Resource allocation in communication networks aims to assign various resources such as power, bandwidth and load in a fair and economic fashion so that the networks can be better utilized and shared by the communicating entities. The design of efficient resource-allocation algorithms is, however, becoming more and more challenging due to the precipitously increasing scale of the networks. This thesis strives to understand how to design such low-complexity algorithms with performance guarantees.In the first part, the link scheduling problem in wireless ad hoc networks is considered. The scheduler is charge of finding a set of wireless data links to activate at each time slot with the considerations of wireless interference, traffic dynamics, network topology and quality-of-service (QoS) requirements. Two different yet essential scenarios are investigated: the first one is when each packet has a specific deadline after which it will be discarded; the second is when each packet traverses the network in multiple hops instead of leaving the network after a one-hop transmission. In both scenarios the links need to be carefully scheduled to avoid starvation of users and congestion on links. One greedy algorithm is analyzed in each of the two scenarios and performance guarantees in terms of throughput of the networks are derived.In the second part, the load-balancing problem in parallel computing is studied. Tasks arrive in batches and the duty of the load balancer is to place the tasks on the machines such that minimum queueing delay is incurred. Due to the huge size of modern data centers, sampling the status of all machines may result in significant overhead. Consequently, an algorithm based on limited queue information at the machines is examined and its asymptotic delay performance is characterized and it is shown that the proposed algorithm achieves the same delay with remarkably less sampling overhead compared to the well-known power-of-two-choices algorithm.Two messages of the thesis are the following: greedy algorithms can work well in a stochastic setting; the fluid model can be useful in "derandomizing" the system and reveal the nature of the algorithm.

This PhD thesis investigates four problems in the context of Large Distributed Systems. This work is motivated by the questions arising with the expansion of Cloud Computing and related technologies. The present work investigates the efficiency of different resource allocation algorithms in this framework. The methods used involve a mathematical analysis of several stochastic models associated to these networks. Chapter 1 provides an introduction to the subject in general, as well as a presentation of the main mathematical tools used throughout the subsequent chapters. Chapter 2 presents a congestion control mechanism in Video on Demand services delivering files encoded in various resolutions. We propose a policy under which the server delivers the video only at minimal bit rate when the occupancy rate of the server is above a certain threshold. The performance of the system under this policy is then evaluated based on both the rejection and degradation rates. Chapters 3, 4 and 5 explore problems related to cooperation schemes between data centres on the edge of the network. In the first setting, we analyse a policy in the context of multi-resource cloud services. In second case, requests that arrive at a congested data centre are forwarded to a neighbouring data centre with some given probability. In the third case, requests blocked at one data centre are forwarded systematically to another where a trunk reservation policy is introduced such that a redirected request is accepted only if there are a certain minimum number of free servers at this data centre.

This thesis addresses the design and analysis of resource allocation policies in largescale stochastic systems, motivated by examples such as the Internet, cloud facilities, wireless networks, etc. A canonical framework for modeling many such systems is provided by "stochastic processing networks" (SPN) (Harrison [28, 29]). In this context, the key operational challenge is efficient and timely resource allocation. We consider two important classes of SPNs: switched networks and bandwidth-sharing networks. Switched networks are constrained queueing models that have been used successfully to describe the detailed packet-level dynamics in systems such as input-queued switches and wireless networks. Bandwidth-sharing networks have primarily been used to capture the long-term behavior of the flow-level dynamics in the Internet. In this thesis, we develop novel methods to analyze the performance of existing resource allocation policies, and we design new policies that achieve provably good performance. First, we study performance properties of so-called Maximum-Weight-[alpha] (MW-[alpha]) policies in switched networks, and of a-fair policies in bandwidth-sharing networks, both of which are well-known families of resource allocation policies, parametrized by a positive parameter [alpha] > 0. We study both their transient properties as well as their steady-state behavior. In switched networks, under a MW-a policy with a 2 1, we obtain bounds on the maximum queue size over a given time horizon, by means of a maximal inequality derived from the standard Lyapunov drift condition. As a corollary, we establish the full state space collapse property when [alpha] > 1. In the steady-state regime, for any [alpha] >/= 0, we obtain explicit exponential tail bounds on the queue sizes, by relying on a norm-like Lyapunov function, different from the standard Lyapunov function used in the literature. Methods and results are largely parallel for bandwidth-sharing networks. Under an a-fair policy with [alpha] >/= 1, we obtain bounds on the maximum number of flows in the network over a given time horizon, and hence establish the full state space collapse property when [alpha] >/= 1. In the steady-state regime, using again a norm-like Lyapunov function, we obtain explicit exponential tail bounds on the number of flows, for any a > 0. As a corollary, we establish the validity of the diffusion approximation developed by Kang et al. [32], in steady state, for the case [alpha] = 1. Second, we consider the design of resource allocation policies in switched networks. At a high level, the central performance questions of interest are: what is the optimal scaling behavior of policies in large-scale systems, and how can we achieve it? More specifically, in the context of general switched networks, we provide a new class of online policies, inspired by the classical insensitivity theory for product-form queueing networks, which admits explicit performance bounds. These policies achieve optimal queue-size scaling, in the conventional heavy-traffic regime, for a class of switched networks, thus settling a conjecture (documented in [51]) on queue-size scaling in input-queued switches. In the particular context of input-queued switches, we consider the scaling behavior of queue sizes, as a function of the port number n and the load factor [rho]. In particular, we consider the special case of uniform arrival rates, and we focus on the regime where [rho] = 1 - 1/f(n), with f(n) >/= n. We provide a new class of policies under which the long-run average total queue size scales as O(n1.5 -f(n) log f(n)). As a corollary, when f(n) = n, the long-run average total queue size scales as O(n2.5 log n). This is a substantial improvement upon prior works [44], [52], [48], [39], where the same quantity scales as O(n3 ) (ignoring logarithmic dependence on n).

This book covers performance analysis of computer networks, and begins by providing the necessary background in probability theory, random variables, and stochastic processes. Queuing theory and simulation are introduced as the major tools analysts have access to. It presents performance analysis on local, metropolitan, and wide area networks, as well as on wireless networks. It concludes with a brief introduction to self-similarity. Designed for a one-semester course for senior-year undergraduates and graduate engineering students, it may also serve as a fingertip reference for engineers developing communication networks, managers involved in systems planning, and researchers and instructors of computer communication networks.

Recently Geometric Programming has been applied to study a variety of problems in the analysis and design of communication systems from information theory and queuing theory to signal processing and network protocols. Geometric Programming for Communication Systems begins its comprehensive treatment of the subject by providing an in-depth tutorial on the theory, algorithms, and modeling methods of Geometric Programming. It then gives a systematic survey of the applications of Geometric Programming to the study of communication systems. It collects in one place various published results in this area, which are currently scattered in several books and many research papers, as well as to date unpublished results. Geometric Programming for Communication Systems is intended for researchers and students who wish to have a comprehensive starting point for understanding the theory and applications of geometric programming in communication systems.

A compact, highly-motivated introduction to some of the stochastic models found useful in the study of communications networks.