Convergence of a Packet Routing Model to Flows over Time

References

• [1] Adamik A, Sering L (2022) Atomic splittable flow over time games. Aspnes J, Michail O, eds. 1st Sympos. Algorithmic Foundations Dynamic Networks (SAND 2022). Leibniz Internat. Proc. Informatics (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Wadern, Germany), 4:1–4:16.Google Scholar
• [2] Cantarella G, Watling D (2016) Modelling road traffic assignment as a day-to-day dynamic, deterministic process: A unified approach to discrete- and continuous-time models. EURO J. Transportation Logist. 5(1):69–98.Crossref, Google Scholar
• [3] Cao Z, Chen B, Chen X, Wang C (2017) A network game of dynamic traffic. Proc. 2017 ACM Conf. Econom. Comput. (Association for Computing Machinery, New York), 695–696.Google Scholar
• [4] Cominetti R, Correa J, Larré O (2011) Existence and uniqueness of equilibria for flows over time. Internat. Colloquium Automata, Languages, Programming (Springer-Verlag, Zurich), 552–563.Google Scholar
• [5] Cominetti R, Correa J, Larré O (2015) Dynamic equilibria in fluid queueing networks. Oper. Res. 63(1):21–34.Link, Google Scholar
• [6] Cominetti R, Correa J, Olver N (2021) Long-term behavior of dynamic equilibria in fluid queuing networks. Oper. Res. 70(1):516–526.Link, Google Scholar
• [7] Cominetti R, Scarsini M, Schröder M, Stier-Moses N (2022) Approximation and convergence of large atomic congestion games. Math. Oper. Res. Forthcoming.Google Scholar
• [8] Correa J, Cristi A, Oosterwijk T (2021) On the price of anarchy for flows over time. Math. Oper. Res., 1–18.Google Scholar
• [9] Fleischer L, Tardos É (1998) Efficient continuous-time dynamic network flow algorithms. Oper. Res. Lett. 23(3–5):71–80.Crossref, Google Scholar
• [10] Frascaria D, Olver N (2022) Algorithms for flows over time with scheduling costs. Math. Programming 192:177–206.Google Scholar
• [11] Graf L, Harks T, Sering L (2020) Dynamic flows with adaptive route choice. Math. Programming 183(1):309–335.Crossref, Google Scholar
• [12] Harks T, Peis B, Schmand D, Tauer B, Vargas Koch L (2018) Competitive packet routing with priority lists. ACM Trans. Econom. Comput. 6(1):1–26.Crossref, Google Scholar
• [13] Hoefer M, Mirrokni V, Röglin H, Teng SH (2011) Competitive routing over time. Theoretical Comput. Sci. 412(39):5420–5432.Crossref, Google Scholar
• [14] Horni A, Nagel K, Axhausen K, eds. (2016) Multi-Agent Transport Simulation MATSim (Ubiquity Press, London).Crossref, Google Scholar
• [15] Ismaili A (2017) Routing games over time with FIFO policy. Internat. Conf. Web Internet Econom. (Springer International Publishing), 266–280.Google Scholar
• [16] Israel J, Sering L (2020) The impact of spillback on the price of anarchy for flows over time. Internat. Sympos. Algorithmic Game Theory (Springer), 114–129.Google Scholar
• [17] Kaiser M (2022) Computation of dynamic equilibria in series-parallel networks. Math. Oper. Res. 47(1):50–71.Google Scholar
• [18] 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
• [19] Meunier F, Wagner N (2010) Equilibrium results for dynamic congestion games. Transportation Sci. 44(4):524–536.Link, Google Scholar
• [20] Olver N, Sering L, Vargas Koch L (2022) Continuity, uniqueness and long-term behavior of Nash flows over time. 2021 IEEE 62nd Annual Sympos. Foundations Comput. Sci., 851–860.Google Scholar
• [21] Otsubo H, Rapoport A (2008) Vickrey’s model of traffic congestion discretized. Transportation Res. Part B Methodological 42(10):873–889.Crossref, Google Scholar
• [22] Pham H, Sering L (2020) Dynamic equilibria in time-varying networks. Internat. Sympos. Algorithmic Game Theory (Springer), 130–145.Google Scholar
• [23] PTV AG (2016) VISUM 16—User Manual (PTV AG, Karlsruhe, Germany).Google Scholar
• [24] Rosenthal R (1973) The network equilibrium problem in integers. Networks 3(1):53–59.Crossref, Google Scholar
• [25] Scarsini M, Schröder M, Tomala T (2018) Dynamic atomic congestion games with seasonal flows. Oper. Res. 66(2):327–339.Link, Google Scholar
• [26] Scheffler R, Strehler M, Vargas Koch L (2022) Routing games with edge priorities. ACM Trans. Econom. Comput. 10(1):1–27.Google Scholar
• [27] Sering L (2020) Nash flows over time. Unpublished PhD thesis, Technische Universität Berlin, Berlin.Google Scholar
• [28] Sering L, Skutella M (2018) Multi-source multi-sink Nash flows over time. 18th Workshop Algorithmic Approaches Transportation Model. Optim. Systems, vol. 65 (Schloss Dagstuhl - Leibniz-Zentrum für Informatik), 1–20.Google Scholar
• [29] Sering L, Vargas Koch L (2019) Nash flows over time with spillback. Proc. 30th Annual ACM-SIAM Sympos. Discrete Algorithms (SIAM), 935–945.Google Scholar
• [30] Wardrop J (1952) Some theoretical aspects of road traffic research. Proc. Inst. Civil Engrg. 1(3):325–378.Crossref, Google Scholar
• [31] Werth T, Holzhauser M, Krumke S (2014) Atomic routing in a deterministic queuing model. Oper. Res. Perspect. 1(1):18–41.Crossref, Google Scholar
• [32] 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