Throughput optimality and overload behavior of dynamical flow networks under monotone distributed routing

IEEE Transactions on Control of Network Systems

Volumn 2, Issue 1, 2015, Pages 57-67

  Como, Giacomo ^a   Lovisari, Enrico ^b   Savla, Ketan ^c  

^a LUND UNIVERSITY   (Sweden)

^b CNRS   (France)

^c University of Southern California ^*  (United States)

Author keywords

distributed routing; dynamical flow networks; monotone dynamical systems; resilience; throughput; transportation networks

Indexed keywords

DIFFERENTIAL EQUATIONS; DIRECTED GRAPHS; DYNAMICAL SYSTEMS; FLOW GRAPHS; ORDINARY DIFFERENTIAL EQUATIONS; THROUGHPUT;

DISTRIBUTED ROUTING; FLOW NETWORK; MONOTONE DYNAMICAL SYSTEMS; RESILIENCE; TRANSPORTATION NETWORK;

NETWORK ROUTING;

EID: 84961346640     PISSN: 23255870     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCNS.2014.2367361     Document Type: Article

References (21)

1. R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, Applications. Englewood Cliffs, NJ, USA: Prentice-Hall, 1993.
2. A. V. Goldberg and R. E. Tarjan, "A new approach to the maximum-flow problem, " J. ACM, vol. 35, no. 4, pp. 921-940, 1988.
3. D. Serre, Systems of Conservation Laws 1. Hyperbolicity, Entropies, Shock Waves. Cambridge, U.K.: Cambridge University Press, 1999.
4. L. Tassiulas and A. Ephremides, "Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks, " IEEE Trans. Autom. Control, vol. 37, no. 12, pp. 1936-1948, Dec. 1992.
5. C. F. Daganzo, "The cell transmission model part II: Network traffic, " Transport. Res. B-Meth., vol. 29B, no. 2, pp. 79-93, 1995.
6. M. Garavello and B. Piccoli, Traffic Flow on Networks. Springfield, MO, USA: American Institute of Mathematical Sciences, 2006.
7. C. F. Daganzo, "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory, " Transport. Res. B-Meth., vol. 28B, no. 4, pp. 269-287, 1994.
8. E. Lovisari, G. Como, and K. Savla, "Stability of monotone dynamical flow networks, " in Proc. 53rd IEEE Conf. Dec. Control, Dec. 2014, pp. 2384-2389.
9. G. Gomes, R. Horowitz, A. Kurzhanskiy, P. Varaiya, and J. Kwon, "Behavior of the cell transmission model and effectiveness of ramp metering, " Transport. Res. C-Emer., no. 16, pp. 485-513, 2008.
10. E. Lovisari, G. Como, A. Rantzer, and K. Savla, "Stability analysis and control synthesis for dynamical transportation networks, " arXiv:1410.5956v2, Oct. 2014.
11. G. Como, K. Savla, D. Acemoglu, M. A. Dahleh, and E. Frazzoli, "Robust distributed routing in dynamical networks-Part i: Locally responsive policies and weak resilience, " IEEE Trans. Autom. Control, vol. 58, no. 2, pp. 317-332, Feb. 2013.
12. G. Como, K. Savla, D. Acemoglu, M. A. Dahleh, and E. Frazzoli, "Robust distributed routing in dynamical networks-Part ii: Strong resilience, equilibrium selection and cascaded failures, " IEEE Trans. Autom. Control, vol. 58, no. 2, pp. 333-348, Feb. 2013.
13. G. Como, K. Savla, D. Acemoglu, M. A. Dahleh, and E. Frazzoli, "Robust distributed routing in dynamical networks with cascading failures, " in Proc. 51st IEEE Conf. Dec. Control, Dec. 2012, pp. 7413-7418.
14. L. R. Ford and D. R. Fulkerson, "Maximal flow through a network, " Can. J. Math., vol. 8, pp. 399-404, 1956.
15. P. Elias, A. Feinstein, and C. Shannon, "A note on the maximum flow through a network, " IRE Trans. Inf. Theory, vol. 2, no. 4, pp. 117-119, 1956.
16. M. Hirsch and H. Smith, "Competitive and cooperative systems: A minireview, " Positive Syst. Lect. Notes Control Inf. Sci., vol. 294, 2003.
17. J. A. Jacquez and C. P. Simon, "Qualitative theory of compartmental systems, " SIAM Rev., vol. 35, no. 1, pp. 43-79, 1993.
18. D. Angeli and E. Sontag, "Monotone control system, " IEEE Trans. Autom. Control, vol. 48, no. 10, pp. 1684-1698, Oct. 2003.
19. D. Shah and D. Wischik, "Fluid models of congestion collapse in overloaded switched networks, " Queueing Syst., vol. 69, pp. 121-143, 2011.
20. L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of functions, vol. 5. Boca Raton, FL, USA: CRC, 1992.
21. G. Como, E. Lovisari, and K. Savla, "Throughput optimality and overload behavior of dynamical flow networks under monotone distributed routing, " arXiv:1308.1993v3, May 2014.