Nio-Mora和Glazebrook条件及一类排队网络的稳定性

Nio-Mora and Glazebrook Global Stability Condition and Stability of a class of Queueing Networks

多级排队网络的稳定性特别是全稳定性一直是随机网络研究的一个热点.Ni o Mora和Glazebrook就多级排队网络的全稳定性给出了一个充分条件,即当每个工作站的峰值流量密度ρ-<1时,该排队网络是全稳定的.通过对该条件的应用得出了此条件成立的必要条件,即当σ(k)≠σ(k+1)时有mk>mk+1.对一类具有两个工作站的重入排队网络证明了若σ(k)≠σ(k+1)时有mk≥mk+1,该排队网络是全稳定的.

In recent years, the researches have focused more and more on the stability and global stability of the multiclass queueing network. Nio-Mora and Glazebrook show that the multiclass queueing network is global stable when ρ-<1. When the Nio-Mora and Glazebrook global stability condition is holding and σ(k)≠σ(k+1),then m_k>m_(k+1). Furthermore, a sufficient condition about the global stability of a class of queueing networks is that m_k≥m_(k+1) when σ(k)≠σ(k+1).