Abstract
Dynamic Traffic Assignment (DTA) has been studied for more than four decades and numerous reviews of this research area have been conducted. This review focuses on the travel choice principle and the classification of DTA models, and is supplementary to the existing reviews. The implications of the travel choice principle for the existence and uniqueness of DTA solutions are discussed, and the interrelation between the travel choice principle and the traffic flow component is explained using the nonlinear complementarity problem, the variational inequality problem, the mathematical programming problem, and the fixed point problem formulations. This paper also points out that all of the reviewed travel choice principles are extended from those used in static traffic assignment. There are also many classifications of DTA models, in which each classification addresses one aspect of DTA modeling. Finally, some future research directions are identified.
[1] Gomes G., Horowitz R., Optimal freeway ramp metering using the asymmetric cell transmission model, Transport. Res. C-Emer., 2006, 14, 244–262 http://dx.doi.org/10.1016/j.trc.2006.08.00110.1016/j.trc.2006.08.001Search in Google Scholar
[2] Meng Q., Khoo H.L., A Pareto-optimization approach for a fair ramp metering, Transport. Res. C-Emer., 2010, 18, 489–506 http://dx.doi.org/10.1016/j.trc.2009.10.00110.1016/j.trc.2009.10.001Search in Google Scholar
[3] Park B.B., Yun I., Ahn K., Stochastic optimization for sustainable traffic signal control, Int. J. Sustain. Transp., 2009, 3, 263–284 http://dx.doi.org/10.1080/1556831080209105310.1080/15568310802091053Search in Google Scholar
[4] Park B.B., Kamarajugadda A., Development and evaluation of a stochastic traffic signal optimization method, Int. J. Sustain. Transp., 2007, 1, 193–207 http://dx.doi.org/10.1080/1556831060073756810.1080/15568310600737568Search in Google Scholar
[5] Lo H.K., Szeto W.Y., Modeling advanced traveler information services: static versus dynamic paradigms, Transport. Res. B-Meth., 2004, 38, 495–515 http://dx.doi.org/10.1016/j.trb.2003.06.00110.1016/j.trb.2003.06.001Search in Google Scholar
[6] Szeto W.Y., Lo H.K., The impact of advanced traveler information services on travel time and schedule delay costs, J. Intell. Transport. S., 2005, 9, 47–55 http://dx.doi.org/10.1080/1547245059091684010.1080/15472450590916840Search in Google Scholar
[7] Lo H.K., Szeto W.Y., Road pricing modeling for hypercongestion, Transport. Res. A-Pol., 2005, 39, 705–722 10.1016/j.tra.2005.02.019Search in Google Scholar
[8] Zhong R.X., Sumalee A., Maruyama T., Dynamic marginal cost, access control, and pollution charge: a comparison of bottleneck and whole link models, J. Adv. Transport., 2011, Accepted 10.1002/atr.195Search in Google Scholar
[9] Ukkusuri S., Waller S., Linear programming models for the user and system optimal dynamic network design problem: formulations, comparisons and extensions, Netw. Spat. Econ., 2008, 8, 383–406 http://dx.doi.org/10.1007/s11067-007-9019-610.1007/s11067-007-9019-6Search in Google Scholar
[10] Szeto W.Y., Ghosh, B., Basu, B., O’Mahony M., Cell-based short-term traffic flow forecasting using time series modelling, Transport. Eng.-J. Asce., 2009, 135, 658–667 http://dx.doi.org/10.1061/(ASCE)0733-947X(2009)135:9(658)10.1061/(ASCE)0733-947X(2009)135:9(658)Search in Google Scholar
[11] Abdelghany A.F., Adbelghany K.F., Mahmassani H.S., Murray P.M., Dynamic traffic assignment in design and evaluation of high-occupancy toll lanes, Transport. Res. Rec., 2000, 1733, 39–48 http://dx.doi.org/10.3141/1733-0610.3141/1733-06Search in Google Scholar
[12] Yagar S., Dynamic traffic assignment by individual path minimization and queuing, Transport. Res., 1971, 5, 179–196 http://dx.doi.org/10.1016/0041-1647(71)90020-710.1016/0041-1647(71)90020-7Search in Google Scholar
[13] Cascetta E., Cantarella G.E., Modelling dynamics in transportation networks: state of the art and future developments, Simulat. Pract. Theory., 1993, 15, 65–91 http://dx.doi.org/10.1016/0928-4869(93)90017-K10.1016/0928-4869(93)90017-KSearch in Google Scholar
[14] Peeta S., Ziliaskopoulos A.K., Foundations of dynamic traffic assignment: the past, the present and the future, Netw. Spat. Econ., 2001, 1, 233–265 http://dx.doi.org/10.1023/A:101282772485610.1023/A:1012827724856Search in Google Scholar
[15] Boyce D., Lee D.H., Ran B., Analytical models of the dynamic traffic assignment problem, Netw. Spat. Econ., 2001, 1, 377–390 http://dx.doi.org/10.1023/A:101285241346910.1023/A:1012852413469Search in Google Scholar
[16] Szeto W.Y., Lo H.K., Dynamic traffic assignment: review and future, Information Technology, 2005, 5, 85–100 Search in Google Scholar
[17] Szeto W.Y., Lo H.K., Properties of dynamic traffic assignment with physical queues, J. East Asia Soc. Transport. Stud., 2005, 6, 2108–2123 Search in Google Scholar
[18] Mun J.S., Traffic performance models for dynamic traffic assignment: an assessment of existing models, Transport. Rev., 2007, 27, 231–249 http://dx.doi.org/10.1080/0144164060097940310.1080/01441640600979403Search in Google Scholar
[19] Jeihani M., A review of dynamic traffic assignment computer packages, J. Transport. Res. Forum, 2007, 46, 35–46 Search in Google Scholar
[20] Szeto W.Y., Cell-based dynamic equilibrium models, dynamic traffic assignment and signal control, in: Dynamic route guidance and traffic control, complex social, Economic and Engineered Networks Series, Ukkusuri S., Ozbay K. (Eds.), Springer, 2011, submitted Search in Google Scholar
[21] Wardrop J., Some theoretical aspects of road traffic research, ICE Proceedings: Part II, Engineering Divisions, 1952, 1, 325–362 http://dx.doi.org/10.1680/ipeds.1952.1125910.1680/ipeds.1952.11259Search in Google Scholar
[22] Oppenheim N., Urban travel demand modelling: from individual choice to general equilibrium, John Wiley & Sons, USA, 1995 Search in Google Scholar
[23] Daganzo C.F., Sheffi Y., On stochastic models of traffic assignment, Transport. Sci., 1977, 11, 253–274 http://dx.doi.org/10.1287/trsc.11.3.25310.1287/trsc.11.3.253Search in Google Scholar
[24] Hall R.W., Travel outcome and performance: the effect of uncertainty on accessibility, Transport. Res. BMeth., 1993, 17, 275–290 http://dx.doi.org/10.1016/0191-2615(83)90046-210.1016/0191-2615(83)90046-2Search in Google Scholar
[25] Lo H.K., Luo X.W., Siu B.W.Y., Degradable transport network: travel time budget of travellers with heterogeneous risk aversion, Transport. Res. B-Meth., 2006, 40, 792–806 http://dx.doi.org/10.1016/j.trb.2005.10.00310.1016/j.trb.2005.10.003Search in Google Scholar
[26] Uchida T., Iida Y., Risk assignment: a new traffic assignment model considering the risk travel time variation, In: Daganzo C.F. (Ed.), Proceedings of the 12th International Symposium on Transportation and Traffic Theory (July 21–23, 1993, Berkeley, CA, USA), Elsevier, Amsterdam, 1993, 89–105 Search in Google Scholar
[27] Jackson W.B., Jucker J.V., An empirical study of travel time variability and travel choice behavior, Transport. Sci., 1982, 16, 460–475 http://dx.doi.org/10.1287/trsc.16.4.46010.1287/trsc.16.4.460Search in Google Scholar
[28] Brastow W.C., Jucker J.V., Use of a mean variance criterion for traffic assignment, unpublished manuscript, Department of Industrial Engineering, Stanford University, 1977 Search in Google Scholar
[29] Szeto W.Y., Solayappan M., Jiang Y., Reliabilitybased transit assignment for congested stochastic transit networks, Comput.-Aided Civ. Inf., 2011, 26, 311–326 http://dx.doi.org/10.1111/j.1467-8667.2010.00680.x10.1111/j.1467-8667.2010.00680.xSearch in Google Scholar
[30] Chen A., Zhou Z., The α-reliable mean-excess traffic equilibrium model with stochastic travel times, Transport. Res. B-Meth., 2010, 44, 493–513 http://dx.doi.org/10.1016/j.trb.2009.11.00310.1016/j.trb.2009.11.003Search in Google Scholar
[31] Franklin J.P., Karlstrom A., Travel time reliability for Stockholm roadways: modeling the mean lateness factor, Transport. Res. Rec., 2009, 2134, 106–113 http://dx.doi.org/10.3141/2134-1310.3141/2134-13Search in Google Scholar
[32] Chan K.S., Lam W.H.K., Impact of road pricing on the road network reliability, J. East Asia Soc. Transport. Stud., 2005, 6, 2060–2075 Search in Google Scholar
[33] Ordóñez F., Stier-Moses N.E., Wardrop equilibria with risk-averse users, Transport. Sci., 2010, 44, 63–86 http://dx.doi.org/10.1287/trsc.1090.029210.1287/trsc.1090.0292Search in Google Scholar
[34] Lam T., Small K., The value of time and reliability: measurement from a value pricing experiment, Transport. Res. E-Log., 2001, 37, 231–251 http://dx.doi.org/10.1016/S1366-5545(00)00016-810.1016/S1366-5545(00)00016-8Search in Google Scholar
[35] Bell M.G.H., Cassir C., Risk-averse user equilibrium traffic assignment: an application of game theory, Transport. Res. B-Meth., 2002, 36, 671–681 http://dx.doi.org/10.1016/S0191-2615(01)00022-410.1016/S0191-2615(01)00022-4Search in Google Scholar
[36] Szeto W.Y., O’Brien L., O’Mahony M., Generalisation of the risk-averse traffic assignment, In: Bell M.G.H., Heydecker B.G., Allsop R.E. (Eds.), Proceedings of 17th International Symposium on Transportation and Traffic Theory (July 23–25, 2007, London, UK), Emerald Group Publishing Limited, 2007, 127–153 Search in Google Scholar
[37] Szeto W.Y., O’Brien L., O’Mahony M., Measuring network reliability by considering paradoxes: the multiple network demon approach, Transport. Res. Rec., 2009, 2090, 42–50 http://dx.doi.org/10.3141/2090-0510.3141/2090-05Search in Google Scholar
[38] Szeto W.Y., Cooperative game approaches to measuring network reliability considering paradoxes, Transport. Res. C-Emer., 2011, 11, 229–241 http://dx.doi.org/10.1016/j.trc.2010.05.01010.1016/j.trc.2010.05.010Search in Google Scholar
[39] Szeto W.Y., O’Brien L., O’Mahony M., Risk-averse traffic assignment with elastic demand: NCP formulation and solution method for assessing performance reliability, Netw. Spat. Econ., 2006, 6, 313–332 http://dx.doi.org/10.1007/s11067-006-9286-710.1007/s11067-006-9286-7Search in Google Scholar
[40] Ordóñez F., Stier-Moses N.E., Robust Wardrop equilibrium, Netw. Control. Optim., 2007, 4465, 247–256 http://dx.doi.org/10.1007/978-3-540-72709-5_2610.1007/978-3-540-72709-5_26Search in Google Scholar
[41] Zhang C., Chen X., Sumalee A., Robust Wardrop’s user equilibrium assignment under stochastic demand and supply: expected residual minimization approach, Transport. Res. B-Meth., 2011, 45, 534–552 http://dx.doi.org/10.1016/j.trb.2010.09.00810.1016/j.trb.2010.09.008Search in Google Scholar
[42] Tversky A., Kahneman D., Advances in prospect theory: cumulative representation of uncertainty, J. Risk Uncertainty, 1992, 5, 297–323 http://dx.doi.org/10.1007/BF0012257410.1007/BF00122574Search in Google Scholar
[43] Kahneman D., Tversky A., Prospect theory: an analysis of decisions under risk, Econometrica, 1979, 47, 263–291 http://dx.doi.org/10.2307/191418510.2307/1914185Search in Google Scholar
[44] Thaler R.H., Tversky A., Kahneman D., Schwartz A., The effect of myopia and loss aversion on risk taking: an experimental test, Quart. J. Econ., 1997, 112, 647–661 http://dx.doi.org/10.1162/00335539755522610.1162/003355397555226Search in Google Scholar
[45] Camerer C.F., Ho T.H., Violations of the betweenness axiom and nonlinearity in probability, J. Risk Uncertainty., 1994, 8, 167–196 http://dx.doi.org/10.1007/BF0106537110.1007/BF01065371Search in Google Scholar
[46] Avineri E., Prashker J.N., Violations of expected utility theory in route-choice stated preferences: certainty effect and inflating of small probabilities, Transport. Res. Rec., 2004, 1894, 222–229 http://dx.doi.org/10.3141/1894-2310.3141/1894-23Search in Google Scholar
[47] Avineri E., The effect of reference point on stochastic network equilibrium, Transport. Sci., 2006, 40, 409–420 http://dx.doi.org/10.1287/trsc.1060.015810.1287/trsc.1060.0158Search in Google Scholar
[48] Mirchandani P., Soroush H., Generalized traffic equilibrium with probabilistic travel times and perceptions, Transport. Sci., 1987, 21, 133–152 http://dx.doi.org/10.1287/trsc.21.3.13310.1287/trsc.21.3.133Search in Google Scholar
[49] Shao H., Lam W.H.K., Tam M.L., A reliability-based stochastic traffic assignment model for network with multiple user classes under uncertainty in demand, Netw. Spat. Econ., 2006, 6, 173–204 http://dx.doi.org/10.1007/s11067-006-9279-610.1007/s11067-006-9279-6Search in Google Scholar
[50] Chen A., Zhou Z., A stochastic α-reliable mean-excess traffic equilibrium model with probabilistic travel times and perception errors, In: Lam W.H.K., Wong S.C., Lo H.K. (Eds.), Proceedings of 18th International Symposium on Transportation and Traffic Theory 2009: Golden Jubilee (July 16–18, 2009), Springer, 2009, 117–145 Search in Google Scholar
[51] Chu Y.L., Work departure time analysis using dogit ordered generalized extreme value model, Transport. Res. Rec., 2009, 2132, 42–49 http://dx.doi.org/10.3141/2132-0510.3141/2132-05Search in Google Scholar
[52] Jou R.C., Kitamura R., Weng M.C., Chen C.C., Dynamic commuter departure time choice under uncertainty, Transport. Res. A-Pol., 2008, 42, 774–783 10.1016/j.tra.2008.01.017Search in Google Scholar
[53] Lemp J.D., Kockelman K.M., Empirical investigation of continuous logit for departure time choice with Bayesian methods, Transport. Res. Rec., 2010, 2165, 59–68 http://dx.doi.org/10.3141/2165-0710.3141/2165-07Search in Google Scholar
[54] Lemp J.D., Kockelman K.M., Damien P., The continuous cross-nested logit model: Formulation and application for departure time choice, Transport. Res. B-Meth., 2010, 44, 646–661 http://dx.doi.org/10.1016/j.trb.2010.03.00110.1016/j.trb.2010.03.001Search in Google Scholar
[55] Friesz T.L., Luque F.J., Tobin R.L., Wie B.W., Dynamic network traffic assignment considered as a continuous time optimal control problem, Oper. Res., 1989, 37, 893–901 http://dx.doi.org/10.1287/opre.37.6.89310.1287/opre.37.6.893Search in Google Scholar
[56] Vickrey W.S., Congestion theory and transport investment, Am. Econ. Rev., 1969, 59, 251–261 Search in Google Scholar
[57] Mahmassani H.S., Herman R., Dynamic user equilibrium departure time and route choice on an idealized traffic arterials, Transport. Sci., 1984, 18, 362–384 http://dx.doi.org/10.1287/trsc.18.4.36210.1287/trsc.18.4.362Search in Google Scholar
[58] Merchant D.K., Nemhauser G.L., A model and an algorithm for the dynamic traffic assignment problem, Transport. Sci., 1978, 12, 183–199 http://dx.doi.org/10.1287/trsc.12.3.18310.1287/trsc.12.3.183Search in Google Scholar
[59] Small, K.A., The scheduling of consumer activities: work trips, Am. Econ. Rev., 1982, 72, 467–479 Search in Google Scholar
[60] Ran B., Boyce D.E., Modelling dynamic transportation networks: an intelligent transportation system oriented approach, 2nd rev. ed., Springer, Berlin, 1996 10.1007/978-3-642-80230-0_14Search in Google Scholar
[61] Vythoulkas P.C., Two models for predicting dynamic stochastic equilibria in urban transportation networks, In: Koshi M. (Ed.), Proceedings of 11th International Symposium on Transportation and Traffic Theory (July 18–20, Yokohama, Japan), Elsevier, 1990, 253–272 Search in Google Scholar
[62] Boyce D.E., Ran B., Li I.Y., Considering travellers’ risk-taking behavior in dynamic traffic assignment, in: Bell M.G.H., Transportation networks: recent methodological advances, Elsevier, Oxford, 1999 Search in Google Scholar
[63] Szeto W.Y., Jiang Y, Sumalee A., A cell-based model for multi-class doubly stochastic dynamic traffic assignment, Comput-Aided Civ. Inf., 2011, 26, 595–611 http://dx.doi.org/10.1111/j.1467-8667.2011.00717.x10.1111/j.1467-8667.2011.00717.xSearch in Google Scholar
[64] Simon H.A., Models of bounded rationality (Vol. 3), The MIT Press, Cambridge, 1997 10.7551/mitpress/4711.001.0001Search in Google Scholar
[65] Simon H.A., A behavioral model of rational choice, Quart. J. Econ., 1955, 69, 99–118 http://dx.doi.org/10.2307/188485210.2307/1884852Search in Google Scholar
[66] Simon H.A., Models of Man, Wiley, New York, 1957 10.2307/2550441Search in Google Scholar
[67] Mahmassani H.S., Chang G.L., On boundedly-rational user equilibrium in transportation systems, Transport. Sci., 1987, 21, 89–99 http://dx.doi.org/10.1287/trsc.21.2.8910.1287/trsc.21.2.89Search in Google Scholar
[68] Szeto W.Y., Lo H.K., Dynamic traffic assignment: properties and extensions, Transportmetrica, 2006, 2, 31–52 http://dx.doi.org/10.1080/1812860060868565410.1080/18128600608685654Search in Google Scholar
[69] Lou Y., Yin Y., Lawphongpanich S., Robust congestion pricing under boundedly rational user equilibrium, Transport. Res. B-Meth., 2010, 44, 15–28 http://dx.doi.org/10.1016/j.trb.2009.06.00410.1016/j.trb.2009.06.004Search in Google Scholar
[70] zeto W.Y., Lo H.K., A cell-based simultaneous route and departure time choice model with elastic demand, Transport. Res. B-Meth., 2004, 38, 593–612 http://dx.doi.org/10.1016/j.trb.2003.05.00110.1016/j.trb.2003.05.001Search in Google Scholar
[71] Pel A.J., Bliemer M.C.J., Hoogendoorn S.P., Hybrid route choice modeling in dynamic traffic assignment, Transport. Res. Rec., 2009, 2091, 100–107 http://dx.doi.org/10.3141/2091-1110.3141/2091-11Search in Google Scholar
[72] Kuwahara M., Akamatsu T., Decomposition of the reactive assignments with queues for many-to-many origin-destination pattern, Transport. Res. B-Meth., 1997, 31, 1–10 http://dx.doi.org/10.1016/S0191-2615(96)00020-310.1016/S0191-2615(96)00020-3Search in Google Scholar
[73] Ben-akiva M., De Palma A., Kaysi, I., Dynamic network models and driver information system, Transport. Res. A-Pol., 1991, 25, 251–266 http://dx.doi.org/10.1016/0191-2607(91)90142-D10.1016/0191-2607(91)90142-DSearch in Google Scholar
[74] Sumalee A., Zhong, R.X., Pan, T.L., Szeto, W.Y., Stochastic cell transmission model (SCTM): a stochastic dynamic traffic model for traffic state surveillance and assignment, Transport. Res. B-Meth., 2011, 45, 507–533 http://dx.doi.org/10.1016/j.trb.2010.09.00610.1016/j.trb.2010.09.006Search in Google Scholar
[75] Lo H.K., Szeto W.Y., A cell-based dynamic traffic assignment model: formulation and properties, Math. Comput. Model., 2002, 35, 849–865 http://dx.doi.org/10.1016/S0895-7177(02)00055-910.1016/S0895-7177(02)00055-9Search in Google Scholar
[76] Tong C.O., Wong S.C., A predictive dynamic traffic assignment model in congested capacity-constrained road networks, Transport. Res. B-Meth., 2000, 34, 625–644 http://dx.doi.org/10.1016/S0191-2615(99)00045-410.1016/S0191-2615(99)00045-4Search in Google Scholar
[77] Horowitz J.L., The stability of stochastic equilibrium in a two-link transportation network, Transport. Res. B-Meth., 1984, 18, 13–28 http://dx.doi.org/10.1016/0191-2615(84)90003-110.1016/0191-2615(84)90003-1Search in Google Scholar
[78] Cascetta E., A stochastic process approach to the analysis of temporal dynamics in transportation networks, Transport. Res. B-Meth., 1989, 23, 1–17 http://dx.doi.org/10.1016/0191-2615(89)90019-210.1016/0191-2615(89)90019-2Search in Google Scholar
[79] Chang G.L., Mahmassani H., Travel time prediction and departure time adjustment behavior dynamics in a congested traffic system, Transport. Res. B-Meth., 1988, 22, 217–232 http://dx.doi.org/10.1016/0191-2615(88)90017-310.1016/0191-2615(88)90017-3Search in Google Scholar
[80] Lam W.H.K., Huang H.J., Dynamic user optimal traffic assignment model for many to one travel demand, Transport. Res. B-Meth., 1995, 29, 243–259 http://dx.doi.org/10.1016/0191-2615(95)00001-T10.1016/0191-2615(95)00001-TSearch in Google Scholar
[81] Ran B., Boyce D., A link-based variational inequality formulation of ideal dynamic user-optimal route choice problem, Transport. Res. C-Emer., 1996, 4, 1–12 http://dx.doi.org/10.1016/0968-090X(95)00017-D10.1016/0968-090X(95)00017-DSearch in Google Scholar
[82] Carey M., Optimal time-varying flows on congested network, Oper. Res., 1987, 35, 58–69 http://dx.doi.org/10.1287/opre.35.1.5810.1287/opre.35.1.58Search in Google Scholar
[83] Carey M., Srinivasan A., Congested network flows: time-varying demands and start-time policies, Eur. J. Oper. Res., 1988, 36, 227–240 http://dx.doi.org/10.1016/0377-2217(88)90429-810.1016/0377-2217(88)90429-8Search in Google Scholar
[84] Lo H.K., Szeto W.Y., A cell-based variational inequality formulation of the dynamic user optimal assignment problem, Transport. Res. B-Meth., 2002, 36, 421–443 http://dx.doi.org/10.1016/S0191-2615(01)00011-X10.1016/S0191-2615(01)00011-XSearch in Google Scholar
[85] Szeto W.Y., The enhanced lagged cell transmission model for dynamic traffic assignment, Transport. Res. Rec., 2008, 2085, 76–85 http://dx.doi.org/10.3141/2085-0910.3141/2085-09Search in Google Scholar
[86] Lo H.K., Ran B., Hongola B., Multiclass dynamic traffic assignment model: formulation and computational experiences, Transport. Res. Rec., 1996, 1537, 74–82 http://dx.doi.org/10.3141/1537-1110.1177/0361198196153700111Search in Google Scholar
[87] Liu Y.H., Mahmassani H.S., Dynamic aspects of commuter decisions under advanced traveler information systems — modeling framework and experimental results, Transport. Res. Rec., 1998, 1645, 111–119 http://dx.doi.org/10.3141/1645-1410.3141/1645-14Search in Google Scholar
[88] Ben-Akiva M., Cuneo D., Hasan M., Jha M., et al., Evaluation of freeway control using a microscopic simulation laboratory, Transport. Res. C-Emer., 2003, 11, 29–50 http://dx.doi.org/10.1016/S0968-090X(02)00020-710.1016/S0968-090X(02)00020-7Search in Google Scholar
[89] Jiang Y.Q., Wong S.C., Ho H.W., Zhang P., et al., A dynamic traffic assignment model for a continuum transportation system, Transport. Res. B-Meth., 2011, 45, 343–363 http://dx.doi.org/10.1016/j.trb.2010.07.00310.1016/j.trb.2010.07.003Search in Google Scholar
[90] Hughes R.L., A continuum theory for the flow of pedestrians, Transport. Res. B-Meth., 2002, 36, 507–535 http://dx.doi.org/10.1016/S0191-2615(01)00015-710.1016/S0191-2615(01)00015-7Search in Google Scholar
[91] Hoogendoorn S.P., Bovy P.H.L., Dynamic useroptimal assignment in continuous time and space, Transport. Res. B-Meth., 2004, 38, 571–592 http://dx.doi.org/10.1016/j.trb.2002.12.00110.1016/j.trb.2002.12.001Search in Google Scholar
[92] Hoogendoorn S.P., Bovy P.H.L., Pedestrian routechoice and activity scheduling theory and models, Transport. Res. B-Meth., 2004, 38, 169–190 http://dx.doi.org/10.1016/S0191-2615(03)00007-910.1016/S0191-2615(03)00007-9Search in Google Scholar
[93] Xia Y., Wong S.C., Zhang M., Shu C.W., et al., An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model, Int. J. Numer. Meth. Eng., 2008, 76, 337–350 http://dx.doi.org/10.1002/nme.232910.1002/nme.2329Search in Google Scholar
[94] Huang L., Wong S.C., Zhang M.P., Shu C.W., et al., Revisiting Hughes’ dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm. Transport. Res. B-Meth., 2009, 43, 127–141 http://dx.doi.org/10.1016/j.trb.2008.06.00310.1016/j.trb.2008.06.003Search in Google Scholar
[95] Huang L., Xia Y., Wong S.C., Shu C.W., et al., Dynamic continuum model for bi-directional pedestrian flows, P. I. Civil Eng.: Eng. Comput. Mec., 2009, 162, 67–75 10.1680/eacm.2009.162.2.67Search in Google Scholar
[96] Xia Y., Wong S.C., Shu C.W., Dynamic continuum pedestrian flow model with memory effect, Phys. Rev. E, 2009, 79, 066113 http://dx.doi.org/10.1103/PhysRevE.79.06611310.1103/PhysRevE.79.066113Search in Google Scholar
[97] Jiang Y.Q., Xiong T., Wong S.C., Shu C.W., et al., A reactive dynamic continuum user equilibrium model for bi-directional pedestrian flows, Acta. Math. Sci., 2009, 29, 1541–1555 10.1016/S0252-9602(10)60002-1Search in Google Scholar
[98] Guo R.Y., Huang H.J., Wong S.C., Collection, spillback, and dissipation in pedestrian evacuation: a network-based method, Transport. Res. B-Meth., 2011, 45, 490–506 http://dx.doi.org/10.1016/j.trb.2010.09.00910.1016/j.trb.2010.09.009Search in Google Scholar
[99] Xiong T., Zhang M., Shu C.W., Wong S.C., et al., Highorder computational scheme for a dynamic continuum model for bi-directional pedestrian flows, Comput.—Aided Civ. Inf., 2011, 26, 298–310 http://dx.doi.org/10.1111/j.1467-8667.2010.00688.x10.1111/j.1467-8667.2010.00688.xSearch in Google Scholar
[100] Nagurney A., Network economics: a variational inequality approach, Kluwer Academic Publishers, Norwell, Massachusetts, 1993 http://dx.doi.org/10.1007/978-94-011-2178-110.1007/978-94-011-2178-1Search in Google Scholar
[101] Chow A.H.F., Properties of system optimal traffic assignment with departure time choice and its solution method, Transport. Res. B-Meth., 2009, 43, 325–344 http://dx.doi.org/10.1016/j.trb.2008.07.00610.1016/j.trb.2008.07.006Search in Google Scholar
[102] Chow A.H.F., Dynamic system optimal traffic assignment — a state-dependent control theoretic approach, Transportmetrica, 2009, 5, 85–106 http://dx.doi.org/10.1080/1812860090271748310.1080/18128600902717483Search in Google Scholar
[103] Long J.C., Szeto W.Y., Gao Z.Y., Discretised link travel time models based on cumulative flows: formulations and properties, Transport. Res. B-Meth., 2011, 45, 232–254 http://dx.doi.org/10.1016/j.trb.2010.05.00210.1016/j.trb.2010.05.002Search in Google Scholar
© 2011 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.