CONTENTS 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 11.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

11.2.1 Data Collection Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 11.2.2 Multicast Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 11.2.3 Uni/Broadcast Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

11.2.3.1 Uni/Broadcast Capacity for Random Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

11.2.3.2 Uni/Broadcast Capacity for Arbitrary Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

11.2.3.3 Unicast Capacity for Mobile Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

11.2.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 11.3 Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 11.4 Carrier-sensing Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 11.5 Distributed Data Collection and Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

11.5.1 Distributed Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 11.5.2 Capacity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

11.6 R0-PCR-based Distributed Data Aggregation . . . . . . . . . . . . . . . . . . . . . . . 280 11.7 Data Collection and Aggregation under Poisson Distribution Model . 283

. . . . . . . . . . . 11.8.1 DDC Capacity versus R0 and α . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 11.8.2 Scalability of DDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 11.8.3 Performance of DDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

11.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

11.1 Introduction One of the most important functions provided by wireless sensor networks (WSNs) is directly gathering data from the physical world. Generally, data gathering can be categorized as data collection [1][171][10], which gathers all the data from a network without any data aggregation or merging, and data aggregation [17]- [18], which obtains some aggregation values, e.g., MAX, MIN, SUM, etc. To evaluate network performance, network capacity, which reflects the data transmission/collection/broadcast rate, is usually used, e.g., multicast capacity [173], unicast capacity [175][176], broadcast capacity [177], and data collection capacity [1][171][10]. For data collection capacity, it is defined as the average data receiving rate at the sink, i.e., data collection capacity reflects how fast data been collected by the sink. We use data collection capacity and network capacity interchangeably throughout this chapter.