Transition graphs of population protocols lead its to the consideration of graph powers. We consider the direct product of graphs and its new variant which we call the lexicographic direct product (or the clique product). We show that invariants concerning transposable walks in direct graph powers and transposable independent sets in graph families generated by the lexicographic direct product are uncomputable. The last part of this dissertation makes contributions to the area of storage systems. We propose a sequential access detect ion and prefetching scheme and a dynamic cache sizing scheme for large storage systems. We evaluate the cache sizing scheme theoretically and through simulations. We compute the expected hit ratio of our and competing schemes and bound the expected size of our dynamic cache sufficient to obtain an optimal hit ratio. We also develop a stand-alone simulator for studying our proposed scheme and integrate it with an empirically validated disk simulator

Spare parts planning and control for maintenance operations

This paper presents a framework for planning and control of the spare parts supply chain inorganizations that use and maintain high-value capital assets. Decisions in the framework aredecomposed hierarchically and interfaces are described. We provide relevant literature to aiddecision making and identify open research topics. The framework can be used to increasethe e¿ciency, consistency and sustainability of decisions on how to plan and control a spareparts supply chain. This point is illustrated by applying it in a case-study. Applicability of theframework in di¿erent environments is also investigated