  This work started out with our accidental discovery of a pattern of
throughput distributions among links in IEEE 802.11 networks from experimental
results. This pattern gives rise to an easy computation method, which we term
back-of-the-envelop (BoE) computation, because for many network configurations,
very accurate results can be obtained within minutes, if not seconds, by simple
hand computation. BoE beats prior methods in terms of both speed and accuracy.
While the computation procedure of BoE is simple, explaining why it works is by
no means trivial. Indeed the majority of our investigative efforts have been
devoted to the construction of a theory to explain BoE. This paper models an
ideal CSMA network as a set of interacting on-off telegraph processes. In
developing the theory, we discovered a number of analytical techniques and
observations that have eluded prior research, such as that the carrier-sensing
interactions among links in an ideal CSMA network result in a system state
evolution that is time-reversible; and that the probability distribution of the
system state is insensitive to the distributions of the "on" and "off"
durations given their means, and is a Markov random field. We believe these
theoretical frameworks are useful not just for explaining BoE, but could also
be a foundation for a fundamental understanding of how links in CSMA networks
interact. Last but not least, because of their basic nature, we surmise that
some of the techniques and results developed in this paper may be applicable to
not just CSMA networks, but also to other physical and engineering systems
consisting of entities interacting with each other in time and space.
