A multiplexing communications channel is considered. The network stations share the channel on a time-division multiple-access (TDMA) basis or by using a slotted frequency-division multiple-access (FDMA) scheme. Messages are categorized by their differing priorities. Two service disciplines are considered: nonpreemptive and preemptive-resume. A discrete-time priority queuing system is introduced and investigated. Message-delay distributions are obtained for priority and ordinary messages in a two-class system model, under each service discipline. Next, delay analysis for a p-class model is carried out. The results are then applied to general, slotted, priority FDMA and TDMA schemes. >