Computation of Dynamic Equilibria in Series-Parallel Networks

References

• [1] Bhaskar U, Fleischer L, Anshelevich E (2015) A Stackelberg strategy for routing flow over time. Games Econom. Behav. 92:232–247.Crossref, Google Scholar
• [2] Brandstädt A, Le V, Spinrad J (1999) Graph Classes: A Survey (Society for Industrial and Applied Mathematics, Philadelphia).Google Scholar
• [3] Cominetti R, Correa J, Larré O (2011) Existence and uniqueness of equilibria for flows over time. Aceto L, Henzinger M, Sgall J, eds. Automata, Languages and Programming (Springer, Berlin, Heidelberg), 552–563.Crossref, Google Scholar
• [4] Cominetti R, Correa J, Larré O (2015) Dynamic equilibria in fluid queueing networks. Oper. Res. 63(1):21–34.Link, Google Scholar
• [5] Cominetti R, Correa J, Olver N (2017) Long term behavior of dynamic equilibria in fluid queuing networks. Eisenbrand F, Koenemann J, eds. Integer Programming and Combinatorial Optimization (Springer, Cham), 161–172.Crossref, Google Scholar
• [6] Cominetti R, Harks T, Osorio C, Peis B (2018) Dynamic traffic models in transportation science (Dagstuhl Seminar 18102). Dagstuhl Rep. 8(3):21–38.Google Scholar
• [7] Correa J, Cristi A, Oosterwijk T (2019) On the price of anarchy for flows over time. Proc. 2019 ACM Conf. Econom. Comput. (Association for Computing Machinery, New York), 559–577.Google Scholar
• [8] Cottle R, Pang J, Stone R (2009) The Linear Complementarity Problem (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
• [9] Filippov AF (1988) Differential equations with discontinuous righthand sides. Arscott FM, ed. Mathematics and Its Applications (Soviet Series), vol 18 (Springer, Dordrecht).Google Scholar
• [10] Ford LR, Fulkerson DR (1962) Flows in Networks (Princeton University Press, Princeton).Crossref, Google Scholar
• [11] Geršgorin S (1931) Über die Abgrenzung der Eigenwerte einer Matrix. Bull. l’Académie des Sciences de l’URSS. 6:749–754.Google Scholar
• [12] Graf L, Harks T (2019) Dynamic flows with adaptive route choice. Lodi A, Nagarajan V, eds. Integer Programming and Combinatorial Optimization (Springer, Cham), 219–232.Crossref, Google Scholar
• [13] Koch R, Skutella M (2011) Nash equilibria and the price of anarchy for flows over time. Theory Comput. Systems 49(1):71–97.Crossref, Google Scholar
• [14] Merchant DK, Nemhauser GL (1978) A model and an algorithm for the dynamic traffic assignment problems. Transportation Sci. 12(3):183–199.Link, Google Scholar
• [15] Merchant DK, Nemhauser GL (1978) Optimality conditions for a dynamic traffic assignment model. Transportation Sci. 12(3):200–207.Link, Google Scholar
• [16] Meunier F, Wagner N (2010) Equilibrium results for dynamic congestion games. Transportation Sci. 44(4):524–536.Link, Google Scholar
• [17] Papadimitriou CH (1994) On the complexity of the parity argument and other inefficient proofs of existence. J. Comput. System Sci. 48(3):498–532.Crossref, Google Scholar
• [18] Peeta S, Ziliaskopoulos AK (2001) Foundations of dynamic traffic assignment: The past, the present and the future. Networks Spatial Econom. 1(3):233–265.Crossref, Google Scholar
• [19] Sering L, Skutella M (2018) Multi-source multi-sink Nash flows over time. Borndörfer R, Storandt S, eds. 18th Workshop Algorithmic Approaches Transportation Model., Optim. Systems, vol. 65 (Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl), 12:1–12:20.Google Scholar
• [20] Sering L, Vargas Koch L (2019) Nash flows over time with spillback. Chan TM, ed. Proc. 30th Annual ACM-SIAM Sympos. Discrete Algorithms (Society for Industrial and Applied Mathematics, Philadelphia), 935–945.Google Scholar
• [21] Skutella M (2009) An introduction to network flows over time. Cook W, Lovász L, Vygen J, eds. Research Trends in Combinatorial Optimization (Springer, Berlin, Heidelberg), 451–482.Crossref, Google Scholar
• [22] Vickrey WS (1969) Congestion theory and transport investment. Amer. Econom. Rev. 59(2):251–260.Google Scholar
• [23] Zhu D, Marcotte P (2000) On the existence of solutions to the dynamic user equilibrium problem. Transportation Sci. 34(4):402–414.Link, Google Scholar