It is desirable to have a protocol which has low delay in light traffic condition and does not suffer from losing the channel capacity in heavy traffic condition. One solution to this problem is the use of a collision-avoidance switch. In this paper, we present models for broadcast star networks with collision-avoidance switch in two cases: a broadcast star network with small propagation delay and a broadcast star network with large propagation delay. Also, we propose a service discipline which is easy to implement and exhibits relatively low variance of message delay. The proposed service discipline is a combination of first-come first-served (FCFS) and random-order of service (ROS) discipline, and it uses reservation and priority fields in the message header. We analyze the models to obtain distributions of message delay for the proposed service discipline, and compare the results with that for other service disciplines. From numerical results, we show that the variance of message delay for the proposed service discipline is almost the same as that for the FCFS discipline for any distribution of message length and also for any value of normalized propagation delay.