Stability of Fluid Queueing Systems With Parallel Servers and Stochastic Capacities
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Publication:4562261
DOI10.1109/TAC.2018.2808044zbMATH Open1423.90060arXiv1604.02008OpenAlexW2964227028MaRDI QIDQ4562261
Publication date: 19 December 2018
Published in: IEEE Transactions on Automatic Control (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1604.02008
Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)
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