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Multiplexer-concentrators (or asynchronous multiplexers) are devices used to increase the efficiency of telecommunication systems into which the flow of information is erratic. In the analysis of such systems, many assumptions about the statistical nature of the input traffic can be made. The assumptions made here are constant message length, constrained buffer size, and finite number of message sources. The numerical technique given copes with the case of multiple output trunks, and the complete statistical behavior of the system is revealed in transient as well as steady-state form. Results are given graphically which show the effect of various statistical assumptions, the transient response of the system, the behavior of the tail of the distribution of queue states, and the effect of message clustering.