Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network

We argue the importance both of developing simple sufficient conditions for the stability of general multiclass queueing networks and also of assessin g such conditions under a range of assumptions on the weight of the traffic Bowing between service stations. To ach;eve the former, we review a peak-r ate stability condition and extend its range of application and for the lat ter, we introduce a generalisation of the Lu-Kumar network on which the sta bility condition may be tested for a range of traffic configurations. The p eak-rate condition is close to exact when the between-station traffic is li ght, but degrades as this traffic increases.