Stability of Fluid Queueing Systems With Parallel Servers and Stochastic Capacities
Stability of Fluid Queueing Systems With Parallel Servers and Stochastic Capacities
复制标题
具有并行服务器和随机容量的流动排队系统的稳定性
DOI：
10.1109/tac.2018.2808044
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发表时间：
2016
影响因子：
6.8
通讯作者：
Saurabh Amin
中科院分区：
文献类型：
--
作者：
Li Jin;Saurabh Amin
引入分段确定性排队(PDQ)模型，研究了容量随机波动的平行链路运输系统中交通排队的稳定性问题。PDQ模型的饱和率(容量)根据马尔科夫链在有限的模式集之间切换，链路流入由状态反馈策略控制。只有当时间平均链路流入的下界不超过相应的时间平均饱和率时，PDQ系统才是稳定的。此外，如果满足以下两个条件，则PDQ系统是稳定的：标称模式的饱和率足够高，使得在该模式下所有队列都消失，并且包含低估各个模式下PDQ的放电率的双线性矩阵不等式是可行的。双模PDQ的稳定性条件可以得到加强。这些结果可用于设计在随机容量波动下保证业务队列稳定性的路由策略。
This note introduces a piecewise-deterministic queueing (PDQ) model to study the stability of traffic queues in parallel-link transportation systems facing stochastic capacity fluctuations. The saturation rate (capacity) of the PDQ model switches between a finite set of modes according to a Markov chain, and link inflows are controlled by a state-feedback policy. A PDQ system is stable only if a lower bound on the time-average link inflows does not exceed the corresponding time-average saturation rate. Furthermore, a PDQ system is stable if the following two conditions hold: the nominal mode's saturation rate is high enough that all queues vanish in this mode, and a bilinear matrix inequality involving an underestimate of the discharge rates of the PDQ in individual modes is feasible. The stability conditions can be strengthened for two-mode PDQs. These results can be used for design of routing policies that guarantee stability of traffic queues under stochastic capacity fluctuations.