A data transmission system is considered with N independent sources and a single transmitter and a large buffer. The sources alternate between on and off states in various Markovian ways and create messages during the on periods. The creation model might be either the classical model or a Poisson stream. The traffic is heavy in that the service rate is only slightly greater than the stationary rate of creation of messages. Asymptotic results on the scaled queue length process are obtained as the number of sources tends to infinity. Weak convergence methods are used. The limit process is of the reflected diffusion type. The approach is very flexible and relatively simple to use. The service time process can be rather arbitrary. Several classes of customer types can be readily handled, and the intervals of on and off periods can be of general Erlang type. A transient period can be handled, so that it is not necessary to start with a stationary system. The dynamical systems flavor of both the derivation and the form of the limit processes makes it easy to visualize the results and extensions. The method is appropriate for use for control problems for the physical systems, and numerical methods are available for the approximate computation of functionals of the limit process. Numerical results indicate the power of the method, even when operating not too close to the heavy traffic regime.
