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

Glazebrook, Kevin; Niño-Mora, José

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

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Citation

Journal of Applied Probability, 37, 3, (2000), pp. 890-899

Abstract

We argue the importance both of developing simple sufficient conditions for the stability of general multiclass queueing networks and also of assessing such conditions under a range of assumptions on the weight of the traffic flowing between service stations. To achieve the former, we review a peak-rate stability condition and extend its range of application and for the latter, we introduce a generalisation of the Lu-Kumar network on which the stability condition may be tested for a range of traffic configurations. The peak-rate condition is close to exact when the between-station traffic is light, but degrades as this traffic increases.