Abstract
When analyzing equilibrium traffic flows it is usually the link flows and link travel demands that are of interest, but in some certain cases analyses require the knowledge of route flows. It is well known that the route flows are non-unique in the static and deterministic cases of traffic equilibrium. Furthermore, different assignment methods can generate different route flow output. We show how this non-uniqueness can affect the results in applications such as in the O-D estimation/adjustment problem, in the construction of induced O-D matrices, exhaust fume emission analyses and in link toll usage analyses. We state a model for finding, uniquely, the most likely route flows given the equilibrium link flows, and propose a solution algorithm for the problem based on partial dualization. We present computational results for the proposed algorithm and results from an application to exhaust fume emissions.
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References
T. Akamatsu, Y. Tsuchiya, T. Shimazaki, Parallel distributed processing on neural network for some transportation equilibrium assignment problems, In Proceedings of the 11th International Symposium on the Theory of Traffic Flow and Transportation, Ed. M. Koshi, Yokohama, Elsevier, NY, (1990), 369–386.
T. Akamatsu, Cyclic flows, Markov process and stochastic traffic assignment, Transportation Research 30 (1996), 369–386.
T. Akamatsu, Decomposition of path choice entropy in general transport networks, Transportation Science 31 (1997), 349–362
R.R. Barton, D.W. Hearn, S. Lawphongpanich, The equivalence of transfer and generalized Benders decomposition methods for traffic assignment, Transportation Research 23B (1989), 61–73.
M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming: Theory and Algorithms, John Wiley & Sons, New York, NY, 1993.
M.G.H. Bell, Y. Iida, Transportation Network Analysis, John Wiley & Sons, Chichester, England, 1997.
D.P. Bertsekas, Nonlinear Programming. Athena Scientific, Belmont, MA., 1995.
E. Cascetta, S. Nguyen, A unified framework for estimating or updating origin/destination matrices from traffic counts, Transportation Research 22B (1988), 437–455
Drive project v1054, 1st. Deliverable, Report on model requirements, 1989.
S. Erlander, N.F. Stewart, The Gravity Model in Transportation Analysis, VSP BV, Utrecht, The Netherlands, 1990.
H. Edwards, Estimation of excess cold start emissions on links in traffic networks, (In Swedish) Working paper, VTI, S-581 95 Linköing, Sweden, 1998.
S.C. Fang, H.S.J. Tsao, A quadratic convergent global algorithm for the linearly-constrained minimum cross-entropy problem, European Journal of Operations Research 79 (1994), 369–378.
C.S. Fisk, Some developments in equilibrium traffic assignment, Transportation Research 14B (1980), 243–255.
C.S. Fisk, On combing maximum entropy trip matrix estimation with user optimal assignment, Transportation Research 22B (1988), 69–79.
M. Florian, S. Nguyen, An application and validation of equilibrium trip assignment methods, Transportation Science 10 (1976), 374–390.
D.W. Hearn, Practical and theoretical aspects of aggregation problems in transportation models, In Transportation Planning Models, Proceedings of the course given at the International Center for Transportation Studies, Amalfi, Italy, October 11–16, 1982, Ed. M. Florian. North-Holland, Amsterdam (1984), 257–287.
B.N. Janson, Most likely origin-destination link uses from equilibrium assignment, Transportation Research 27B (1993), 333–350.
B. Lamond, N.F. Stewart, Bregman’s balancing method, Transportation Research 15B (1981), 239–248.
T. Larsson, M. Patriksson, Simplicial decomposition with disaggregate representation for the traffic assignment problem, Transportation Science 26 (1992), 4–17.
L.J. LeBlanc, E.K. Morlok, W.P. Pierskalla, An efficient approach to solving the road network equilibrium traffic assignment problem, Transportation Research 9 (1975), 309–318.
M. Patriksson, The Traffic Assignment Problem-Models and Methods, VSP BV, Utrecht, The Netherlands, 1994.
B.T. Polyak, Introduction to Optimization, Optimization Software, Inc., Publications Division, N.Y., 1987.
T.F. Rossi, S. McNeil, C. Hendrickson, Entropy model for consistent impact fee assessment, Journal of Urban Planning and Development/ ASCE 115 (1989), 51–63.
E. Sérié, R. Joumard, Modelling of cold start emissions for road vehicles, INRETS report LEN 9731, 1997.
K.A. Small, Using revenues from congestion pricing, Transportation 19 (1992), 359–381.
T.E. Smith, A cost-efficiency of spatial interaction behaviour, Regional Science and Urban Economics 8 (1978), 137–168.
T.E. Smith, A cost-efficiency approach to the analysis of congested spatial-interaction behavior, Environment and Planning 15A (1983), 435–464.
F. Snickars, J.W. Weibull, A minimum information principle: Theory and practice, Regional Science and Urban Economics 7 (1977), 137–168.
Y. Sheffi, Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods, Prentice-Hall. Englewood Cliffs, NJ, 1985.
The Economist, December 6 1997, 21–24.
D. Van Vliet, Selected node-pair analysis in Dial’s assignment algorithm, Transportation Research 15B (1981), 65–68.
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© 2001 Kluwer Academic Publishers
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Larsson, T., Lundgren, J.T., Rydergren, C., Patriksson, M. (2001). Most Likely Traffic Equilibrium Route Flows Analysis and Computation. In: Giannessi, F., Maugeri, A., Pardalos, P.M. (eds) Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models. Nonconvex Optimization and Its Applications, vol 58. Springer, Boston, MA. https://doi.org/10.1007/0-306-48026-3_9
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DOI: https://doi.org/10.1007/0-306-48026-3_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4020-0161-1
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