Stability of Fluid Queueing Systems with Parallel Servers and Stochastic Capacities

• Main Authors: Jin, Li (Contributor), Amin, Saurabh (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Civil and Environmental Engineering (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers (IEEE), 2018-08-20T12:00:44Z.
• Subjects: Article
• Online Access: Get fulltext

 IEEE This article 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.