中文摘要：

This paper is concerned with the stability of multiclass queueing networks of 2 stations and4 buffers under the longest queue first served discipline (LQFS). For this network, the service priority of a customer is determined by the length of the queue that customer resides in at that time. The main result includes two parts. Firstly, the corresponding fluid model is established, and then it is shown that the queueing networks under LQFS are stable whenever the traffic intensity is strictly less than one for each station.

英文摘要：

This paper is concerned with the stability of multiclass queueing networks of 2 stations and 4 buffers under the longest queue first served discipline （LQFS）. For this network, the service priority of a customer is determined by the length of the queue that customer resides in at that time. The main result includes two parts. Firstly, the corresponding fluid model is established, and then it is shown that the queueing networks under LQFS are stable whenever the traffic intensity is strictly less than one for each station.