具有并行服务器和随机容量的流队列系统的稳定性
Stability of Fluid Queuing Systems with Parallel Servers and Stochastic Capacities
AI总结：
本文提出了一种分段确定性队列模型，用于研究面对随机容量波动的并联链交通系统中交通队列的稳定性，通过马尔可夫链切换模式和状态反馈策略控制流入，提出稳定性条件。
摘要：
本文介绍了一种分段确定性队列（PDQ）模型，用于研究面对随机容量波动的并联链交通系统中交通队列的稳定性。PDQ模型的饱和率（容量）根据马尔可夫链在有限模式集之间切换，链流入由状态反馈策略控制。PDQ系统稳定当且仅当时间平均链流入的下界不超过相应的时间平均饱和率。此外，PDQ系统稳定当且仅当名义模式的饱和率足够高，使得所有队列在该模式下消失，并且涉及PDQ在各个模式中 discharge rates 的低估的双线性矩阵不等式（BMI）可行。这些稳定性条件可以针对两种模式的PDQ进一步加强。这些结果可用于设计路由策略，以在随机容量波动下保证交通队列的稳定性。
英文摘要：
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 (BMI) 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
