Improved Solution Algorithm for Multicommodity Continuous Distribution and Assignment Model
Publication: Journal of Urban Planning and Development
Volume 130, Issue 1
Abstract
Consider a city, with multiple regional activity centers (RACs), in which the locations of traveler demand are continually dispersed. The total demand generated from a particular location in the city is fixed, but the demands from this location to the RACs are subject to a distribution function with respect to the relative transportation cost to each RAC. We take into account the cost of transportation in characterizing travelers’ choices. The congestion effect is explicitly built into the model by using a flow- and location-dependent transportation cost function. The routing behavior of travelers in the city and the user equilibrium choices of RACs are modeled by constructing a spatial user equilibrium flow pattern. The problem is formulated as a combined distribution and assignment model. A solution algorithm that is improvement upon a previously adopted iterative algorithm between the distribution function for the choice of RAC and a mixed finite-element method for route choices is proposed to solve the resultant continuous problem. A numerical example is given to demonstrate the superiority of the improved algorithm.
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References
Beckmann, M.(1952). “A continuous model of transportation.” Econometrica, 20, 643–660.
Boyce, D. E.(1984). “Urban transportation network-equilibrium and design models: Recent achievements and future prospects.” Environ. Plan., A, 16, 1445–1474.
Buckley, D. J.(1979). “Traffic assignment in a two-dimensional continuous representation of a traffic network with flow-dependent speeds.” Transp. Res., Part B: Methodol., 13B, 167–179.
D’Este, G.(1987). “Trip assignment to radial major roads.” Transp. Res., Part B: Methodol., 21B, 433–442.
Dafermos, S. C.(1980). “Continuum modeling of transportation networks.” Transp. Res., Part B: Methodol., 14B, 295–301.
Drezner, Z. (1995). Facility location: A survey of applications and methods, Springer, Berlin.
Drezner, T., and Drezner, Z.(1997). “Replacing continuous demand with discrete demand in a competitive location model.” Naval Res. Logistics Quart., 44, 81–95.
Eiselt, H. A., Laporte, G., and Thisse, J. F.(1993). “Competitive location models: A framework and bibliography.” Transp. Sci., 27, 44–54.
Fernandez, L. J. E., and Freisz, T. L.(1983). “Equilibrium predictions in transportation markets: The state of the art.” Transp. Res., Part B: Methodol., 17B, 155–172.
Lam, T. N., and Newell, G. F.(1967). “Flow dependent traffic assignment on a circular city.” Transp. Sci., 1, 318–361.
Miller, T. C., Friesz, T. L., and Tobin, R. L. (1996). Equilibrium facility location on networks, Springer, Berlin.
Puu, T.(1977). “A proposed definition of traffic flow in continuous transportation models.” Environ. Plan., 9A, 559–567.
Sasaki, T., Iida, Y., and Yang, H. (1990). “User equilibrium traffic assignment by continuum approximation of network flow.” Proc., 11th Int. Symp. on Transportation and Traffic Theory, 233–252.
Taguchi, A., and Iri, M.(1982). “Continuum approximation to dense networks and its application to the analysis of urban road networks.” Math. Program., 20, 178–217.
Vaughan, R. J. (1987). Urban spatial traffic patterns, Pion, London.
Wardrop, J. G. (1952). “Some theoretical aspects of road traffic research.” Proc., Inst. of Civil Engineers, Part II, 325–378.
Wardrop, J. G. (1971). “Minimum cost paths when the cost per unit length depends on location and direction.” 5th Symp. on Transportation and Traffic Flow, 429–437.
Williams, H. C. W. L., and Ortuzar, J. D.(1976). “Some generalizations and applications of the velocity field concept: Trip patterns in idealized cities.” Transp. Res., 10, 65–73.
Wong, S. C.(1994). “An alternative formulation of D’Este’s trip assignment model.” Transp. Res., Part B: Methodol., 28B, 187–196.
Wong, S. C.(1998). “Multicommodity traffic assignment by continuum approximation of network flow with variable demand.” Transp. Res., Part B: Methodol., 32B, 567–581.
Wong, S. C., Lee, C. K., and Tong, C. O.(1998). “Finite element solution for the continuum traffic equilibrium problems.” Int. J. Numer. Methods Eng., 43, 1253–1273.
Wong, S. C., and Sun, S. H.(2001). “A combined distribution and assignment model for continuous facility location problem.” Ann. Regional Sci., 35, 267–281.
Wong, S. C., and Tong, C. O. (1996). “Flow dependent traffic assignment in a circular city with a major circumference ring road.” Proc., Highways into the Next Century Conf. 793–801.
Wong, S. C., Tong, C. O., and Wong, C. K. (1996). “Flow dependent traffic assignment in a circular city: Ring-radial routing system.” Proc., Int. Conf. on Urban Engineering in Asian Cities in the 21st Century, E7–E12.
Wong, S. C., and Yang, H.(1999). “Determining market areas captured by competitive facilities: A continuous equilibrium modeling approach.” J. Regional Sci., 39, 51–72.
Yang, H., and Wong, S. C.(2000). “A continuous equilibrium model for estimating market areas by competitive facilities with elastic demand and market externality.” Transp. Sci., 34, 216–227.
Yang, H., Yagar, S., and Iida, Y.(1994). “Traffic assignment in a congested discrete/continuous transportation system.” Transp. Res., Part B: Methodol., 28B, 161–174.
Zienkiewicz, O. C., and Taylor, R. L. (1989). The finite element method, Int. Ed., McGraw-Hill, New York.
Zitron, N. R.(1974). “A continuous model of optimal-cost routes in a circular city.” J. Optim. Theory Appl., 14, 291–303.
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Copyright © 2004 American Society of Civil Engineers.
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Received: Feb 27, 2002
Accepted: Nov 20, 2002
Published online: Feb 19, 2004
Published in print: Mar 2004
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