Abstract
As a means to relieve traffic congestion, toll pricing has recently received significant attention by transportation planners. Inappropriate use of transportation networks is one of the major causes of network congestion. Toll pricing is a method of traffic management in which traffic flow is guided to proper time and path in order to reduce the total delay in the network. This article investigates a method for solving the minimum toll revenue problem in real and large-scale transportation networks. The objective of this problem is to find link tolls that simultaneously cause users to efficiently use the transportation network and to minimize the total toll revenues to be collected. Although this model is linear, excessive number of variables and constraints make it very difficult to solve for large-scale networks. In this paper, a path-generation algorithm is proposed for solving the model. Implementation of this algorithm for different networks indicates that this method can achieve the optimal solution after a few iterations and a proper CPU time.
Similar content being viewed by others
References
Bai, L., Hearn, D.W., Lawphongpanich, S.: Decomposition techniques for the minimum toll revenue problem. Networks 44(2), 142–150 (2004)
Wardrop, J.G.: Some theoretical aspects of road traffic research. In: Proceedings of the Institution of Civil Engineers, pp. 325–378 (1952)
Bergendorff, P., Hearn, D.W., Ramana, M.V.: Congestion toll pricing of traffic networks. In: Pardalos, P.M., Hearn, D.W., Hager, W.W. (eds.) Network Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 450, pp. 51–71. Springer (1997)
Hearn, D.W., Ramana, M.V.: Solving congestion toll pricing models. In: Marcotte, P., Nguyen, S. (eds.) Equilibrium and Advanced Transportation Modeling, pp. 109–124. Kluwer Academic Publishers, Dordrecht (1998)
Penchina, M.: Minimal revenue tolls: price stability for networks with BPR cost function. Open Transp. J. 3, 87–92 (2009)
Dial, R.: Minimal-revenue congestion pricing part I: a fast algorithm for the single-origin case. Transp. Res. Part B 33, 189–202 (1999)
Dial, R.: Minimal-revenue congestion pricing part II: an efficient algorithm for the general case. Transp. Res. Part B 34, 645–665 (2000)
Penchina, M.: Minimal-revenue congestion pricing: some more good-news and bad-news. Transp. Res. Part B 38, 559–570 (2004)
Hearn, D.W., Yildirim, M.B., Ramana, M.V., Bai, L.: Computational methods for congestion toll pricing models. In: IEEE Intelligent Transportation Systems Proceedings, pp. 257–262 (2001)
LeBlanc, L.J., Helgason, R.V., Boyce, D.E.: Improved efficiency of the frank-wolfe algorithm for convex network problems. Transp. Sci. 19, 445–462 (1985)
Toobaie, S., Aashtiani, H.Z., Hamedi, M., Haghani, A.: Application of complementarity approach to large-scale traffic equilibrium problems. In: 89th Transportation Research Board Annual Meetings (2010)
Nie, Y.: A class of bush-based algorithms for the traffic assignment problem. Transp. Res. Part B 44, 73–89 (2010)
Aashtiani, H.Z.: The multi-modal traffic assignment problem. Ph.D. Dissertation, MIT, Cambridge, MA (1979)
Aashtiani, H.Z., Magnanti, T.L.: A linearization and decomposition algorithm for computing urban traffic equilibria. In: Proceedings of 1982 IEEE Large Scale Systems Symposium, pp. 8–19 (1982)
Golden, B.: Shortest-path algorithms: a comparison. Oper. Res. 24, 1164–1168 (1976)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shirazi, M., Aashtiani, H.Z. Solving the minimum toll revenue problem in real transportation networks. Optim Lett 9, 1187–1197 (2015). https://doi.org/10.1007/s11590-014-0817-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-014-0817-8