Kim Blackmore

An analysis framework for mobility metrics in mobile ad hoc networks

Mobile ad hoc networks (MANETs) have inherently dynamic topologies. Under these difficult circumstances, it is essential to have some dependable way of determining the reliability of communication paths. Mobility metrics are well suited to this purpose. Several mobility metrics have been proposed in the literature, including link persistence, link duration, link availability, link residual time, and their path equivalents. However, no method has been provided for their exact calculation. Instead, only statistical approximations have been given. In this paper, exact expressions are derived for each of the aforementioned metrics, applicable to both links and paths. We further show relationships between the different metrics, where they exist. Such exact expressions constitute precise mathematical relationships between network connectivity and node mobility. These expressions can, therefore, be employed in a number of ways to improve performance of MANETs such as in the development of efficient algorithms for routing, in route caching, proactive routing, and clustering schemes.

On entropy measures for dynamic network topologies: limits to MANET

What are the fundamental limits on the communications potential of wireless networks? We contend that quantifying topological dynamics resulting from node movement enables one to: find the minimum overhead required by the network to maintain connectivity and, calculate the communication potential of the network. A mobility metric is proposed for the unbiased comparison of networks. This is an entropy measure based on the uncertainty of change in the topology of the network, and is referred to as topological uncertainty. Topological uncertainty determines the minimum overhead required by the network to correctly identify the topology and hence, provide node connectivity. We use topological uncertainty to derive fundamental bounds on the maximum bit rate available within a mobile ad-hoc networking environment. Our work demonstrates the potential of entropy measures to describe the complexities of node connectivity within wireless networks

Mobile Base Station and Clustering to Maximize Network Lifetime in Wireless Sensor Networks

Using a mobile base station (BS) in a wireless sensor network can alleviate nonuniform energy consumption among sensor nodes and accommodate partitioned networks. In the work of Jerew and Liang (2009) we have proposed a novel clustering-based heuristic algorithm for finding a trajectory of the mobile BS that strikes a nontrivial tradeoff between the traffic load among sensor nodes and the tour time constraint of the mobile BS. In this paper, we first show how to choose the number of clusters to ensure there is no packet loss as the BS moves between clusters. We then provide an analytical solution to the problem in terms of the speed of the mobile BS. We also provide analytical estimates of the unavoidable packet loss as the network size increases. We finally conduct experiments by simulation to evaluate the performance of the proposed algorithm. The results show that the use of clustering in conjunction with a mobile BS for data gathering can significantly prolong network lifetime and balance energy consumption of sensor nodes.

Decision region approximation by polynomials or neural networks

We give degree of approximation results for decision regions which are defined by polynomial and neural network parametrizations. The volume of the misclassified region is used to measure the approximation error, and results for the degree of L/sub 1/ approximation of functions are used. For polynomial parametrizations, we show that the degree of approximation is at least 1, whereas for neural network parametrizations we prove the slightly weaker result that the degree of approximation is at least r, where r can be any number in the open interval (0, 1).

Strong stochastic stability for Dynamic Source Routing

Node movement in a mobile ad-hoc network (MANET) simulation is defined by the mobility model. To ensure reliable simulation results, many research papers have investigated the stability (or instability) of popular mobility models. In general, these works have been concerned with the following question: Will time-averaged measurements of ldquomobility model eventsrdquo converge? For example, will average node speed or position converge as simulation time increases? These works, however, do not address stability questions at different network layers. In this paper, we study the following problem: When is the output of a network protocol stable? Network protocols are complex distributed systems, which may (or may not) preserve the stability of the mobility model. We study a basic version of the popular dynamic source routing (DSR) protocol and show that if a pointwise ergodic theorem (a generalized strong law of large numbers) holds for the mobility model, then it also holds for the output of DSR; that is, time averaged measurements made at the network layer will converge almost everywhere. This, the first stability result for a network layer protocol, opens up a new area of research.

Word-Valued Sources: An Ergodic Theorem, an AEP, and the Conservation of Entropy

A word-valued source Y = Y₁,Y₂,<i>...</i> is discrete random process that is formed by sequentially encoding the symbols of a random process X = X₁,X₂<i>,...</i> with codewords from a codebook <i>C</i>. These processes appear frequently in information theory (in particular, in the analysis of source-coding algorithms), so it is of interest to give conditions on <i>X</i> and <i>C</i> for which <i>Y</i> will satisfy an ergodic theorem and possess an asymptotic equipartition property (AEP). In this paper, we prove the following: 1) if <i>X</i> is asymptotically mean stationary (AMS), then <i>Y</i> will satisfy a pointwise ergodic theorem and possess an AEP; and 2) if the codebook <i>C</i> is prefix-free, then the entropy rate of <i>Y</i> is equal to the entropy rate of <i>X</i> normalized by the average codeword length.

Online learning via congregational gradient descent

We propose and analyse a populational version of stepwise gradient descent suitable for a wide range of learning problems. The algorithm is motivated by genetic algorithms which update a population of solutions rather than just a single representative as is typical for gradient descent. This modification of traditional gradient descent (as used, for example, in the backpropogation algorithm) avoids getting trapped in local minima. We use an averaging analysis of the algorithm to relate its behaviour to an associated ordinary differential equation. We derive a result concerning how long one has to wait in order that, with a given high probability, the algorithm is within a certain neighbourhood of the global minimum. We also analyse the effect of different population sizes. An example is presented which corroborates our theory very well.

Number of Paths and Neighbours Effect on Multipath Routing in Mobile Ad Hoc Networks

In this paper the number of paths in a multipath routing protocol and distribution of neighbour nodes in the discovered routes are studied for networks with frequent topology changes. Specifically, we consider how the placement of neighbour nodes, which are used by the source node to reach a destination in a multipath routing protocol, affects total network power consumption. We develop an analytical model, verified by simulation, which shows that, while the network performance is affected by source node speed and route length, it also depends on the geometric arrangement of neighbour nodes around the source node. The results reveal that total network power consumption is minimized when the moving source node has six well distributed neighbour nodes, and one path to the destination via each neighbour node.

Estimation of hop count in multi-hop wireless sensor networks with arbitrary node density

In multi-hop wireless sensor networks, the number of hops between the source and the destination has a significant impact on network performance and has been extensively identified in the literature. However, the methods most commonly used significantly underestimate the number of hops for sparse networks. The impact of node density is significant, and this factor is not adequately addressed. In effect, many schemes to calculate hop count imply geographic routing, even if they intend to consider the shortest path routes. Therefore, we propose a new technique for estimating hop count. We consider the hop progress when the network nodes are uniformly deployed and the shortest path between the source and the destination is selected. We determine a distribution of the remaining distance to destination. In order to correctly capture the situation for a sparse network, we examine the selection of the next neighbour node as a relaying node for the next hop. The analytical model is verified by simulation.