Gupta and Kumar (2000) showed that the throughput capacity of static ad hoc networks with n randomly positioned nodes is /spl Theta/(/spl radic/(n/log n)). Grossglauser and Tse showed that node mobility increases the capacity to /spl Theta/(n), a substantial improvement. Achieving maximum capacity requires nodes to relay transmissions through other nodes. Each node must have a relay buffer for temporarily storing packets before forwarding them to their destination. We establish that if relay buffer sizes are bounded above by a constant, then mobility does not substantially increase the throughput capacity of mobile ad hoc networks. In particular, we show that the capacity of mobile networks with finite buffers is at most /spl Theta/(/spl radic/n). Finally we establish a scaling law relationship that characterizes the fundamental tradeoff between throughput capacity and relay buffer size. In particular, we show that the throughput capacity is at most /spl Theta/(/spl radic/(nb/sub n/)), where b/sub n/ is the size of the relay buffers.

In cellular wireless communication systems, uplink power control is needed to provide each mobile user with an acceptable signal to interference ratio (SIR) while simultaneously minimizing transmit power levels. We consider a class of distributed asynchronous power control algorithms based on the schemes used in IS-95 inner loop power control. Each user's received SIR is measured (using possibly outdated information) and compared to a threshold, and a single control bit is then sent to the user, indicating whether its power level should be increased or decreased. The SIR measurements and power updates do not require synchronization. We show that under certain conditions, this class of algorithms is stable and converges to a region around the optimal power assignment. We characterize this region and show that it can be made as small as desired by choosing the algorithm parameters appropriately. For an appropriate choice of algorithm parameters, we show that convergence occurs in a finite number of iterations and derive an upper bound. To illustrate our general results, we apply them to systems with fixed base station assignment, dynamic base station assignment, and macrodiversity. Finally, we give an example to illustrate the algorithm's robustness to errors in the power control commands.