Abstract:

A multi-server queuing system was studied with two classes of customers which shared a limited buffer. The customers of the first class had the preemptive priority,while the second class included positive and negative customers. The negative customers would not be served and the positive customers were removed one by one at the tail. According to the state transition figure,  the stationary balance equations were obtained. By using matrix analysis theory, the average queuing length and the loss rate of the two classes were separately given, and a numerical example was presented to prove the effectiveness of this model. Then the influence of various parameters on the system was analyzed in combination with figures.

Key words: multi-server; preemptive priority; negative customer; average queuing length; loss rate