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- Ekström, Joakim, 1980-, et al.
(author)
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A heuristic method for finding congestion pricing schemes in transportation networks with modal choice
- 2008
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In: International conference of Hong Kong society for transportation studies,2008. - Hong Kong, China : Hong Kong Society of Transportation Studies Ltd.. - 9789889884734 ; , s. 773-782
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Conference paper (peer-reviewed)abstract
- In this paper we extend a previously developed heuristic procedure, with a modal choice model, to solve the congestion pricing problem of simultaneously finding the optimal number of toll facilities, their corresponding location and toll levels. When considering a congestion pricing scheme the cost of collecting the tolls can not be disregarded. The objective is where-fore to maximize the net social surplus, which is the social surplus minus the cost of collect-ing the tolls. The heuristic method is an iterative solution procedure, in which the integer part of the objec-tive function is approximated by a continuous function. A version of the Sioux Falls network (76 links) is used to demonstrate the solution procedure. The solution is a congestion pricing scheme which divide the network into four zones, by locating tolls on 27 links. This solution yields a social surplus which is only 13.5% lower than the marginal social cost pricing solu-tion.
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| 2. |
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| 3. |
- Ekström, Joakim, 1980-, et al.
(author)
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Decision support for finding locations and toll levels within a congestion pricing scheme
- 2008
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In: Transportation Research Board Annual Meeting,2008. - Washington D.C. : TRB.
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Conference paper (peer-reviewed)abstract
- Designing a congestion pricing scheme involves a number of complex decisions. Focusing on the quantitative parts of a congestion pricing system with link tolls, the problem involves finding the number of tolled links, the link toll locations and their corresponding toll level and schedule. In this paper, we develop and evaluate methods for finding a most efficient design of a congestion pricing scheme in a road network with elastic demand. The design efficiency is measured by the net social surplus, which is computed as the difference between the social surplus and the collection costs (i.e. setup and operation cost) of the congestion pricing system. The problem of finding such a scheme is stated as a combinatorial bi-level optimization problem. On the upper level we maximize the net social surplus and on the lower level we solve a user equilibrium problem with elastic demand, given the toll locations and toll levels, to simulate the user response. We modify a known heuristic procedure for finding the optimal locations and toll levels given a fixed number of tolls to locate, to find the optimal number of tolls to locate as well. A new heuristic procedure is also presented which is based on repeated solutions of a continuous approximation of the combinatorial problem. Numerical results for two small scale test networks are presented. Both methods perform satisfactory on the two networks. Comparing the two methods, the iterative approximation procedure is the one which shows the best results. The results are compared to solutions obtained by an exhaustive search.
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| 5. |
- Ekström, Joakim, 1980-
(author)
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Designing Urban Road Congestion Charging Systems : Models and Heuristic Solution Approaches
- 2008
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Licentiate thesis (other academic/artistic)abstract
- The question of how to design a congestion pricing scheme is difficult to answer and involves a number of complex decisions. This thesis is devoted to the quantitative parts of designing a congestion pricing scheme with link tolls in an urban car traffic network. The problem involves finding the number of tolled links, the link toll locations and their corresponding toll level. The road users are modeled in a static framework, with elastic travel demand.Assuming the toll locations to be fixed, we recognize a level setting problem as to find toll levels which maximize the social surplus. A heuristic procedure based on sensitivity analysis is developed to solve this optimization problem. In the numerical examples the heuristic is shown to converge towards the optimum for cases when all links are tollable, and when only some links are tollable.We formulate a combined toll location and level setting problem as to find both toll locations and toll levels which maximize the net social surplus, which is the social surplus minus the cost of collecting the tolls. The collection cost is assumed to be given for each possible toll location, and to be independent of toll level and traffic flow. We develop a new heuristic method which is based on repeated solutions of an approximation to the combined toll location and level setting problem. Also, a known heuristic method for locating a fixed number of toll facilities is extended, to find the optimal number of facilities to locate. Both heuristics are evaluated on two small networks, where our approximation procedure shows the best results.Our approximation procedure is also employed on the Sioux Falls network. The result is compared with different judgmental closed cordon structures, and the solution suggested by our method clearly improves the net social surplus more than any of the judgmental cordons.
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| 6. |
- Ekström, Joakim, 1980-, et al.
(author)
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Heuristic algorithms for a second-best congestion pricing problem
- 2009
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In: Netnomics. - : Springer Science and Business Media LLC. - 1385-9587 .- 1573-7071. ; 10:1, s. 85-102
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Journal article (peer-reviewed)abstract
- Designing a congestion pricing scheme involves a number of complex decisions.Focusing on the quantitative parts of a congestion pricing system with link tolls, the problem involves findingthe number of toll links, the link toll locations and their corresponding toll level and schedule.In this paper, we develop and evaluate methods for finding the most efficient design for a congestion pricing scheme in a road network model with elastic demand. The design efficiency is measured by the net social surplus, which is computed as the difference between the social surplus and the collection costs (i.e. setup and operational costs) of the congestion pricing system. The problem of finding such a scheme is stated as a combinatorial bi-level optimization problem. At the upper level, we maximize the net social surplus and at the lower level we solve a user equilibrium problem with elastic demand, given the toll locations and toll levels,to simulate the user response. We modify a known heuristic procedure for finding the optimal locations and toll levels given a fixed number of tolls to locate, to find the optimal number of toll facilities as well. A new heuristic procedure, based on repeated solutions of a continuous approximation of the combinatorial problem is also presented. Numerical results for two small test networks are presented. Both methods perform satisfactorily on the two networks. Comparing the two methods, we find that the continuous approximation procedure is the one which shows the best results.
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| 7. |
- Ekström, Joakim, 1980-, et al.
(author)
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Optimizing toll levels using linear approximation approach
- 2009
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In: 4th Kuhmo Nectar Conference.
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Conference paper (peer-reviewed)abstract
- This paper proposes a heuristic solution algorithm for solving the non-convex toll level problem for fixed demand networks in which the road users are distributed according to a user equilibrium. In the toll level problem we search for continuous toll levels, given a fixed set of tollable links, to minimize the total travel time in the traffic network. The toll level problem is converted by a linearization scheme to approximate the objective function and constraints in the original problem. This approximation gives a mixed integer linear program (MILP) which has the property of global optimum, and gives a lower bound estimation of the original non-linear problem. The user equilibrium condition is represented by the variational inequality (VI) constraints, and the MILP approximation is solved by applying a cutting constraint algorithm (to deal with the VI-constraints) together with a commercial MILP-solver. Numerical results are presented for a small network, and the results are encouraging.
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| 8. |
- Ekström, Joakim, 1980-, et al.
(author)
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Towards optimal locations and toll levels in congestion pricing schemes
- 2009
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In: 16th ITS World Congress. - : World Congress on Intelligent Transport Systems (ITS).
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Conference paper (peer-reviewed)abstract
- This paper addresses the problem of designing a road congestion pricing scheme with link tolls. The problem involves decisions on where to locate the toll collecting facilities and what tolls to charge the road users. We formulate this problem as a bi-level program, with the objective to maximize the net social surplus, which include the cost of setting up and operate the toll collection system. A previously developed heuristic method is applied to find close to optimal toll locations and charges for a traffic network representing the Stockholm region. The result is compared with the current congestion pricing scheme in Stockholm.
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