Stability of Fluid Queueing Systems with Parallel Servers and Stochastic Capacities

Li Jin, Saurabh Amin

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number8295039
Pages (from-to)3948-3955
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number11
StatePublished - Nov 2018


  • Queueing systems
  • stability analysis
  • stochastic switching systems
  • traffic control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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