Continuity, Uniqueness, and Long-Term Behavior of Nash Flows over Time

References

• Bhaskar U, Fleischer L, Anshelevich E (2015) A Stackelberg strategy for routing flow over time. Games Econom. Behav. 92:232–247.Crossref, Google Scholar
• Cao Z, Chen B, Chen X, Wang C (2017) A network game of dynamic traffic. Daskalakis C, Babaioff M, Moulin H, eds. Proc. 18th ACM Conf. Econom. Comput. (Association for Computing Machinery (ACM), New York), 695–696.Google Scholar
• Cominetti R, Correa J, Larré O (2011) Existence and uniqueness of equilibria for flows over time. Aceto L, Henzinger M, Sgall J, eds. Proc. 28th Internat. Colloquium Automata Languages Programming (Springer, Berlin, Heidelberg), 552–563.Google Scholar
• Cominetti R, Correa J, Larré O (2015) Dynamic equilibria in fluid queueing networks. Oper. Res. 63(1):21–34.Link, Google Scholar
• Cominetti R, Correa J, Olver N (2021) Long-term behavior of dynamic equilibria in fluid queuing networks. Oper. Res. 70(1):516–526.Google Scholar
• Cominetti R, Scarsini M, Schröder M, Stier-Moses N (2022) Approximation and convergence of large atomic congestion games. Math. Oper. Res. 48(2):784–811.Link, Google Scholar
• Correa J, Cristi A, Oosterwijk T (2019) On the price of anarchy for flows over time. Karlin A, Immorlica N, Johari R, eds. Proc. 20th ACM Conf. Econom. Comput. (Association for Computing Machinery (ACM), New York), 559–577.Google Scholar
• Frascaria D (2021) Dynamic traffic equilibria with route and departure time choice. Unpublished PhD thesis, Vrije Universiteit Amsterdam, Amsterdam, Netherlands.Google Scholar
• Friesz TL, Han K (2019) The mathematical foundations of dynamic user equilibrium. Transportation Res. Part B Methodological 126:309–328.Crossref, Google Scholar
• Fulkerson DR, Ford LR (1956) Maximal flow through a network. Canadian J. Math. 8:399–404.Crossref, Google Scholar
• Graf L, Harks T, Sering L (2020) Dynamic flows with adaptive route choice. Math. Programming 183(1):309–335.Crossref, Google Scholar
• Graf L, Harks T, Kollias K, Markl M (2022) Machine-learned prediction equilibrium for dynamic traffic assignment. Sycara K, Honavar V, Spaan M, eds. Proc. AAAI Conf. Artificial Intelligence (AAAI Press, Palo Alto, CA), 5059–5067.Google Scholar
• Han K, Friesz TL, Yao T (2013) Existence of simultaneous route and departure choice dynamic user equilibrium. Transportation Res. Part B Methodological 53:17–30.Crossref, Google Scholar
• Iryo T (2011) Multiple equilibria in a dynamic traffic network. Transportation Res. Part B Methodological 45(6):867–879.Crossref, Google Scholar
• Iryo T (2013) Properties of dynamic user equilibrium solution: Existence, uniqueness, stability, and robust solution methodology. Transportmetrica B Transport Dynamics 1(1):52–67.Crossref, Google Scholar
• Iryo T, Smith MJ (2018) On the uniqueness of equilibrated dynamic traffic flow patterns in unidirectional networks. Transportation Res. Part B Methodological 117:757–773.Crossref, Google Scholar
• Ismaili A (2017) Routing games over time with FIFO policy. Devanur NR, Lu P, eds. Proc. 14th Internat. Conf. Web Internet Econom. (Springer International Publishing, Cham, Switzerland), 266–280.Google Scholar
• Kaiser M (2022) Computation of dynamic equilibria in series-parallel networks. Math. Oper. Res. 47(1):50–71.Google Scholar
• Koch R (2012) Routing games over time. Unpublished PhD thesis, Technische Universität Berlin, Berlin.Google Scholar
• 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
• Kulkarni J, Mirrokni VS (2015) Robust price of anarchy bounds via LP and Fenchel duality. Indyk P, ed. Proc. 26th Annual ACM-SIAM Sympos. Discrete Algorithms (SIAM (Society for Industrial and Applied Mathematics), Philadelphia), 1030–1049.Google Scholar
• Kuwahara M, Akamatsu T (1993) Dynamic equilibrium assignment with queues for a one-to-many od pattern. Daganzo, ed. Proc. 12th Internat. Sympos. Transportation Traffic Theory (Elsevier, Berkeley, CA), 185–204.Google Scholar
• Lighthill MJ, Whitham GB (1955) On kinematic waves II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London. Ser. A Math. Physical Sci. 229(1178):317–345.Google Scholar
• Meunier F, Wagner N (2010) Equilibrium results for dynamic congestion games. Transportation Sci. 44(4):524–536.Link, Google Scholar
• Mounce R (2006) Convergence in a continuous dynamic queueing model for traffic networks. Transportation Res. Part B Methodological 40(9):779–791.Crossref, Google Scholar
• Olver N, Sering L, Vargas Koch L (2023) Convergence of approximate and packet routing equilibria to Nash flows over time. Proc. 64th Annual Sympos. Foundations Comput. Sci. (IEEE Computer Society, Washington, DC), 123–133.Google Scholar
• Pham HM, Sering L (2020) Dynamic equilibria in time-varying networks. Harks T, Klimm M, eds. Proc. 13th Internat. Sympos. Algorithmic Game Theory (Springer Nature Switzerland, Cham, Switzerland), 130–145.Google Scholar
• Richards PI (1956) Shock waves on the highway. Oper. Res. 4(1):42–51.Link, Google Scholar
• Roughgarden T (2005) Selfish Routing and the Price of Anarchy (The MIT Press, Cambridge, MA; London).Google Scholar
• Scarsini M, Schröder M, Tomala T (2018) Dynamic atomic congestion games with seasonal flows. Oper. Res. 66(2):327–339.Link, Google Scholar
• Sering L (2020) Nash flows over time. Unpublished PhD thesis, Technische Universität Berlin, Germany.Google Scholar
• Sering L, Skutella M (2018) Multi-source multi-sink Nash flows over time. Borndörfer R, Storandt S, eds. Proc. 18th Workshop Algorithmic Approaches Transportation Model. Optim. Systems, vol. 65 (Schloss Dagstuhl — Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Wadern, Germany), 12:1–12:20.Google Scholar
• Sering L, Vargas Koch L (2019) Nash flows over time with spillback. Chan TM, ed. Proc. 30th Annual ACM-SIAM Sympos. Discrete Algorithms (SIAM (Society for Industrial Applied Mathematics), Philadelphia), 935–945.Google Scholar
• Sering L, Vargas Koch L, Ziemke T (2021) Convergence of a packet routing model to flows over time. Biró P, Chawla S, Echenique F, eds. Proc. 22nd ACM Conf. Econom. Comput. (Association for Computing Machinery, New York), 797–816.Google Scholar
• Smith MJ, Mounce R (2007) Chapter 13: Uniqueness of equilibrium in steady state and dynamic traffic networks. Allsop RE, Bell MGH, Heydecker BG, eds. Transportation Traffic Theory: Internat. Sympos. Transportation Traffic Theory, vol. 17 (Elsevier, Oxford, UK), 281–299.Google Scholar
• Tauer B, Vargas Koch L (2021) FIFO and randomized competitive packet routing games. Koenemann J, Peis B, eds. Proc. 19th International Workshop Approximation Online Algorithms (Springer Nature Switzerland, Cham, Switzerland), 165–187.Google Scholar
• Vickrey WS (1969) Congestion theory and transport investment. Amer. Econom. Rev. 59(2):251–260.Google Scholar
• 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
• Ziemke T, Sering L, Vargas Koch L, Zimmer M, Nagel K, Skutella M (2021) Flows over time as continuous limit of packet-based network simulations. Transportation Res. Procedia 52:123–130.Crossref, Google Scholar