Analytical modeling of swarm intelligence in wireless sensor networks through Markovian Agents Dario Bruneo Dipartimento di Matematica Università di Messina Messina, Italy dbruneo@unime.it Marco Scarpa Dipartimento di Matematica Università di Messina Messina, Italy mscarpa@unime.it Andrea Bobbio Dipartimento di Informatica Università del Piemonte Orientale Alessandria, Italy bobbio@mfn.unipmn.it Davide Cerotti Dipartimento di Informatica Università di Torino Torino, Italy cerotti@di.unito.it Marco Gribaudo Dipartimento di Informatica Università di Torino Torino, Italy marcog@di.unito.it ABSTRACT Wireless Sensor Networks (WSN) consist of a large number of tiny sensor nodes that are usually randomly distributed over a geographical region. In order to reduce power con- sumption, battery operated sensors undergo cycles of sleep- ing - active periods; furthermore, sensors may be located in hostile environments increasing their attitude to failure. As a result, the topology of the WSN may be varying in time in an unpredictable manner. For this reason multi-hop rout- ing algorithms to carry messages from a sensor node to a sink should be rapidly adaptable to the changing topology. Swarm intelligence has been proposed for this purpose, since it allows to emerge a single global behavior from the interac- tion of many simple local agents. Swarm intelligent routing has been traditionally studied by resorting to simulation. The present paper is aimed to show that the recently pro- posed modeling technique, known as Markovian Agents, is suited to implement swarm intelligent algorithms for large networks of interacting sensors. Various experimental re- sults and quantitative performance indices are evaluated to support the previous claim. Keywords Wireless Sensor Networks, Markovian Agents, Swarm intel- ligence, Gradient-based routing, Performance evaluation. 1. INTRODUCTION Wireless Sensor Networks (WSN) are application-specific networks composed by a multitude of tiny sensor nodes with limited computation, communication, and power capabili- ties. Sensor nodes collect measures of physical parameters 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. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. VALUETOOLS 2009 October 20-22, 2009 - Pisa, Italy. Copyright 2009 ICST 978-963-9799-70-7/00/0004 $5.00. and transmit them to a sink node. Sensors may be scat- tered randomly over a geographical region and in order to save battery energy they may undergo cycles of sleeping - ac- tive periods [3]. Furthermore, nodes deployed in real fields might get damaged, or just fail at any time. As a result, the topology of the network may be varying in time in an unpredictable manner. For this reason routing algorithms to carry messages from a sensor node to a sink in a multi-hop fashion should rapidly adapt to the changing topology. A survey of routing algorithms is in [2]. Swarm intelligence (SI) techniques [9] are population-based stochastic methods in which the collective behavior of rel- atively simple individuals arises from their local interac- tions to produce global patterns. Through the adoption of the swarm intelligence concept, it is possible to design distributed, self-organizing, and fault tolerant routing pro- tocols able to self-adapt to the environmental changes. The main properties of swarm intelligence are that: i) Single nodes are assumed to be simple with low computational in- telligence and communication capabilities; ii) Nodes com- municate indirectly, i.e., messages are not directed to any particular node; iii) The range of the messages may be very short, nevertheless a robust global behavior emerges from the interaction of the nodes; iv) The global behavior adapts to the environmental changes. SI in WSN is inspired from the observation on how ant colonies forage for food. Ants tend to move along paths of high pheromone intensity and release pheromone during their passage thus reinforcing the pheromone trail. However, pheromone evaporates allowing the system to forget old in- formation and randomly search for new solutions. In this way, large groups of simple agents, interacting only locally with neighboring agents, work together to coordinate their actions toward fulfilling a common goal. In such systems, modeling the state of the entire system as a cross-product of the states of individual nodes results in the well-known state explosion problem. In fact, the usual way to study these systems is through simulation [12, 16]. An attempt to tackle the problem analytically is in [14], but the analysis is limited to the asymptotic behavior of a two-nodes two-links system. This paper describes how the performance analysis of large Digital Object Identifier: 10.4108/ICST.VALUETOOLS2009.7672 http://dx.doi.org/10.4108/ICST.VALUETOOLS2009.7672