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A TDMA access-control scheme operating under a nonpreemptive message-based priority discipline is considered and analyzed. The moment generating function (MGF) of the message waiting-time is obtained, at an arbitrary station of the network, under the assumptions of a Poisson message arrival stream and random message lengths governed by a general distribution, for each priority class. Using these results, explicit formulas for any moment of the message delay can be obtained. In particular, expressions for the average and standard deviation of the message waiting-time are presented, for the case when short (e.g., interactive) messages have priority over longer (e.g., batch) messages.