Convergence Results for Ant Routing Algorithms via Stochastic Approximation and Optimization
Abstract
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 swarmof 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 bya 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2007
- Accession Number
- AD1006926
Entities
People
- John Baras
- Punyaslok Purkayastha
Organizations
- University of Maryland