We consider a multiple-access broadcast communication channel which serves a network of terminals, each characterized by a distinct priority level. Higher priority terminals require, on the average, faster access across the communication channel than lower priority ones. We present a terminal priority contentionless access (TPCA) control scheme for sharing such a channel on a conflict-free basis. A ready terminal wishing to access the channel will wait for the channel to become idle, and then defer its access untill after higher priority terminals are given the opportunity to transmit. The model accounts for acquisition delays (including propagation and timearound delay components), idle detection times, multipacket message structures and different arrival intensities at different terminals, Analytical results are derived for the moments and transform of the message waiting-time distribution at each network terminal by relating the waiting times in our model to those in an appropriate

queue with HOL (head of the line) priorities. Performance curves are presented under varirous system parameter conditions which correspond to applications involving digital radio local distribution systems and metropolitan-area, packet radio, and local-area communicatiton networks.