Throughputs in processor sharing models for integrated stream and elastic traffic

We present an analytical study of throughput measures in processor sharing queueing systems with randomly varying service rates, modelling a communication link in an integrated services network carrying prioritised stream traffic and elastic traffic. A number of distinct throughput measures for the elastic traffic are defined and analysed. In particular, the differences between the various throughput measures and the impact of the elastic call size distribution are investigated. It is concluded that the call-average throughput, which is most relevant from the user point of view but typically hard to analyse, is very well approximated by the newly proposed so-called expected instantaneous throughput, which can easily be obtained from the system's steady state distribution. \u

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

Semi-distributed Traffic Engineering for Elastic Flows in Software Defined Networks

Software-Defined Networking (SDN) is becoming the reference paradigm to provide advanced Traffic Engineering (TE) solutions for future networks. However, taking all TE decisions at the controller, in a centralized fashion, may require long delays to react to network changes. With the most recent advancements in SDN programmability some decisions can (and should indeed) be offloaded to switches. In this paper we present a model to route elastic demands in a general network topology adopting a semi-distributed approach of the control plane to deal with path congestion. Specifically, we envision a Stackelberg approach where the SDN controller takes the role of Leader, choosing the most appropriate subset of routing paths for the selfish users (network switches), which behave as Followers, making local routing decisions based on path congestion. To overcome the complexity of the problem and meet the time requirements of real-life settings, we propose effective heuristic procedures which take into accurate account traffic dynamics, considering a stochastic scenario where both the number and size of flows change over time. We test our framework with a custom-developed simulator in different network topologies and instance sizes. Numerical results show how our model and heuristics achieve the desired balance between making global decisions and reacting rapidly to congestion events

Equilibrium of Heterogeneous Congestion Control: Optimality and Stability

When heterogeneous congestion control protocols that react to different pricing signals share the same network, the current theory based on utility maximization fails to predict the network behavior. The pricing signals can be different types of signals such as packet loss, queueing delay, etc, or different values of the same type of signal such as different ECN marking values based on the same actual link congestion level. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be non-unique, suboptimal and unstable. In Tang et al. (“Equilibrium of heterogeneous congestion control: Existence and uniqueness,” IEEE/ACM Trans. Netw., vol. 15, no. 4, pp. 824–837, Aug. 2007), existence and uniqueness of equilibrium of heterogeneous protocols are investigated. This paper extends the study with two objectives: analyzing the optimality and stability of such networks and designing control schemes to improve those properties. First, we demonstrate the intricate behavior of a heterogeneous network through simulations and present a framework to help understand its equilibrium properties. Second, we propose a simple source-based algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns by only updating a linear parameter in the sources’ algorithms on a slow timescale. It steers a network to the unique optimal equilibrium. The scheme can be deployed incrementally as the existing protocol needs no change and only new protocols need to adopt the slow timescale adaptation

Editorial introduction

We are pleased to present this special issue “Recent Trends in the Mathematics of Wireless Communication Networks: Algorithms, Models, and Methods.” Wireless communication systems have experienced a spectacular expansion over the last few decades, now providing the predominant means of Internet access. The capacity of these systems is constrained by a set of scarce resources such as radio frequencies, transmit power, and time slots. Information theory offers a powerful mathematical framework to understand how these transmission resources should be allocated so as to maximize the capacity at the physical layer, yielding valuable insights for the design of efficient schemes for, e.g., modulation, coding, and power control. Typically, however, information-theoretic models pertain to idealized scenarios: They do not account for random user behavior and dynamics at higher network layers; the practical application-specific performance requirements are largely ignored, and algorithmic implementation constraints are usually not considered. Designing systems while systematically addressing all of these aspects has posed major challenges in the last few decades. The vital need for wireless networks with significantly better performance has rejuvenated research activities toward tackling these challenges

Flow Level QoE of Video Streaming in Wireless Networks

The Quality of Experience (QoE) of streaming service is often degraded by frequent playback interruptions. To mitigate the interruptions, the media player prefetches streaming contents before starting playback, at a cost of delay. We study the QoE of streaming from the perspective of flow dynamics. First, a framework is developed for QoE when streaming users join the network randomly and leave after downloading completion. We compute the distribution of prefetching delay using partial differential equations (PDEs), and the probability generating function of playout buffer starvations using ordinary differential equations (ODEs) for CBR streaming. Second, we extend our framework to characterize the throughput variation caused by opportunistic scheduling at the base station, and the playback variation of VBR streaming. Our study reveals that the flow dynamics is the fundamental reason of playback starvation. The QoE of streaming service is dominated by the first moments such as the average throughput of opportunistic scheduling and the mean playback rate. While the variances of throughput and playback rate have very limited impact on starvation behavior.Comment: 14 page

Receiver-Based Flow Control for Networks in Overload

We consider utility maximization in networks where the sources do not employ flow control and may consequently overload the network. In the absence of flow control at the sources, some packets will inevitably have to be dropped when the network is in overload. To that end, we first develop a distributed, threshold-based packet dropping policy that maximizes the weighted sum throughput. Next, we consider utility maximization and develop a receiver-based flow control scheme that, when combined with threshold-based packet dropping, achieves the optimal utility. The flow control scheme creates virtual queues at the receivers as a push-back mechanism to optimize the amount of data delivered to the destinations via back-pressure routing. A novel feature of our scheme is that a utility function can be assigned to a collection of flows, generalizing the traditional approach of optimizing per-flow utilities. Our control policies use finite-buffer queues and are independent of arrival statistics. Their near-optimal performance is proved and further supported by simulation results.Comment: 14 pages, 4 figures, 5 tables, preprint submitted to IEEE INFOCOM 201

Flow-level performance analysis of data networks using processor sharing models

Most telecommunication systems are dynamic in nature. The state of the network changes constantly as new transmissions appear and depart. In order to capture the behavior of such systems and to realistically evaluate their performance, it is essential to use dynamic models in the analysis. In this thesis, we model and analyze networks carrying elastic data traffic at flow level using stochastic queueing systems. We develop performance analysis methodology, as well as model and analyze example systems. The exact analysis of stochastic models is difficult and usually becomes computationally intractable when the size of the network increases, and hence efficient approximative methods are needed. In this thesis, we use two performance approximation methods. Value extrapolation is a novel approximative method developed during this work and based on the theory of Markov decision processes. It can be used to approximate the performance measures of Markov processes. When applied to queueing systems, value extrapolation makes possible heavy state space truncation while providing accurate results without significant computational penalties. Balanced fairness is a capacity allocation scheme recently introduced by Bonald and Proutière that simplifies performance analysis and requires less restrictive assumptions about the traffic than other capacity allocation schemes. We introduce an approximation method based on balanced fairness and the Monte Carlo method for evaluating large sums that can be used to estimate the performance of systems of moderate size with low or medium loads. The performance analysis methods are applied in two settings: load balancing in fixed networks and the analysis of wireless networks. The aim of load balancing is to divide the traffic load efficiently between the network resources in order to improve the performance. On the basis of the insensitivity results of Bonald and Proutière, we study both packet- and flow-level balancing in fixed data networks. We also study load balancing between multiple parallel discriminatory processor sharing queues and compare different balancing policies. In the final part of the thesis, we analyze the performance of wireless networks carrying elastic data traffic. Wireless networks are gaining more and more popularity, as their advantages, such as easier deployment and mobility, outweigh their downsides. First, we discuss a simple cellular network with link adaptation consisting of two base stations and customers located on a line between them. We model the system and analyze the performance using different capacity allocation policies. Wireless multihop networks are analyzed using two different MAC schemes. On the basis of earlier work by Penttinen et al., we analyze the performance of networks using the STDMA MAC protocol. We also study multihop networks with random access, assuming that the transmission probabilities can be adapted upon flow arrivals and departures. We compare the throughput behavior of flow-optimized random access against the throughput obtained by optimal scheduling assuming balanced fairness capacity allocation