Wireless sensor networks are networks of wireless nodes that are deployed over an area for the purpose of monitoring certain phenomena of interest. The nodes perform certain measurements, process the measured data and transmit the processed data to a base station over a wireless channel. The base station collects data from all the nodes, and analyzes this data to draw conclusions about the activity in the area of interest. These networks are different from the traditional wireless ad hoc networks, because the nodes in an ad hoc network are in general less energy constrained [1]. In ad hoc networks the communication paradigm is any-to-any, since any node may wish to communicate with any other node. However in most sensor networks the many-to-one communication paradigm is more common. This is because in case of sensor networks, nodes send their data to common sinks or cluster head nodes for processing. This many-to-one paradigm often results in non-uniform energy drainage patterns in the network.
In the context of ad hoc networks it is well-known that when the propagation loss exponent is high, multi-hop communication should be used to counter the high path loss. However when nodes are organized in clusters, and when they use multi-hop communication to reach the cluster head, the nodes closer to a cluster head have a higher load of relaying packets as compared to other nodes. When the nodes are mobile (as is the case in ad hoc networks), due to the randomness induced by the time varying node positions, this relaying load gets (more or less) evenly distributed over all the nodes. However in most sensor networks nodes are static. Consequently the nodes closer to the cluster head get overburdened constantly. On the other hand when the nodes use single hop communication to reach the cluster heads, the nodes located farther away from a cluster head have the highest energy burden due to long range communication. The cluster heads themselves have the extra burden of performing long range transmissions to the distant base station.
The problem we address is that of determining the optimum number of cluster heads, of dimensioning, and determining the battery energy of the nodes, and determining the optimum mode of communication in each cluster (single hop or multi-hop). Most of the work in the sensor network literature assumes one of the two modes (single hop or multi-hop) and then optimizes the system for that particular mode. However in our work we present a systematic cost-based comparison of the two modes for 1-D (linear), 2-D (planar) and 3-D (spatial) clusters. We also propose a model for data aggregation which serves as an entry point for the application in the overall network design problem that we study next. We then propose and analyze a hybrid communication mode which alternates between single hop and multi-hop modes to ensure a more uniform energy drainage pattern. In this study we mainly focus on the trade-offs involved between communication, clustering and aggregation, and hence it is difficult to account for all other aspects of sensor networks such as MAC and routing. Our objective is to study these trade-offs and provide guidelines to the sensor network designers. Our analysis pertains only to the data gathering sensor networks, and not to the event detection sensor networks. In data gathering networks the nodes periodically send their sensed data to the base station, while in event detection sensor networks the nodes are idle for long periods of time, and spring into activity only when the event of interest occurs.
The rest of the paper is organized as follows. In Section 2 we discuss some of the related work. Section 3 contains a brief outline of the problem statement and our approach. In Section 4 we study single hop versus multi-hop modes in a single cluster. In Section 5 we propose a new model for data aggregation and solve the overall system design problem with this model. In Section 6 we propose and study a hybrid mode of communication. Section 7 presents some case studies for some typical sensor network settings. Finally we conclude the paper in Section 8.
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