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

Convergence Results for Ant Routing Algorithms via Stochastic Approximations

In this paper, we provide convergence results for an Ant-Based Routing (ARA) Algorithm for wireline, packet-switched communication networks, that are acyclic. Such algorithms are inspired by the foraging behavior of ants in nature. We consider an ARA algorithm proposed by Bean and Costa. The algorithm has the virtues of being adaptive and distributed, and can provide a multipath routing solution. We consider a scenario where there are multiple incoming data traffic streams that are to be routed to their respective destinations via the network. Ant packets, which are nothing but probe packets, are introduced to estimate the path delays in the network. The node routing tables, which consist of routing probabilities for the outgoing links, are updated based on these delay estimates. In contrast to the available analytical studies in the literature, the link delays in our model are stochastic, time-varying, and dependent on the link traffic. The evolution of the delay estimates and the routing probabilities are described by a set of stochastic iterative equations. In doing so, we take into account the distributed and asynchronous nature of the algorithm operation. Using methods from the theory of stochastic approximations, we show that the evolution of the delay estimates can be closely tracked by a deterministic ODE (Ordinary Differential Equation) system, when the step-size of the delay estimation scheme is small. We study the equilibrium behavior of the ODE system in order to obtain the equilibrium behavior of the routing algorithm. We also explore properties of the equilibrium routing probabilities, and provide illustrative simulation results.Prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U. S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon

Convergence Results for Ant Routing Algorithms via Stochastic Approximation and Optimization

``Ant algorithms'' have been proposed to solve a variety of problems arising in optimization and distributed control. They form a subset of the larger class of ``Swarm Intelligence'' algorithms. The central idea is that a "swarm" of relatively simple agents can interact through simple mechanisms and collectively solve complex problems. Instances that exemplify the above idea abound in nature. The abilities of ant colonies to collectively accomplish complex tasks have served as sources of inspiration for the design of ``Ant algorithms''. Examples of ``Ant algorithms'' are the set of ``Ant Routing'' algorithms that have been proposed for communication networks. We analyze in this paper Ant Routing Algorithms for packet-switched wireline networks. The algorithm retains most of the salient and attractive features of Ant Routing Algorithms. The scheme is a multiple path probabilistic routing scheme, that is fully adaptive and distributed. Using methods from adaptive algorithms and stochastic approximation, we show that the evolution of the link delay estimates can be closely tracked by a deterministic ODE system. A study of the equilibrium points of the ODE gives us the equilibrium behavior of the routing algorithm, in particular, the equilibrium routing probabilities, and mean delays in the links under equilibrium. We also show that the fixed-point equations that the equilibrium routing probabilities satisfy are actually the necessary and sufficient conditions of an appropriate optimization problem. Simulations supporting the analytical results are provided.Research supported by the U.S. Army Research Laboratory under the CTA C & N Consortium Coop. Agreement DAAD19-01-2-0011 and by the U.S. Army Research Office under MURI01 Grant No. DAAD19-01-1-0465

Component Based Performance Modelling of the Wireless Routing Protocols

In this paper, we propose a component based methodology for modelling and design of wireless routing protocols. Componentization is a standard methodology for analysis and synthesis of complex systems. Throughout the paper, we use Optimized Link State Routing (OLSR) protocol as a case study to demonstrate effectiveness of our methodology. We focus on modelling of three main components: neighborhood discovery, selector of topology information to disseminate, and the path selection components. For each component, we identify the inputs, outputs, and a generic methodology for modelling. Using the neighborhood discovery component, we will present our design methodology and design a modified enhanced version of the OLSR NDC, and compare its performance to the neighborhood discovery component of the OLSR protocol

Stability and Analysis of TCP Connections with RED Control and Exogenous Traffic

In this paper we study the stability and performance of a system involving several TCP connections passing through a tandem of RED controlled queues each of which has an incoming exogenous stream. The exogenous stream, representing the superposition of all incoming UDP connections into a queue, has been modeled as an MMPP stream. We consider both the TCP Tahoe and the TCP Reno versions. We start with the analysis of a single TCP connection sharing a RED controlled queue with an exogenous stream. The effect of the exogenous stream (which is almost always present in large networks) is to cause the system to converge to a stationary distribution from any initial conditions. This stability result holds good for any work conserving discipline. We also obtain the performance indices of the system; specifically the goodputs and the mean sojourn times of the various connections. The complexity involved in computation of performance indices for the system is reduced by approximating the evolution of the average queue length process of the RED queue by a deterministic ODE. Then, by using a decomposition approach of two time scales, we reduce the study of the system to that of a simplified one for which the performance measures can be obtained under stationarity. Finally, we extend the above results to the case when multiple TCP connections share a RED controlled queue with an exogenous stream and to the case when a TCP connection passes through several RED controlled tandem queues each of which has an incoming exogenous stream. We also consider an example of multiple TCPs passing through a tandem of queues. A number of simulation results have been provided which support the analysis

The InsTITuTe for sysTems research Component Based Performance Modelling of the Wireless Routing Protocols Component Based Performance Modelling of the Wireless Routing Protocols

Isr develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, heterogeneous and dynamic problems of engineering technology and systems for industry and government. Isr is a permanent institute of the university of maryland, within the a. James clark school of engineering. It is a graduated national science foundation engineering research center