1. Results Showing the potential of the method for arbitrary networks The following diagram show the increase of networks’ lifetime in which SR I =CR I versus their density (the pattern is the same for the other types of networks). The increase rate is low given that even sleeping nodes consume energy at a high rate. Aim Provide a fully localized solution towards prolonging the lifetime of arbitrary sensor networks with autonomous nodes, whose objective is to monitor a geographic area and report data to a single station. Relax limitations that hold in other approaches such as the topology and nodes’ abilities. Ensure full area coverage, system’s connectivity and node’s autonomy. Contribution The paper contributes towards relaxing limitations, assumptions and constraints as far as the topology and nodes’ abilities are concerned, ensuring full area coverage, system’s connectivity and node’s autonomy. Introduction Aiming at deploying fully autonomous sensor nodes in hostile and inaccessible terrains so as to report data to a single server station, we deal with arbitrary sensor networks’ self- organization capabilities. Arbitrary Sensor Network : Arbitrary sensor networks have a random topology and comprise fully autonomous sensors with differing capabilities and capacities. Sensors capabilities : Each sensor has a sensing (SR) and a communication (CR) radii that may differ among themselves (i.e. CR I ≠SR I for the node I) as well as between different sensors (i.e. given two nodes I and J, in the general case it holds that CR I ≠CR j, SR I ≠SR j, SR I ≠CR j and CR I ≠SR j ). Sensors energy capacities : At any given time the energy capacity of each sensor may differ from the capacity of other nodes in the network. Problem Statement At every time point t during network’s lifetime a sensor is specified by. I : identification number of each sensor, unique for every node. Pr t I : the priority of each node, which is specified to be a function of node’s remaining battery. Cr t I : the communication range of each node. SR t I : the sensing range of each node. ST t I : the state of the node and can be either “active” or “sleeping”. BL t I : the remaining battery level of the node at time t in mA. CM I : the consumption matrix that specifies the consumption rate of each sensor component in active and in static states Let G be an arbitrary sensor network and L(G) its lifetime. The addressed problem is to maximize L(G) subject to preserving the connectivity of the network at every time point t, 0≤t≤L(G). In other words, since L(G) depends on consumption, our goal is to minimize system's consumption. Taken that sleeping nodes consume much less energy, lifetime extension can be achieved by maximizing the number of sleeping nodes at every time point t. Method Lifetime Division System's lifetime is divided into rounds the duration of which is predefined. Each round is further divided into 3 phases: Neighbours Detection, during which each node transmits a hello message, within its CR, advertising its location and its capabilities. Scheduling phase, during which each node decides whether to sleep or not. Task phase, during which active nodes carry out their task. The neighbouring sensors N(I) of a sensor I at time t are those whose distance from I is less that CR t I. N(I) may change between different time points due to the changing CR I. Scheduling A node can enter in sleep mode when: Its sensing area is fully covered It is not needed for preserving system's connectivity Sensing Area Coverage Anode is fully covered when its sensing area is fully covered by the sensing areas of its neighbours. Following Tian and Georganas approach, this is calculated by joining the central angles of the sector drawn by the touching points of the two areas and the node itself. If the final angle is ≥360° the node is fully covered. As it is known, if nodes decide simultaneously whether to enter in sleep mode or not, blind points may appear and loss of connectivity may occur. Every node whose sensing area is fully covered, it waits for a random time period and then transmits a status message to its neighbours, announcing them its intention to enter in sleep mode. It then waits for another random time period before proceeding. If a status message from another node arrives during these periods, the node checks if it's still fully covered without taking in count the node that sent the message. Otherwise, it proceeds to connectivity checking. If a node is not fully covered, it remains active, raising his priority by a large number and entering in task phase. Connectivity Necessity Although we avoided the appearance of blind points, we still haven't ensure connectivity. For that purpose, before entering in sleep mode, a node wait for a time period, which is inversely proportional to its priority, and then checks if its active neighbours are connected. If that's true, this node safely enter in sleep mode. Otherwise, it means that the node is necessary to system's connectivity, and has to remain active. The calculation a neighbours connectivity, can be easily done by simple mathematics, taken that node's sensing and communication radii are known to their neighbours. Energy efficient area coverage in arbitrary sensor networks Sigalas Markos, Vouros George Information and Communication Systems Engineering Department, University of the Aegean, Samos, Greece (contact: georgev@aegean.gr) Round Division into 3 phases Random deployment of 1000 nodes in a 500x500 area. Dialog box of our simulation software where one may specify CM. Assumptions The system is synchronized. Nodes are static. Radii reduction is calculated by a linear formula Neighbours Detection Scheduling Task Phase (a) Sector drawn by sensing areas of two neighbouring nodes, (b) central angle of sector, (c) fully covered node by its neighbours SR i =CR I Conclusions We have shown the potential of a method for prolonging the lifetime of an arbitrary sensor network subject to keeping it connected so as nodes to report to a single server. Future work concerns the enhancement of the method towards asynchronous networks and the study for further reduction of the number of messages by using enhancements of the Tian & Georganas method [1]. SR t = CR t =10 The following diagram shows the percentage of active nodes versus network’ density