A model for a personal rapid transit system is proposed, using an embedded Markov chain to manage traffic behavior at a grade-separated interchange. The interchange is composed of a main line and a sub line. There are two kinds of vehicles in both the main line and the sub line; branching vehicles and transit vehicles. A vehicle on the main line has priority. Thus, a queue forms on only the sub line. The waiting times of the sub line vehicles are restricted to a fixed value called the restricted entry waiting time. If the waiting time exceeds this value, a vehicle will be detoured. We analyze the embedded Markov chain model using the generating function technique. The relationship between restricted entry waiting time and traffic behavior is examined; the obtained results show how to choose the optimum value of the restricted entry waiting time.