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

A characteristic particle method for traffic flow simulations on highway networks

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth International Workshop Meshfree Methods for PDE 201

Synchronization in Weighted Uncorrelated Complex Networks in a Noisy Environment: Optimization and Connections with Transport Efficiency

Motivated by synchronization problems in noisy environments, we study the Edwards-Wilkinson process on weighted uncorrelated scale-free networks. We consider a specific form of the weights, where the strength (and the associated cost) of a link is proportional to $(k_{i}k_{j})^{\beta}$ with $k_{i}$ and $k_{j}$ being the degrees of the nodes connected by the link. Subject to the constraint that the total network cost is fixed, we find that in the mean-field approximation on uncorrelated scale-free graphs, synchronization is optimal at $\beta^{*}$$=$-1. Numerical results, based on exact numerical diagonalization of the corresponding network Laplacian, confirm the mean-field results, with small corrections to the optimal value of $\beta^{*}$. Employing our recent connections between the Edwards-Wilkinson process and resistor networks, and some well-known connections between random walks and resistor networks, we also pursue a naturally related problem of optimizing performance in queue-limited communication networks utilizing local weighted routing schemes.Comment: Papers on related research can be found at http://www.rpi.edu/~korniss/Research

Supporting Service Differentiation with Enhancements of the IEEE 802.11 MAC Protocol: Models and Analysis

As one of the fastest growing wireless access technologies, Wireless LANs must evolve to support adequate degrees of service differentiation. Unfortunately, current WLAN standards like IEEE 802.11 Distributed Coordination Function (DCF) lack this ability. Work is in progress to define an enhanced version capable of supporting QoS for multimedia traffic at the MAC layer. In this paper, we aim at gaining insight into three mechanisms to differentiate among traffic categories, i.e., differentiating the minimum contention window size, the Inter-Frame Spacing (IFS) and the length of the packet payload according to the priority of different traffic categories. We propose an analysis model to compute the throughput and packet transmission delays. In additions, we derive approximations to get simpler but more meaningful relationships among different parameters. Comparisons with discrete-event simulation results show that a very good accuracy of performance evaluation can be achieved by using the proposed analysis model