In wireless networks, in particular for ad hoc networks, there is a need for network models that accurately capture the uncertainties present in such systems. We introduce some basic models for node distributions and channels and combine them into an "uncertainty cube" as a way of visualizing and capturing the three main sources of non-determinism. Within this framework, we determine interference distributions and outage probabilities for large networks and propose a new joint link model that incorporates both node distances and fading states. As applications of the theory developed, we discuss three specific problems: the sentry selection problem in sensor networks; the analysis and design of time and path diversity schemes in networks with Rayleigh fading; and the question of short-hop vs. long-hop routing.

Martin Haenggi received the Dipl. Ing. (M.Sc.) degree in electrical engineering from the Swiss Federal Institute of Technology in Zurich (ETHZ) in 1995. In 1995, he joined the Signal and Information Processing Laboratory at ETHZ as a Teaching and Research Assistant. In 1996 he earned the Dipl. NDS ETH (post-diploma) degree in information technology, and in 1999, he completed his Ph.D. thesis on the analysis, design, and optimization of cellular neural networks. After a postdoctoral year at the Electronics Research Laboratory at the University of California in Berkeley, he joined the faculty of the electrical engineering department at the University of Notre Dame as an assistant professor in January 2001. For both his M.Sc.and his Ph.D. theses, he was awarded the ETH medal, and he received an NSF CAREER award in 2005. For 2005/06, he is a Distinguished Lecturer for the IEEE Circuits and Systems Society. His current scientific interests include networking and wireless communications, with an emphasis on ad hoc and sensor networks.