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When a superposition of on/off sources is offered to a deterministic server, we are faced with a particular queueing system, the analysis of which has a significant role in ATM networks. Periodic cell generation during active times is a major feature of these sources. We provide an analytical approach to solve for this queueing system via an approximation to the transient behavior of the nD/D/l queue. The solution to the queue length distribution is given in terms of a solution to a lineardoi:10.1016/0166-5316(93)e0058-d fatcat:or4qfndkzbcalncpdaeo5ykbse