Linear programming formulation for strategic dynamic traffic assignment.

*(English)*Zbl 1332.90161Summary: This work introduces a novel formulation of system optimal dynamic traffic assignment that captures strategic route choice in users under demand uncertainty. We define strategic route choice to be that users choose a path prior to knowing the true travel demand which will be experienced (therefore users consider the full set of possible demand scenarios). The problem is formulated based on previous work by A. K. Ziliaskopoulos [Transp. Sci. 34, No. 1, 37–49 (2000; Zbl 1002.90013)]. The resulting novel formulation requires substantial enhancement to account for path-based flows and scenariobased stochastic demands. Further, a numerical demonstration is presented on a network with different demand loading profiles. Finally, model complexity, implications on scalability and future research directions are discussed.

##### Software:

pyuvdata
PDF
BibTeX
XML
Cite

\textit{S. T. Waller} et al., Netw. Spat. Econ. 13, No. 4, 427--443 (2013; Zbl 1332.90161)

Full Text:
DOI

##### References:

[1] | Andreatta, G; Romeo, L, Stochastic shortest paths with recourse, Networks, 18, 193-204, (1988) · Zbl 0659.90085 |

[2] | Asakura Y, Kashiwadani M (1991) Road network reliability caused by daily fluctuation of traffic flow. In: Proceedings of the 19th PTRC Summer Annual Meeting, Brighton, Seminar G, pp 73-84 |

[3] | Boyles S, Waller ST (2007) A stochastic delay prediction model for real-time incident management. ITE Journal 77:18-24 · Zbl 1002.90013 |

[4] | Cantarella, GE; Cascetta, E, Dynamic process and equilibrium in transportation networks: toward a unifying theory, Transp Sci, 29, 305-329, (1995) · Zbl 0855.90054 |

[5] | Carey, M; Subrahmanian, E, An approach to modeling time-varying flows on congested networks, Transp Res, 34B, 157-183, (2000) |

[6] | Chriqui, C; Robillard, P, Common bus line, Transp Sci, 9, 115-121, (1975) |

[7] | Clark SD, Watling DP (2005) Modelling network travel time reliability under stochastic demand. Transp Res B Methodol 39(2):119-140 · Zbl 0771.90045 |

[8] | Daganzo, CF, The cell transmission model: a simple dynamic representation of highway traffic consistent with the hydrodynamic theory, Transp Res, 28B, 269-287, (1994) |

[9] | Daganzo, CF, The cell transmission model, part II: network traffic, Transp Res, 29B, 79-93, (1995) |

[10] | Daganzo, CF; Sheffi, Y, On stochastic models of traffic assignment, Transp Sci, 11, 253-273, (1977) |

[11] | Fan Y, Nie Y (2006) Optimal routing for maximizing the travel time reliability. Netw Spat Econ 6(3-4):333-344 · Zbl 1128.90015 |

[12] | Gao, S; Chabini, I, Optimal routing policy problems in stochastic time dependent networks, Transp Res B Methodol, 40, 93-122, (2006) |

[13] | Hamdouch, Y; Marcotte, P; Nguyen, S, A strategic model for dynamic traffic assignment, Netw Spat Econ, 4, 291-315, (2004) · Zbl 1097.90014 |

[14] | Horowitz, JL, The stability of stochastic equilibrium in a two-link transportation network, Transp Res B, 18, 13-28, (1984) |

[15] | Li, Y; Ziliakopoulos, AK; Waller, ST, Linear programming formulations for system optimum dynamic traffic assignment with arrival time based and departure time based demands, Transp Res Rec, 1667, 52-59, (1999) |

[16] | Li, Y; Waller, ST; Ziliaskopoulos, AK, A decomposition scheme for system optimal dynamic traffic assignment models, Netw Spat Econ, 3, 441-455, (2003) |

[17] | Maher MJ, Hughes PC (1997) A probit-based stochastic user equilibrium assignment model. Transp Res B 31(4) |

[18] | Marcotte P, Nguyen S (1998) Hyperpath formulations of traffic assignment problems. In: Marcotte P, Nguyen S (eds) Equilibrium and advanced transportation modelling. Kluwer Academic Publishers, pp 175-199 · Zbl 0972.90016 |

[19] | Marcotte, P; Nguyen, S; Schoeb, A, A strategic flow model of traffic assignment in static networks, Oper Res, 52, 191-212, (2004) · Zbl 1165.90348 |

[20] | Merchant, DK; Nemhauser, GI, A model and an algorithm for dynamic traffic assignment problems, Transp Sci, 12, 183-199, (1978) |

[21] | Merchant, DK; Nemhauser, GI, Optimality conditions for a dynamic traffic assignment model, Transp Sci, 12, 200-207, (1978) |

[22] | Miller-Hooks, E; Mahmassani, HS, Least expected time paths in stochastic, time-varying transportation networks, Transp Sci, 34, 198-215, (2000) · Zbl 0990.90011 |

[23] | Peeta, S; Ziliaskopoulos, AK, Foundations of dynamic traffic assignment: the past, the present and the future, Netw Spat Econ, 1, 233-265, (2001) |

[24] | Polychronopoulos, GH; Tsitsiklis, JN, Stochastic shortest path problems with recourse, Networks, 27, 133-143, (1996) · Zbl 0851.90129 |

[25] | Psaraftis, HN; Tsitsiklis, JN, Dynamic shortest paths in acyclic networks with Markovian arc costs, Oper Res, 41, 91-101, (1993) · Zbl 0771.90045 |

[26] | Sheffi, Y; Powell, WB, An algorithm for the equilibrium assignment problem with random link times, Networks, 12, 191-207, (1982) · Zbl 0485.90082 |

[27] | Unnikrishnan, A; Waller, ST, User equilibrium with recourse, Netw Spat Econ, 9, 575-593, (2009) · Zbl 1180.90047 |

[28] | Waller, ST; Ziliaskopoulos, AK, On the online shortest path problem with limited arc cost dependencies, Networks, 40, 216-227, (2002) · Zbl 1026.90088 |

[29] | Waller, ST; Ziliaskopoulos, AK, A chance-constrained based stochastic dynamic traffic assignment model: analysis, formulation and solution algorithms, Transp Res C Emerg Technol, 14, 418-427, (2006) |

[30] | Watling, DP, Stability of the stochastic assignment problem: a dynamical systems approach, Transp Res B, 33, 281-312, (1999) |

[31] | Watling, D; Hazelton, ML, The dynamics and equilibria of day-to-day assignment models, Netw Spat Econ, 3, 349-370, (2003) |

[32] | Ziliaskopoulos, AK, A linear programming model for the single destination system optimum dynamic traffic assignment problem, Transp Sci, 34, 37-49, (2000) · Zbl 1002.90013 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.