  We consider a multi-channel communication system under ALOHA and CSMA
protocols, resepctively, in continuous time. We derive probabilistic formulas
for the most important quantities: the numbers of sending attempts and the
number of successfully delivered messages in a given time interval. We derive
(1) explicit formulas for the large-time limiting throughput, (2) introduce an
explicit and ergodic Markov chain for a deeper probabilistic analysis, and use
this to (3) derive exponential asymptotics for rare events for these quantities
in the limit of large time, via large-deviation principles.
