On the System Optimum Dynamic Traffic Assignment and Earliest Arrival Flow Problems

References

• Baumann N (2007) Evacuation by earliest arrival flows. Ph.D. thesis, TU Dortmund, Dortmund, Germany.Google Scholar
• Baumann N, Skutella M (2009) Earliest arrival flows with multiple sources. Math. Oper. Res. 34(2):499–512.Link, Google Scholar
• Burkard RE, Dlaska K, Klinz B (1993) The quickest flow problem. ZOR Methods Models Oper. Res. 37(1):31–58.Crossref, Google Scholar
• Carey M, Ge YE, McCartney M (2003) A whole-link travel-time model with desirable properties. Transportation Sci. 37(1):83–96.Link, Google Scholar
• Chiu Y-C, Zheng H (2007) Real-time mobilization decisions for multi-priority emergency response resources and evacuation groups: Model formulation and solution. Transportation Res. Part E: Logistics and Transportation Rev. 43(6):710–736.Crossref, Google Scholar
• Chiu Y-C, Zheng H, Villalobos J, Gautam B (2007) Modeling no-notice mass evacuation using a dynamic traffic flow optimization model. IIE Trans. 39(1):83–94.Crossref, Google Scholar
• Daganzo CF (1994) The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Res. Part B: Methodological 28(4):269–287.Crossref, Google Scholar
• Daganzo CF (1995a) The cell transmission model part II: Network traffic. Transportation Res. Part B: Methodological 29(2):79–93.Crossref, Google Scholar
• Daganzo CF (1995b) Properties of link travel time functions under dynamic loads. Transportation Res. Part B: Methodological 29(2):95–98.Crossref, Google Scholar
• Fleischer L, Skutella M (2007) Quickest flows over time. SIAM J. Comput. 36(6):1600–1630.Crossref, Google Scholar
• Fleischer L, Tardos E (1998) Efficient continuous-time dynamic network flow algorithms. Oper. Res. Lett. 23(3–5):71–80.Crossref, Google Scholar
• Fleischer LK (2001) Faster algorithms for the quickest transshipment problem. SIAM J. Optim. 12(1):18–35.Crossref, Google Scholar
• Ford LR Jr, Fulkerson DR (1958) Constructing maximal dynamic flows from static flows. Oper. Res. 6(3):419–433.Link, Google Scholar
• Gale D (1959) Transient flows in networks. Michigan Math. J. 6(1):59–63.Crossref, Google Scholar
• Hoppe B, Tardos E (2000) The quickest transshipment problem. Math. Oper. Res. 25(1):36–62.Link, Google Scholar
• Jarvis JJ, Ratliff HD (1982) Some equivalent objectives for dynamic network flow problems. Management Sci. 28(1):106–109.Link, Google Scholar
• Kalafatas G, Peeta S (2007) An exact graph structure for dynamic traffic assignment: Formulation, properties, computational experience. Proc. 86th Annual Meeting of the Transportation Res. Board (CD-ROM), Washington, DC.Google Scholar
• Kalafatas G, Peeta S (2008) A direct bridge between dynamic traffic assignment and graph theory. Proc. 10th Internat. Conf. Appl. Adv. Tech. Transportation, Athens, Greece.Google Scholar
• Kalafatas G, Peeta S (2009) A common modeling framework for dynamic traffic assignment and supply chain management systems with congestion phenomena. Lam WHK, Wong SC, Lo HK, eds. Transportation and Traffic Theory 2009: Golden Jubilee—Papers Selected for Presentation at ISTTT 18 (Springer, Hong Kong), 541–558.Crossref, Google Scholar
• Li Y, Waller ST, Ziliaskopoulos T (2003) A decomposition scheme for system optimal dynamic traffic assignment models. Network Spat. Econ. 3(4):441–455.Crossref, Google Scholar
• Lin W-H (2009) Personal communication. Interview by Hong Zheng, May.Google Scholar
• Lin W-H, Ahanotu D (1994) Validating the basic cell transmission model on a single freeway link. Report, Institute of Transportation Studies and Department of Civil Engineering, Berkeley, CA.Google Scholar
• Lin W-H, Lo HK (2000) Are the objective and solutions of dynamic user-equilibrium models always consistent? Transportation Res. Part A: Policy and Practice 34(2):137–144.Crossref, Google Scholar
• Lo HK, Szeto WY (2002) A cell based variational inequality formulation of the dynamic user optimal assignment problem. Transportation Res. Part B: Methodologica 36(1):421–443.Crossref, Google Scholar
• Megiddo N (1979) Combinatorial optimization with rational objective functions. Math. Oper. Res. 4(4):414–424.Link, Google Scholar
• Minieka E (1973) Maximal, lexicographic, and dynamic network flows. Oper. Res. 21(2):517–527.Link, Google Scholar
• Nie X, Zhang HM (2005) Delay-function-based link models: Their properties and computational issues. Transportation Res. Part B: Methodological 39(8):729–751.Crossref, Google Scholar
• Peeta S, Ziliaskopoulos AK (2001) Foundations of dynamic traffic assignment: The past, the present and the future. Network Spat. Econom. 1:233–265.Crossref, Google Scholar
• Perakis G, Roels G (2006) An analytical model for traffic delays and the dynamic user equilibrium problem. Oper. Res. 54(6):1151–1171.Link, Google Scholar
• Philpott AB (1990) Continuous time flows in networks. Math. Oper. Res. 15(4):640–661.Link, Google Scholar
• Richardson D, Tardos E (2002) Cited as personal communication in Fleischer L, Skutella M (2007).Google Scholar
• Shen W (2009) System optimal dynamic traffic assignment: A graph-theoretic approach and its engineering application. Ph.D. thesis, University of California, Davis, Davis.Google Scholar
• Shen W, Zhang HM (2008) What do different traffic flow models mean for system-optimal dynamic traffic assignment in a many-to-one network? Transportation Res. Record 2088:157–166.Crossref, Google Scholar
• Shen W, Nie Y, Zhang HM (2007) Dynamic network simplex method for designing emergency evacuation plans. Transportation Res. Record 2022:83–93.Crossref, Google Scholar
• So SK, Daganzo CF (2010) Managing evacuation routes. Transportation Res. Part B: Methodological 44(4):514–520.Crossref, Google Scholar
• Wilkinson WL (1971) An algorithm for universal maximal dynamic flows in a network. Oper. Res. 19(7):1602–1612.Link, Google Scholar
• Zadeh N (1973) A bad network problem for the simplex method and other minimum cost flow algorithms. Math. Programming 5(1):255–266.Crossref, Google Scholar
• Zhang M, Shen W (2010) Access control policies without inside queues: Their properties and public policy implementations. Transportation Res. Part B: Methodological 44(8–9):1132–1147.Crossref, Google Scholar
• Zheng H (2009) Efficient algorithms for the cell-based single destination system optimal dynamic traffic assignment problem. Ph.D. thesis, University of Arizona, Tucson.Google Scholar
• Zheng H, Chiu Y-C (2011) A network flow algorithm for the cell-based single-destination system optimal dynamic traffic assignment problem. Transportation Sci. 45(1):121–137.Link, Google Scholar
• Zheng H, Chiu Y-C, Mirchandani PB (2013) A heuristic algorithm for the earliest arrival flow with multiple sources. J. Math. Model. Algorithms Oper. Res. 13(2):169–189.Crossref, Google Scholar
• Ziliaskopoulos AK (2000) A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transportation Sci. 34(1):37–49.Link, Google Scholar