A comprehensive and representative logical ring random service system with priority is discussed.It is asymmetric and the queue length and the upper limit of the service are all finite.The main contents include:the performance feature of the system;the transition characteristics of the queue states;the approximate algorithm of the transition probability of the queue states;the unconventional algorithm of the state probabilities of the queues etc.New concepts such as the state conditional transition and the state transition combination

and the methods of substituting the distribution parameters by the lumped ones are proposed in the paper.