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Convergence results for ant routing algorithms viastochastic approximation

Published: 12 April 2010 Publication History

Abstract

In this paper, we provide convergence results for an Ant 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 [2]. 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 destinations via the network. Ant packets, which are nothing but probe packets, are used 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 in order to obtain the equilibrium behavior of the algorithm. We also provide illustrative simulation results.

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Cited By

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  • (2018)A mathematical analysis of improved EigenAnt algorithmJournal of Experimental & Theoretical Artificial Intelligence10.1080/0952813X.2018.154420331:2(291-309)Online publication date: 16-Nov-2018
  • (2013)Convergence results for ant routing algorithms via stochastic approximationACM Transactions on Autonomous and Adaptive Systems10.1145/2451248.24512518:1(1-34)Online publication date: 19-Apr-2013

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cover image ACM Conferences
HSCC '10: Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
April 2010
308 pages
ISBN:9781605589558
DOI:10.1145/1755952
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 12 April 2010

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  1. ant routing algorithms
  2. queuing networks
  3. stochastic approximations and learning algorithms

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Cited By

View all
  • (2018)A mathematical analysis of improved EigenAnt algorithmJournal of Experimental & Theoretical Artificial Intelligence10.1080/0952813X.2018.154420331:2(291-309)Online publication date: 16-Nov-2018
  • (2013)Convergence results for ant routing algorithms via stochastic approximationACM Transactions on Autonomous and Adaptive Systems10.1145/2451248.24512518:1(1-34)Online publication date: 19-Apr-2013

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