zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Alternative formulations of a combined trip generation, trip distribution, modal split, and trip assignment model. (English) Zbl 1163.90380
Summary: The traditional four-step model has been widely used in travel demand forecasting by considering trip generation, trip distribution, modal split and traffic assignment sequentially in a fixed order. However, this sequential approach suffers from the inconsistency among the level-of-service and flow values in each step of the procedure. In the last two decades, this problem has been addressed by many researchers who have sought to develop combined (or integrated) models that can consider travelers’ choice on different stages simultaneously and give consistent results. In this paper, alternative formulations, including mathematical programming (MP) formulation and variational inequality (VI) formulations, are provided for a combined travel demand model that integrates trip generation, trip distribution, modal split, and traffic assignment using the random utility theory framework. Thus, the proposed alternative formulations not only allow a systematic and consistent treatment of travel choice over different dimensions but also have behavioral richness. Qualitative properties of the formulations are also given to ensure the existence and uniqueness of the solution. Particularly, the model is analyzed for a special but useful case where the probabilistic travel choices are assumed to be a hierarchical logit model. Furthermore, a self-adaptive Goldstein-Levitin-Polyak (GLP) projection algorithm is adopted for solving this special case.
90B06Transportation, logistics
[1]Ahn, B.-H., 1978. Computation of Market Equilibria for Policy Analysis: The Project Independence Evaluation System Approach, Ph.D. Dissertation, Department of Engineering-Economic Systems, Stanford University.
[2]Bar-Gera, H.; Boyce, D.: Origin-based algorithms for combined travel forecasting models, Transportation research part B 37, 403-422 (2003)
[3]Bar-Gera, H.; Boyce, D.: Solving a non-convex combined travel forecasting model by the method of successive averages with constant step sizes, Transportation research part B 40, No. 5, 351-367 (2006)
[4]Beckmann, M. J.; Mcguire, C. B.; Winsten, C. B.: Studies in the economics of transportation, (1956)
[5]Ben-Akiva, M., Lerman, S.R., 1978. Disaggregate travel and mobility-choice models and measures of accessibility. In: Proceedings of the Third International Conference on Behavioural Travel Modelling, pp. 654 – 679.
[6]Bertsekas, D. R.: On the goldstein – levitin – Polyak gradient projection method, IEEE transactions on automatic control 21, 174-184 (1976) · Zbl 0326.49025 · doi:10.1109/TAC.1976.1101194
[7]Boyce, D. E.: Is the sequential travel forecasting procedure counterproductive?, ASCE journal of urban planning and development 128, 169-183 (2002)
[8]Boyce, D. E.: Forecasting travel on congested urban transportation networks: review and prospects for network equilibrium models, Networks and spatial economics 7, No. 2, 99-128 (2007) · Zbl 1144.90320 · doi:10.1007/s11067-006-9009-0
[9]Boyce, D.; Bar-Gera, H.: Network equilibrium models of travel choices with multiple classes, Regional science in economic analysis, 85-98 (2001)
[10]Boyce, D.; Bar-Gera, H.: Multiclass combined models for urban travel forecasting, Network and spatial economics 4, 115-124 (2004) · Zbl 1079.90017 · doi:10.1023/B:NETS.0000015659.39216.83
[11]Boyce, D. E.; Daskin, M. S.: Urban transportation, Design and operation of civil and environmental engineering systems (1997)
[12]Boyce, D.; Xiong, C.: Forecasting travel for very large cities: challenges and opportunities for China, Transportmetrica 3, 1-19 (2007)
[13]Boyce, D.; Chon, K. S.; Lee, Y. J.; Lin, K. T.; Leblanc, L. J.: Implementation and evaluation of combined models of location, destination, mode and route choice, Environment and planning A 15, 1219-1230 (1983)
[14]Boyce, D. E.; Leblanc, L. J.; Chon, K. S.: Network equilibrium models of urban location and travel choices: A retrospective survey, Journal of regional science 28, 159-183 (1988)
[15]Chen, A.; Lo, H. K.; Yang, H.: A self-adaptive projection and contraction algorithm for the traffic assignment problem with path-specific costs, European journal of operational research 135, 27-41 (2001) · Zbl 1077.90516 · doi:10.1016/S0377-2217(00)00287-3
[16]Chen, A.; Lee, D. H.; Jayakrishnan, R.: Computational study of state-of-the-art path-based traffic assignment algorithms, Mathematics and computers in simulation 59, 509-518 (2002) · Zbl 1030.90012 · doi:10.1016/S0378-4754(01)00437-2
[17]Dafermos, S. C.: Relaxation algorithm for the general asymmetric traffic equilibrium problem, Transportation science 16, No. 2, 231-240 (1982)
[18]Daganzo, C. F.: Multinomial probit: the theory and its application to demand forecasting, (1979) · Zbl 0476.62090
[19]Daganzo, C. F.: Unconstrained extremal formulation of some transportation equilibrium problems, Transportation science 16, 332-360 (1982)
[20]Daganzo, C. F.; Kusnic, M.: Two properties of the nested logit model, Transportation science 27, 395-400 (1993) · Zbl 0800.90217 · doi:10.1287/trsc.27.4.395
[21]Daganzo, C. F.; Sheffi, Y.: On stochastic models of traffic assignment, Transportation science 11, 253-274 (1977)
[22]de Cea, J., Fernandez, J.E., 2001. ESTRAUS: A simultaneous equilibrium model to analyze and evaluate multimodal urban transportation systems with multiple user classes. In: Proceedings of the Ninth World Conference on Transport Research, Seoul, Korea.
[23]de Cea, J., Fernandez, J.E., Dekock, V. Soto, A., Friesz, T.L., 2003. ESTRAUS: A computer package for solving supply-demand equilibrium problems on multimodal urban transportation networks with multiple user classes. In: Presented at the Annual Meeting of the Transportation Research Board, Washington, DC.
[24]Evans, S.: Derivation and analysis of some models for combining trip distribution and assignment, Transportation research 9, 241-246 (1976)
[25]Facchinei, F.; Pang, J. S.: Finite-dimensional variational inequalities and complementarity problems, (2003)
[26]Florian, M.: A traffic equilibrium model of travel by car and public transit modes, Transportation science 11, 166-179 (1977)
[27]Florian, M.; Nguyen, S.: A combined trip distribution modal split and assignment model, Transportation research 12, 241-246 (1978)
[28]Florian, M.; Spiess, H.: The convergence of diagonalization algorithms for asymmetric network equilibrium problems, Transportation research part B 16, No. 6, 447-483 (1982)
[29]Florian, M.; Nguyen, S.; Ferland, J.: On the combined distribution-assignment of traffic, Transportation science 9, 43-53 (1975)
[30]Florian, M.; Wu, J. H.; He, S. G.: A multi-class multi-mode variable demand network equilibrium model with hierarchical logit structures, Transportation and network analysis: current trends miscellaneous in honor of michael florian (2002)
[31]Gabriel, S.; Bernstein, D.: The traffic equilibrium problem with nonadditive path costs, Transportation science 31, No. 4, 337-348 (1997) · Zbl 0920.90058 · doi:10.1287/trsc.31.4.337
[32]García, R.; Marín, A.: Network equilibrium models with combined modes: models a and solution algorithms, Transportation research part B 39, 223-254 (2005)
[33]Garret, M.; Wachs, M.: Transportation planning on trial, (1996)
[34]Goldstein, A. A.: Convex programming in Hilbert space, Bulletin of the American mathematical society 70, 709-710 (1964) · Zbl 0142.17101 · doi:10.1090/S0002-9904-1964-11178-2
[35]Han, D. R.; Sun, W.: A new modified goldstein – levitin – Polyak projection method for variational inequality problems, Computers & mathematics with applications 47, No. 12, 1817-1825 (2004) · Zbl 1057.49011 · doi:10.1016/j.camwa.2003.12.002
[36]Harker, P. T.; Pang, J. S.: Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms, and applications, Mathematical programming 48, 161-220 (1988) · Zbl 0734.90098 · doi:10.1007/BF01582255
[37]Hasan, M. K.; Dashti, H. M.: A multiclass simultaneous transportation equilibrium model, Networks and spatial economics 7, No. 3, 197-211 (2007) · Zbl 1170.90004 · doi:10.1007/s11067-006-9014-3
[38]Heydecker, B.: Some consequences of detailed intersection modeling in road traffic assignment, Transportation science 17, No. 3, 263-281 (1983)
[39]Lam, W. H. K.; Huang, H. J.: A combined trip distribution and assignment model for multiple user classes, Transportation research part B 26, 275-287 (1992)
[40]Levitin, E. S.; Polyak, B. T.: Constrained minimization methods, USSR computational mathematics and mathematical physics 6, 1-50 (1965)
[41]Lo, H. K.; Chen, A.: Traffic equilibrium problem with route-specific costs: formulation and algorithms, Transportation research part B 34, 493-513 (2000)
[42]Mahmassani, H. S.; Mouskos, K. C.: Some numerical results on the diagonalization algorithm for network assignment with asymmetric interactions between cars and trucks, Transportation research part B 22, 275-290 (1988)
[43]Mcfadden, D.: Econometric models of probabilistic choice, Structural analysis of discrete data with econometric applications (1981) · Zbl 0598.62145
[44]Mcnally, M. G.: The activity-based approach, Handbook of transport modelling, 53-69 (2000)
[45]Meneguzzer, C.: An equilibrium route choice model with explicit treatment of the effect of intersections, Transportation research part B 29, 329-356 (1995)
[46]Nagurney, A.: Network economics: A variational inequality approach, (1993)
[47]Nagurney, A.; Zhang, D.: Projected dynamical systems and variational inequality with applications, (1996)
[48]Oppenheim, N.: Urban travel demand modeling, (1995)
[49]Ortuzar, J. D.; Willumsen, L. G.: Modelling transport, (2001)
[50]Patriksson, M.: The traffic assignment problem: models and methods, (1994)
[51]Safwat, K. N. A.; Magnanti, T. L.: A combined trip generation, trip distribution, modal split, and trip assignment model, Transportation science 22, 14-30 (1988) · Zbl 0639.90032
[52]Sheffi, Y.: Urban transportation networks: equilibrium analysis with mathematical programming methods, (1985)
[53]Sheffi, Y.; Daganzo, C. F.: Hypernetworks and supply demand equilibrium with disaggregate demand models, Transportation research record 673, 113-121 (1978)
[54]Sheffi, Y.; Powell, W.: An algorithm for the equilibrium assignment problem with random link times, Networks 12, No. 2, 191-207 (1982) · Zbl 0485.90082 · doi:10.1002/net.3230120209
[55]Smith, M. J.: Junction interactions and monotonicity in traffic assignment, Transportation research part B 16, l-3 (1982)
[56]Williams, H. C. W.L.: On the formation of travel demand models and economic evaluation measures of user benefit, Environ plan A 9, 285-344 (1977)
[57]Wong, K. I.; Wong, S. C.; Wu, J. H.; Yang, H.; Lam, W. H. K.: D.h.leeurban and regional transportation modeling: essays in honor of david boyce, Urban and regional transportation modeling: essays in honor of david boyce 2, 25-42 (2004)
[58]Wu, J. H.; Florian, M.; He, S.: An algorithm for multiclass network equilibrium problem in PCE of trucks: application to the SCAG travel demand model, Transportmetrica 2, 1-19 (2006)
[59]Zhou, Z.; Chen, A.: A self-adaptive scaling technique embedded in the projection traffic assignment algorithm, Journal of eastern Asia society for transportation studies 5, 1647-1662 (2003)
[60]Zhou, Z., Chen, A., 2006. A self-adaptive gradient projection algorithm for solving the nonadditive traffic equilibrium problem. In: Proceedings of the 85th annual meeting of the Transportation Research Board, Washington, DC, USA.