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

Taming Uncertainties In Real-Time Routing For Wireless Networked Sensing And Control

Real-time routing is a basic element of closed-loop, real-time sensing and control, but it is challenging due to dynamic, uncertain link/path delays. The probabilistic nature of link/path delays makes the basic problem of computing the probabilistic distribution of path delays NP-hard, yet quantifying probabilistic path delays is a basic element of real-time routing and may well have to be executed by resource-constrained devices in a distributed manner; the highly-varying nature of link/path delays makes it necessary to adapt to in-situ delay conditions in real-time routing, but it has been observed that delay-based routing can lead to instability, estimation error, and low data delivery performance in general. To address these challenges, we propose the emph{Multi-Timescale Estimation (MTE)} method; by accurately estimating the mean and variance of per-packet transmission time and by adapting to fast-varying queueing in an accurate, agile manner, MTE enables accurate, agile, and efficient estimation of probabilistic path delay bounds in a distributed manner. Based on MTE, we propose the emph{Multi-Timescale Adaptation (MTA)} routing protocol; MTA integrates the stability of an ETX-based directed-acyclic-graph (DAG) with the agility of spatiotemporal data flow control within the DAG to ensure real-time data delivery in the presence of dynamics and uncertainties. We also address the challenges of implementing MTE and MTA in resource-constrained devices such as TelosB motes. We evaluate the performance of MTA using the NetEye and Indriya sensor network testbeds. We find that MTA significantly outperforms existing protocols, e.g., improving deadline success ratio by 89% and reducing transmission cost by a factor of 9.7

CURSA-SQ: a methodology for service-centric traffic flow analysis

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The rapid availability of new services means that network operators cannot exhaustively test their impact on the network or anticipate any capacity exhaustion. This situation will be worse with the imminent introduction of 5G technology and the kind of totally new services that it will support. In addition, the increasing complexity of the network makes analyzing its behavior challenging against the specific traffic that needs to be supported; this prevents from training human operators and, much less, machine learning algorithms that might automatize network operation. In this paper, we present CURSA-SQ, a methodology to analyze network behavior when specific traffic that would be generated by groups of service consumers is injected. CURSA-SQ includes input traffic flow modeling with second and sub-second granularity based on specific service and consumer behavior, as well as a continuous G/G/1/k queue model based on the logistic function. The methodology allows for accurately studying the traffic flows at the input and outputs of complex scenarios with multiples queue systems, as well as other metrics such as delays, while showing noticeable scalability. Application use cases include packet and optical network planning, service introduction assessment, and autonomic networking, just to mention a few.Peer ReviewedPostprint (author's final draft

Performance analysis of networks on chips

Modules on a chip (such as processors and memories) are traditionally connected through a single link, called a bus. As chips become more complex and the number of modules on a chip increases, this connection method becomes inefficient because the bus can only be used by one module at a time. Networks on chips are an emerging technology for the connection of on-chip modules. In networks on chips, switches are used to transmit data from one module to another, which entails that multiple links can be used simultaneously so that communication is more efficient. Switches consist of a number of input ports to which data arrives and output ports from which data leaves. If data at multiple input ports has to be transmitted to the same output port, only one input port may actually transmit its data, which may lead to congestion. Queueing theory deals with the analysis of congestion phenomena caused by competition for service facilities with scarce resources. Such phenomena occur, for example, in traffic intersections, manufacturing systems, and communication networks like networks on chips. These congestion phenomena are typically analysed using stochastic models, which capture the uncertain and unpredictable nature of processes leading to congestion (such as irregular car arrivals to a traffic intersection). Stochastic models are useful tools for the analysis of networks on chips as well, due to the complexity of data traffic on these networks. In this thesis, we therefore study queueing models aimed at networks on chips. The thesis is centred around two key models: A model of a switch in isolation, the so-called single-switch model, and a model of a network of switches where all traffic has the same destination, the so-called network of polling stations. For both models we are interested in the throughput (the amount of data transmitted per time unit) and the mean delay (the time it takes data to travel across the network). Single-switch models are often studied under the assumption that the number of ports tends to infinity and that traffic is uniform (i.e., on average equally many packets arrive to all buffers, and all possible destinations are equally likely). In networks on chips, however, the number of buffers is typically small. We introduce a new approximation specifically aimed at small switches with (memoryless) Bernoulli arrivals. We show that, for such switches, this approximation is more accurate than currently known approximations. As traffic in networks on chips is usually non-uniform, we also extend our approximation to non-uniform switches. The key difference between uniform and nonuniform switches is that in non-uniform switches, all queues have a different maximum throughput. We obtain a very accurate approximation of this throughput, which allows us to extend the mean delay approximation. The extended approximation is derived for Bernoulli arrivals and correlated arrival processes. Its accuracy is verified through a comparison with simulation results. The second key model is that of concentrating tree networks of polling stations (polling stations are essentially switches where all traffic has the same output port as destination). Single polling stations have been studied extensively in literature, but only few attempts have been made to analyse networks of polling stations. We establish a reduction theorem that states that networks of polling stations can be reduced to single polling stations while preserving some information on mean waiting times. This reduction theorem holds under the assumption that the last node of the network uses a so-called HoL-based service discipline, which means that the choice to transmit data from a certain buffer may only depend on which buffers are empty, but not on the amount of data in the buffers. The reduction theorem is a key tool for the analysis of networks of polling stations. In addition to this, mean waiting times in single polling stations have to be calculated, either exactly or approximately. To this end, known results can be used, but we also devise a new single-station approximation that can be used for a large subclass of HoL-based service disciplines. Finally, networks on chips typically implement flow control, which is a mechanism that limits the amount of data in the network from one source. We analyse the division of throughput over several sources in a network of polling stations with flow control. Our results indicate that the throughput in such a network is determined by an interaction between buffer sizes, flow control limits, and service disciplines. This interaction is studied in more detail by means of a numerical analysis