Arrival time reliability in strategic user equilibrium.

*(English)*Zbl 07258059Summary: Although traffic assignment models remain heavily utilized globally for the planning and evaluation of new transport infrastructure, commonly applied assignment approaches continue to make very restrictive assumptions regarding determinism and perfect system knowledge to achieve regional scalability. Strategic user equilibrium (StrUE) has been previously proposed as a computationally scalable network assignment model which incorporates demand variability and expectation-minimizing traveler behavior. The proposed model extends the StrUE model to account for travel time penalties thereby enhancing the travel behavioral assumptions which are critical for reliability analyses. Under mild assumptions, we show that the path arrival time penalty is additive by link, allowing us to formulate traffic assignment as a convex program. Furthermore, we show that strategic user equilibrium results in expected link travel times that differ significantly from those predicted by user equilibrium. Finally, the expected arrival time penalties are shown to deviate non-uniformly by link, thereby having diverse impacts on traveler route choice.

##### MSC:

90 | Operations research, mathematical programming |

91 | Game theory, economics, finance, and other social and behavioral sciences |

##### Software:

pyuvdata
PDF
BibTeX
XML
Cite

\textit{M. W. Levin} et al., Netw. Spat. Econ. 20, No. 3, 803--831 (2020; Zbl 07258059)

Full Text:
DOI

##### References:

[1] | Asakura Y, Kashiwadani M (1991) Road network reliability caused by daily fluctuation of traffic flow. In: PTRC Summer annual meeting, 19th, 1991, University of Sussex, United Kingdom |

[2] | Bar-Gera, H., Traffic assignment by paired alternative segments, Transport Res B Meth, 44, 8, 1022-1046 (2010) |

[3] | Bar-Gera H (2016). Transportation test problems. online; accessed 4 February 2016. [Online]. Available: http://www.bgu.ac.il/bargera/tntp/ |

[4] | Beckmann M, McGuire C, Winsten CB (1956) Studies in the Economics of Transporta-tion |

[5] | Bell, MG, Measuring network reliability: a game theoretic approach, J Adv Transport, 33, 2, 135-146 (1999) |

[6] | Bell, MG, A game theory approach to measuring the performance reliability of transport networks, Transport Res B Meth, 34, 6, 533-545 (2000) |

[7] | Bliemer, MC; Bovy, PH, Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem, Transport Res B Meth, 37, 6, 501-519 (2003) |

[8] | Boyles, SD; Kockelman, KM; Waller, S., Congestion pricing under operational, supply-side uncertainty, Transport Res Part C Emerg Technol, 18, 4, 519-535 (2010) |

[9] | Castillo, E.; Calviño, A.; Nogal, M.; Lo, HK, On the probabilistic and physical consistency of traffic random variables and models, Comput-Aided Civ Inf, 29, 7, 496-517 (2014) |

[10] | Chen, A.; Zhou, Z., The α-reliable mean-excess traffic equilibrium model with stochastic travel times, Transport Res B Meth, 44, 4, 493-513 (2010) |

[11] | Chen, BY; Lam, W.; Sumalee, A.; Shao, H., An efficient solution algorithm for solving multi-class reliability-based traffic assignment problem, Math Comput Model, 54, 5, 1428-1439 (2011) · Zbl 1228.90024 |

[12] | Chiu Y-C, Bottom J, Mahut M, Paz A, Balakrishna R, Waller T, Hicks J (2011) Dynamic traffic assignment: a primer. Transportation Research E-Circular, no E-C153 |

[13] | Clark, S.; Watling, D., Modelling network travel time reliability under stochastic demand, Transport Res B Meth, 39, 2, 119-140 (2005) |

[14] | Daganzo, CF; Sheffi, Y., On stochastic models of traffic assignment, Transport Sci, 11, 3, 253-274 (1977) |

[15] | Dixit V, Gardner L, Waller S (2013) Strategic user equilibrium assignment under trip variability |

[16] | Duell M (2015). Strategic traffic assignment: models and applications to capture day-to-day flow volatility |

[17] | Duell, M.; Waller, S., Implications of volatility in day-to-day travel flow and road capacity on traffic network design projects, Transport Res Rec, 2498, 56-63 (2015) |

[18] | Duell, M.; Gardner, L.; Dixit, V.; Waller, S., Evaluation of a strategic road pricing scheme accounting for day-to-day and long-term demand uncertainty, Transport Res Rec, 2467, 12-20 (2014) |

[19] | Frank, M.; Wolfe, P., An algorithm for quadratic programming, Naval Res Logist Q, 3, 1-2, 95-110 (1956) |

[20] | Friesz, TL; Bernstein, D.; Smith, TE; Tobin, RL; Wie, B., A variational inequality formulation of the dynamic network user equilibrium problem, Oper Res, 41, 1, 179-191 (1993) · Zbl 0771.90037 |

[21] | Gabriel, SA; Bernstein, D., The traffic equilibrium problem with nonadditive path costs, Transport Sci, 31, 4, 337-348 (1997) · Zbl 0920.90058 |

[22] | Hamdouch, Y.; Marcotte, P.; Nguyen, S., A strategic model for dynamic traffic assignment, Netw Spat Econ, 4, 3, 291-315 (2004) · Zbl 1097.90014 |

[23] | Hazelton, ML, Total travel cost in stochastic assignment models, Netw Spat Econ, 3, 4, 457-466 (2003) |

[24] | Jackson, WB; Jucker, JV, An empirical study of travel time variability and travel choice behavior, Transport Sci, 16, 4, 460-475 (1982) |

[25] | Karush W (1939) Minima of functions of several variables with inequalities as side constraints, Ph.D. dissertation, Master’s thesis, Dept. of Mathematics, Univ. of Chicago |

[26] | Khani A, Boyles SD (2015) An exact algorithm for the mean-standard deviation shortest path problem. Transport Res B Meth |

[27] | Kuhn H, Tucker A (1951) Nonlinear programming. In: 2nd berkeley symposium, Berkeley, University of California Press · Zbl 0044.05903 |

[28] | Lam, W.; Shao, H.; Sumalee, A., Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply, Transport Res B Meth, 42, 10, 890-910 (2008) |

[29] | Li M, Zhou X, Rouphail NM (2011) Quantifying benefits of traffic information provision under stochastic demand and capacity conditions: a multi-day traffic equilibrium approach. In: 2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC). IEEE, pp 2118-2123 |

[30] | Liu, Y.; Nie, Y., Morning commute problem considering route choice, user heterogeneity and alternative system optima, Transport Res B Meth, 45, 4, 619-642 (2011) |

[31] | Lo, HK; Tung, Y-K, Network with degradable links: capacity analysis and design, Transport Res B Meth, 37, 4, 345-363 (2003) |

[32] | Lo, HK; Luo, X.; Siu, BW, Degradable transport network: travel time budget of travelers with heterogeneous risk aversion, Transport Res B Meth, 40, 9, 792-806 (2006) |

[33] | Mirchandani, P.; Soroush, H., Generalized traffic equilibrium with probabilistic travel times and perceptions, Transport Sci, 21, 3, 133-152 (1987) · Zbl 0626.90026 |

[34] | Moylan E, Gardner L, Dixit V (2015) Validation of proportionality assumptions in traffic assignment accounting for day-to-day variability |

[35] | Nakayama, S.; Watling, D., Consistent formulation of network equilibrium with stochastic flows, Transport Res B Meth, 66, 50-69 (2014) |

[36] | Nie, Y., A class of bush-based algorithms for the traffic assignment problem, Transport Res B Meth, 44, 1, 73-89 (2010) |

[37] | Nie, Y., Multi-class percentile user equilibrium with flow-dependent stochasticity, Transport Res B Meth, 45, 10, 1641-1659 (2011) |

[38] | Peeta, S.; Ziliaskopoulos, AK, Foundations of dynamic traffic assignment: the past, the present and the future, Netw Spat Econ, 1, 3-4, 233-265 (2001) |

[39] | Pitombeira-Neto AR, Loureiro CFG, Carvalho LE (2020) A dynamic hierarchical bayesian model for the estimation of day-to-day origin-destination flows in transportation networks. Netw Spat Econ 1-29 |

[40] | Shao H, Lam W, Meng Q, Tam M (2006a) Demand driven travel time reliability-based traffic assignment problem. Transport Res Rec 1985:220-230 |

[41] | Shao H, Lam W, Tam ML (2006b) A reliability-based stochastic traffic assignment model for network with multiple user classes under uncertainty in demand. Netw Spat Econ 6(3-4):173-204 · Zbl 1138.90358 |

[42] | Smith, M.; Wisten, M., A continuous day-to-day traffic assignment model and the existence of a continuous dynamic user equilibrium, Ann Oper Res, 60, 1, 59-79 (1995) · Zbl 0839.90040 |

[43] | Szeto, W.; O’Brien, L.; O’Mahony, M., Risk-averse traffic assignment with elastic demands: Ncp formulation and solution method for assessing performance reliability, Netw Spat Econ, 6, 3-4, 313-332 (2006) · Zbl 1128.90016 |

[44] | Tilahun, NY; Levinson, DM, A moment of time: reliability in route choice using stated preference, J Intell Transport Syst, 14, 3, 179-187 (2010) |

[45] | Unnikrishnan, A.; Waller, S., User equilibrium with recourse, Netw Spat Econ, 9, 4, 575-593 (2009) · Zbl 1180.90047 |

[46] | Vickrey WS (1969) Congestion theory and transport investment |

[47] | Waller, S.; Schofer, J.; Ziliaskopoulos, A., Evaluation with traffic assignment under demand uncertainty, Transport Res Rec, 1771, 69-74 (2001) |

[48] | Waller, S.; Fajardo, D.; Duell, M.; Dixit, V., Linear programming formulation for strategic dynamic traffic assignment, Netw Spat Econ, 13, 4, 427-443 (2013) · Zbl 1332.90161 |

[49] | Wardrop JG (1952) Road paper. some theoretical aspects of road traffic research. In: ICE proceedings: engineering divisions. Thomas Telford, vol 1, pp 325-362 |

[50] | Watling D (2002a) A second order stochastic network equilibrium model, i: Theoretical foundation. Transport Sci 36(2):149-166 · Zbl 1134.90331 |

[51] | Watling D (2002b) A second order stochastic network equilibrium model, ii: Solution method and numerical experiments. Transport Sci 36(2):167-183 · Zbl 1134.90332 |

[52] | Watling, D., User equilibrium traffic network assignment with stochastic travel times and late arrival penalty, Eur J Oper Res, 175, 3, 1539-1556 (2006) · Zbl 1142.90359 |

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

[54] | Wu, X.; Nie, Y., Solving the multiclass percentile user equilibrium traffic assignment problem: a computational study, Transport Res Rec, 2334, 75-83 (2013) |

[55] | Xie, C.; Liu, Z., On the stochastic network equilibrium with heterogeneous choice inertia, Transport Res B Meth, 66, 90-109 (2014) |

[56] | Yin, Y.; Ieda, H., Assessing performance reliability of road networks under nonrecurrent congestion, Transport Res Rec, 1771, 148-155 (2001) |

[57] | Zhao, X.; Wan, C.; Bi, J., Day-to-day assignment models and traffic dynamics under information provision, Netw Spat Econ, 19, 2, 473-502 (2019) |

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.