Energy Consumption and Spatial Diversity Trade-off in Autonomic Wireless Sensor Networks: The (m,k)-Gur Game Approach Tiago Semprebom ? , A.R. Pinto † , Carlos Montez  , Francisco Vasques § ? IFSC – Telecommunication Department, Federal Institute of Santa Catarina, Brazil † UNESP – Universidade Estadual Paulista, Brazil  UFSC – Universidade Federal de Santa Catarina, Brazil § IDMEC, FEUP – Faculdade de Engenharia, Universidade do Porto, Portugal tisemp@ifsc.edu.br, arpinto@ibilce.unesp.br, carlos.montez@ufsc.br, vasques@fe.up.pt Abstract—In some Wireless Sensor Network (WSN) applica- tions, it may be necessary to keep a large number of nodes sensing and transmitting data to a base station in order to have unbiased measurement values. Therefore, in addition to the traditional energy consumption issues, the spatial diversity of the monitored area is another relevant metric to evaluate the performance of a WSN. Nevertheless there is a clear trade- off between these two parameters, as keeping the sensors active all the time will deplete the nodes batteries and therefore will shorten the network lifetime. Fortunately, for the case of some applications it is possible to specify as a Quality of Service (QoS) parameter the number of periodically expected messages in the base station. Therefore, it will be possible to balance QoS against energy consumption. This paper proposes an approach called (m,k)-Gur Game that aims a trade-off between the expected QoS and the spatial coverage diversity. Simulation results show the effectiveness of the proposed approach. I. I NTRODUCTION Since the Wireless Sensor Networks (WSN) are often deployed in remote and hostile locations, the battery replace- ment of sensor nodes is usually an infeasible operation. One possible solution is to deploy a large number of nodes, because this strategy increases the lifetime of network through sleep- scheduling techniques and improves the application depend- ability through collaboration among the nodes [1], [2], [3], [4]. Besides the energy consumption, WSN applications may have other concerns, such as meeting the deadlines of periodic messages [5], increasing the spatial diversity of the network coverage [2] and maximizing the number of messages that arrive at the base station (quality of information) [6]. Moreover, a large number of nodes and their deployment in harsh environments may hinder the management of the network, making it necessary to adopt some autonomic communication approach to keep the network operational for longer periods without human intervention [1]. Due to concerns related to power consumption in WSNs, the lifetime of the network tends to be one of the most important metrics to measure the performance of any adopted approach. However, the definition of network lifetime varies according to the application [7] and, depending on the adopted definition, it can benefit or jeopardize the evaluation of any particular scheme. For instance, it is possible to assume the network death from the instant when the first node crashes due to its energy depletion. This definition, however, is meaningless in the case of dense networks applications. On the other hand, another common definition is to assume the network death when the percentage of living nodes falls below a specific value. However, this definition is dependent on the knowledge of the total number of nodes (living and dead nodes) in the network. In networks with a large number of nodes, with constant topology changes, an appropriate lifetime definition is the one that considers that the network remains operational as long as it has a minimum number of living nodes, which are responsible for the monitoring services. It is important to note that this definition is independent of the number of deployed nodes. Using this definition, some nodes may eventually sleep, turning off their radios, remaining inactive for a period of time. But the selection of which nodes will sleep – i.e., the sleep scheduling –, must ensure that an adequate number of nodes remain active, providing a minimum Quality of Service (QoS) for the network [2]. Another metric that is usually adopted in WSN works is the spatial diversity of the network coverage. These works [2], [8], [9] try to keep the monitored area by the nodes in an uniform way. Typically, the larger the number of nodes participating in the monitoring service, and better these nodes are uniformly distributed in the network, more immune it will be to sensor bias. Therefore, the basic idea to increase the spatial diversity of the network is to keep the largest number of network nodes cooperating with the monitoring service. This paper proposes an autonomic approach entitled (m,k)- Gur Game, which targets a trade-off between increasing the Quality of Service of the network and, simultaneously, increas- ing the spatial diversity, aiming a greater number of nodes to participate in the monitoring application. The proposal assumes a dense WSN based on IEEE 802.15.4 [10] standard operating in a CSMA/CA beacon enabled mode. These networks, which are becoming a de facto standard for WSNs, have a coordinator node which periodically sends beacon messages that can be used both to broadcast network parameters and to establish the periodicity of network. The (m,k)-Gur Game is an evolution of the Gur Game