A consequence of bursty traffic in computer communications is that among a large population of network users, at any one time only a small number of them have data to send (ready users). In this environment, the performance of an access protocol for a broadcast network depends mainly upon how quickly one of the ready users can be identified and given sole access to the shared channel. The relative merits of the access protocols of polling, probing and carrier sense multiple access (CSMA) with respect to this channel assignment delay in local networks are considered. A central controller is needed for polling and probing while CSMA employs distributed control. A specific CSMA protocol is defined which requires that “collisions” in the channel be detected and that the users involved in a collision abort their transmissions quickly. In addition, it is assumed that the contention algorithm is adaptive and gives rise to a stable channel. An analytic model is developed. Our main result is the moment generating function of the distributed queue size (number of ready users). Mean value formulas for message delay and channel assignment delay are also derived. These results on queue size and delay are the major contribution of this paper, since they are not available in prior CSMA models in close analytical form. Numerical results are given to illustrate the performance of the CSMA protocol. When the channel utilization is light to moderate, the mean channel assignment delay of the CSMA protocol is significantly less than that of both polling and probing; consequently, the mean message delay is much smaller. It is also shown that when queueing of messages is permitted at individual users, the maximum channel throughput of CSMA approaches unity in the limit of very long queues. Finally, simulation results of several adaptive control algorithms are presented. The accuracy of our analytic formulas was carefully studied and found to be very good in all cases considered.