Multipath Routing Algorithms for Communication Networks: Ant Routing and Optimization Based Approaches

In this dissertation, we study two algorithms that accomplish multipath routing in communication networks. The first algorithm that we consider belongs to the class of Ant-Based Routing Algorithms (ARA) that have been inspired by experimental observations of ant colonies. It was found that ant colonies are able to `discover' the shorter of two paths to a food source by laying and following `pheromone' trails. ARA algorithms proposed for communication networks employ probe packets called ant packets (analogues of ants) to collect measurements of various quantities (related to routing performance) like path delays. Using these measurements, analogues of pheromone trails are created, which then influence the routing tables. We study an ARA algorithm, proposed earlier by Bean and Costa, consisting of a delay estimation scheme and a routing probability update scheme, that updates routing probabilities based on the delay estimates. We first consider a simple scenario where data traffic entering a source node has to be routed to a destination node, with N available parallel paths between them. An ant stream also arrives at the source and samples path delays en route to the destination. We consider a stochastic model for the arrival processes and packet lengths of the streams, and a queuing model for the link delays. Using stochastic approximation methods, we show that the evolution of the link delay estimates can be closely tracked by a deterministic ODE (Ordinary Differential Equation) system. A study of the equilibrium points of the ODE enables us to obtain the equilibrium routing probabilities and the path delays. We then consider a network case, where multiple input traffic streams arriving at various sources have to be routed to a single destination. For both the N parallel paths network as well as for the general network, the vector of equilibrium routing probabilities satisfies a fixed point equation. We present various supporting simulation results. The second routing algorithm that we consider is based on an optimization approach to the routing problem. We consider a problem where multiple traffic streams entering at various source nodes have to be routed to their destinations via a network of links. We cast the problem in a multicommodity network flow optimization framework. Our cost function, which is a function of the individual link delays, is a measure of congestion in the network. Our approach is to consider the dual optimization problem, and using dual decomposition techniques we provide primal-dual algorithms that converge to the optimal routing solution. A classical interpretation of the Lagrange multipliers (drawing an analogy with electrical networks) is as `potential differences' across the links. The link potential difference can be then thought of as `driving the flow through the link'. Using the relationships between the link potential differences and the flows, we show that our algorithm converges to a loop-free routing solution. We then incorporate in our framework a rate control problem and address a joint rate control and routing problem

Random Neural Networks and Optimisation

In this thesis we introduce new models and learning algorithms for the Random Neural Network (RNN), and we develop RNN-based and other approaches for the solution of emergency management optimisation problems. With respect to RNN developments, two novel supervised learning algorithms are proposed. The first, is a gradient descent algorithm for an RNN extension model that we have introduced, the RNN with synchronised interactions (RNNSI), which was inspired from the synchronised firing activity observed in brain neural circuits. The second algorithm is based on modelling the signal-flow equations in RNN as a nonnegative least squares (NNLS) problem. NNLS is solved using a limited-memory quasi-Newton algorithm specifically designed for the RNN case. Regarding the investigation of emergency management optimisation problems, we examine combinatorial assignment problems that require fast, distributed and close to optimal solution, under information uncertainty. We consider three different problems with the above characteristics associated with the assignment of emergency units to incidents with injured civilians (AEUI), the assignment of assets to tasks under execution uncertainty (ATAU), and the deployment of a robotic network to establish communication with trapped civilians (DRNCTC). AEUI is solved by training an RNN tool with instances of the optimisation problem and then using the trained RNN for decision making; training is achieved using the developed learning algorithms. For the solution of ATAU problem, we introduce two different approaches. The first is based on mapping parameters of the optimisation problem to RNN parameters, and the second on solving a sequence of minimum cost flow problems on appropriately constructed networks with estimated arc costs. For the exact solution of DRNCTC problem, we develop a mixed-integer linear programming formulation, which is based on network flows. Finally, we design and implement distributed heuristic algorithms for the deployment of robots when the civilian locations are known or uncertain