Queueing behavior of statistical multiplexers with correlated inputs

The author considers an asynchronous time-division-multiplexing system with a finite number of identical users generating data only during their so-called active periods, which alternate with so-called passive periods. Assuming geometric distributions for the active and passive periods of the users, the author derives a functional equation which describes the full steady-state buffer behavior of the multiplexer. The buffer occupancy at various moments can be derived from this equation and explicit functions of the parameters of the system. The results indicate a strong dependency of the mean buffer occupancy on the actual lengths of the active and passive periods of the users, even for a given mean user activity