TY - JOUR
T1 - Stability of Fluid Queueing Systems with Parallel Servers and Stochastic Capacities
AU - Jin, Li
AU - Amin, Saurabh
N1 - Funding Information:
Manuscript received October 10, 2017; accepted February 5, 2018. Date of publication February 19, 2018; date of current version October 25, 2018. This work was supported by NSF CNS-1239054 CPS Frontiers, NSF CAREER Award CNS-1453126, and AFRL Lablet-Secure and Resilient Cyber-Physical Systems. Recommended by Associate Editor L. Zhang. (Corresponding author: Li Jin.) The authors are with the Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TAC.2018.2808044
Publisher Copyright:
© 2018 IEEE.
PY - 2018/11
Y1 - 2018/11
N2 - 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.
AB - 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.
KW - Queueing systems
KW - stability analysis
KW - stochastic switching systems
KW - traffic control
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U2 - 10.1109/TAC.2018.2808044
DO - 10.1109/TAC.2018.2808044
M3 - Article
AN - SCOPUS:85042178057
SN - 0018-9286
VL - 63
SP - 3948
EP - 3955
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 11
M1 - 8295039
ER -