Performance Modelling and Optimisation of Multi-hop Networks

A major challenge in the design of large-scale networks is to predict and optimise the total time and energy consumption required to deliver a packet from a source node to a destination node. Examples of such complex networks include wireless ad hoc and sensor networks which need to deal with the effects of node mobility, routing inaccuracies, higher packet loss rates, limited or time-varying effective bandwidth, energy constraints, and the computational limitations of the nodes. They also include more reliable communication environments, such as wired networks, that are susceptible to random failures, security threats and malicious behaviours which compromise their quality of service (QoS) guarantees. In such networks, packets traverse a number of hops that cannot be determined in advance and encounter non-homogeneous network conditions that have been largely ignored in the literature. This thesis examines analytical properties of packet travel in large networks and investigates the implications of some packet coding techniques on both QoS and resource utilisation. Specifically, we use a mixed jump and diffusion model to represent packet traversal through large networks. The model accounts for network non-homogeneity regarding routing and the loss rate that a packet experiences as it passes successive segments of a source to destination route. A mixed analytical-numerical method is developed to compute the average packet travel time and the energy it consumes. The model is able to capture the effects of increased loss rate in areas remote from the source and destination, variable rate of advancement towards destination over the route, as well as of defending against malicious packets within a certain distance from the destination. We then consider sending multiple coded packets that follow independent paths to the destination node so as to mitigate the effects of losses and routing inaccuracies. We study a homogeneous medium and obtain the time-dependent properties of the packet’s travel process, allowing us to compare the merits and limitations of coding, both in terms of delivery times and energy efficiency. Finally, we propose models that can assist in the analysis and optimisation of the performance of inter-flow network coding (NC). We analyse two queueing models for a router that carries out NC, in addition to its standard packet routing function. The approach is extended to the study of multiple hops, which leads to an optimisation problem that characterises the optimal time that packets should be held back in a router, waiting for coding opportunities to arise, so that the total packet end-to-end delay is minimised

Analysis of Multiple Flows using Different High Speed TCP protocols on a General Network

We develop analytical tools for performance analysis of multiple TCP flows (which could be using TCP CUBIC, TCP Compound, TCP New Reno) passing through a multi-hop network. We first compute average window size for a single TCP connection (using CUBIC or Compound TCP) under random losses. We then consider two techniques to compute steady state throughput for different TCP flows in a multi-hop network. In the first technique, we approximate the queues as M/G/1 queues. In the second technique, we use an optimization program whose solution approximates the steady state throughput of the different flows. Our results match well with ns2 simulations.Comment: Submitted to Performance Evaluatio

Asymptotic Approximations for TCP Compound

In this paper, we derive an approximation for throughput of TCP Compound connections under random losses. Throughput expressions for TCP Compound under a deterministic loss model exist in the literature. These are obtained assuming the window sizes are continuous, i.e., a fluid behaviour is assumed. We validate this model theoretically. We show that under the deterministic loss model, the TCP window evolution for TCP Compound is periodic and is independent of the initial window size. We then consider the case when packets are lost randomly and independently of each other. We discuss Markov chain models to analyze performance of TCP in this scenario. We use insights from the deterministic loss model to get an appropriate scaling for the window size process and show that these scaled processes, indexed by p, the packet error rate, converge to a limit Markov chain process as p goes to 0. We show the existence and uniqueness of the stationary distribution for this limit process. Using the stationary distribution for the limit process, we obtain approximations for throughput, under random losses, for TCP Compound when packet error rates are small. We compare our results with ns2 simulations which show a good match.Comment: Longer version for NCC 201

HYBRID MODELING OF THE DYNAMIC BEHAVIOR OF MOBILE AD-HOC NETWORKS

The performance of mobile ad-hoc networks is normally studied via simulation over a fixed time horizon using a steady-state type of statistical analysis procedure. However, due to the dynamic nature of the network topology such an approach may be inappropriate in many cases as the network may spend most of the time in a transient or nonstationary state. The objective of this dissertation is to develop a performance modeling framework and detailed techniques for analyzing the time varying performance of mobile ad-hoc networks.Our approach is a performance modeling tool for queueing analysis using a hybrid of discrete event simulation and numerical method techniques. Network queues are modeled using fluid-flow based differential equations which can be solved with any standard numerical integration methods, while node connectivity that represents topology changes is incorporated into the model usingeither discrete event simulation techniques or stochastic modeling of adjacency matrix elements. The hybrid fluid-based approach is believed to be an alternative that can resolve certain issues incurrent simulators and provide flexibility in modeling a more complex network by integrating additional features of nonstationary effect to add higher level of fidelity into the proposed model. Numerical and simulation experiments show that the new approach can provide reasonably accurate results without sacrificing a largeamount of computational resources

Traffic modeling in mobile internet protocol : version 6.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2005.Mobile Internet Protocol Version 6 (lPv6) is the new version of the Internet Protocol (IP) born out of the great success of Internet Protocol version 4 (IPv4). The motivation behind the development of Mobile IPv6 standard stems from user's demand for mobile devices which can connect and move seamlessly across a growing number of connectivity options. It is both suitable for mobility between subnets across homogenous and inhomogeneous media. The protocol allows a mobile node to communicate with other hosts after changing its point of attachment from one subnet to another. The huge address space available meets the requirements for rapid development of internet as the number of mobile nodes increases tremendously with the rapid expansion of the internet. Mobility, security and quality of service (QoS) being integrated in Mobile TPv6 makes it the important foundation stone for building the mobile information society and the future internet. Convergence between current network technologies: the intern et and mobile telephony is taking place, but the internet's IP routing was designed to work with conventional static nodes. Mobile IPv6 is therefore considered to be one of the key technologies for realizing convergence which enables seamless communication between fixed and mobile access networks. For this reason, there is numerous works in location registrations and mobility management, traffic modeling, QoS, routing procedures etc. To meet the increased demand for mobile telecommunications, traffic modeling is an important step towards understanding and solving performance problems in the future wireless IP networks. Understanding the nature of this traffic, identifying its characteristics and developing appropriate traffic models coupled with appropriate mobility management architectures are of great importance to the traffic engineering and performance evaluation of these networks. It is imperative that the mobility management used keeps providing good performance to mobile users and maintain network load due to signaling and packet delivery as low as possible. To reduce this load, Intemet Engineering Task Force (IETF) proposed a regional mobility management. The load is reduced by allowing local migrations to be handled locally transparent from the Home Agent and the Correspondent Node as the mobile nodes roams freely around the network. This dissertation tackles two major aspects. Firstly, we propose the dynamic regional mobility management (DRMM) architecture with the aim to minimize network load while keeping an optimal number of access routers in the region. The mobility management is dynamic based on the movement and population of the mobile nodes around the network. Most traffic models in telecommunication networks have been based on the exponential Poisson processes. This model unfortunately has been proved to be unsuitable for modeling busty IP traffic. Several approaches to model IP traffic using Markovian processes have been developed using the Batch Markovian Alrival Process (BMAP) by characterizing arrivals as batches of sizes of different distributions. The BMAP is constructed by generalizing batch Poisson processes to allow for non-exponential times between arrivals of batches while maintaining an underlying Markovian structure. The second aspect of this dissertation covers the traffic characterization. We give the analysis of an access router as a single server queue with unlimited waiting space under a non pre-emptive priority queuing discipline. We model the arrival process as a superposition of BMAP processes. We characterize the superimposed arrival processes using the BMAP presentation. We derive the queue length and waiting time for this type of queuing system. Performance of this traffic model is evaluated by obtaining numerical results in terms of queue length and waiting time and its distribution for the high and low priority traffic. We finally present a call admission control scheme that supports QoS

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

Formalization of Continuous Time Markov Chains with Applications in Queueing Theory

The performance analysis of engineering systems have become very critical due to their usage in safety and mission critical domains such as military and biomedical devices. Such an analysis is often carried out based on the Markovian (or Markov Chains based) models of underlying software and hardware components. Furthermore, some important properties can only be captured by queueing theory which involves Markov Chains with continuous time behavior. Classically, the analysis of such models has been performed using paper-and-pencil based proofs and computer simulation, both of which cannot provide perfectly accurate results due to the error-prone nature of manual proofs and the non-exhaustive nature of simulation. Recently, model checking based formal methods have also been used to analyze Markovian and queuing systems. However, such an approach is only applicable for small systems and cannot certify generic properties due to the sate-space explosion problem. In this thesis, we propose to use higher-order-logic theorem proving as a complementary approach to conduct the formal analysis of queueing systems. To this aim, we present the higher-order-logic formalization of the Poisson process which is the foremost step to model queueing systems. We also verify some of its classical properties such as exponentially distributed inter-arrival time, memoryless property and independent and stationary increments. Moreover, we used the formalization of the Poisson process to model and verify the error probability of a generic optical communication system. Then we present the formalization of Continuous-Time Markov Chains along with the Birth-Death process. Lastly, we demonstrate the utilization of our developed infrastructure by presenting the formalization of an M/M/1 queue which is widely used to model telecommunication systems. We also formally verified the generic result about the average waiting time for any given queue

Time Dependent Performance Analysis of Wireless Networks

Many wireless networks are subject to frequent changes in a combination of network topology, traffic demand, and link capacity, such that nonstationary/transient conditions always exist in packet-level network behavior. Although there are extensive studies on the steady-state performance of wireless networks, little work exists on the systematic study of their packet-level time varying behavior. However, it is increasingly noted that wireless networks must not only perform well in steady state, but must also have acceptable performance under nonstationary/transient conditions. Furthermore, numerous applications in today's wireless networks are very critical to the real-time performance of delay, packet delivery ratio, etc, such as safety applications in vehicular networks and military applications in mobile ad hoc networks. Thus, there exists a need for techniques to analyze the time dependent performance of wireless networks. In this dissertation, we develop a performance modeling framework incorporating queuing and stochastic modeling techniques to efficiently evaluate packet-level time dependent performance of vehicular networks (single-hop) and mobile ad hoc networks (multi-hop). For vehicular networks, we consider the dynamic behavior of IEEE 802.11p MAC protocol due to node mobility and model the network hearability as a time varying adjacency matrix. For mobile ad hoc networks, we focus on the dynamic behavior of network layer performance due to rerouting and model the network connectivity as a time varying adjacency matrix. In both types of networks, node queues are modeled by the same fluid flow technique, which follows flow conservation principle to construct differential equations from a pointwise mapping of the steady-state queueing relationships. Numerical results confirm that fluid-flow based performance models are able to respond to the ongoing nonstationary/transient conditions of wireless networks promptly and accurately. Moreover, compared to the computation time of standard discrete event simulator, fluid-flow based model is shown to be a more scalable evaluation tool. In general, our proposed performance model can be used to explore network design alternatives or to get a quick estimate on the performance variation in response to some dynamic changes in network conditions