A modeling framework and a solution methodology are presented for the toll problem of dynamic revenue maximization. The problem requires determining the optimal time-varying toll prices for a multigantry toll road facility so that total revenue is maximized subject to agency-mandated constraints on average speed and average traffic volume. The framework extends a real-time traffic network state estimation and prediction system to provide dynamic pricing capabilities. The presented framework overcomes limitations of most existing approaches by considering two factors: consistency between the toll value and drivers’ willingness-to-pay behavior and drivers’ route choice dynamics in regard to competition between the toll facility and alternative routes. The paper presents the results of a set of simulation-based experiments that were conducted to examine the robustness of the proposed prices under several operational scenarios.
Get full access to this article
View all access options for this article.
References
1.
BeckmannM., McGuireC., and WinstenC.Studies in the Economics in Transportation.Yale University Press, New Haven, Conn., 1956.
2.
WaltersA.The Theory and Measurement of Private and Social Cost of Highway Congestion. Econometrica, Vol. 29, No. 4, 1961, pp. 676–699.
3.
NewberyD.Road Damage Externalities and Road User Charges. Econometrica, Vol. 56, No. 2, 1988, pp. 295–316.
4.
ArnottR., De PalmaA., and LindseyR.Route Choice with Heterogeneous Drivers and Group-Specific Congestion Costs. Regional Science and Urban Economics, Vol. 22, No. 1, 1992, pp. 71–102.
5.
VerhoefE., EmmerinkR., NijkampP., and RietveldP.Information Provision, Flat and Fine Congestion Tolling, and the Efficiency of Road Usage. Regional Science and Urban Economics, Vol. 26, No. 5, 1996, pp. 505–529.
6.
MayetJ., and HansenM.Congestion Pricing with Continuously Distributed Values of Time. Journal of Transport Economics and Policy, Vol. 34, Part 3, 2000, pp. 359–370.
7.
BelleiG., GentileG., and PapolaN.Network Pricing Optimization in Multi-User and Multimodal Context with Elastic Demand. Transportation Research B, Vol. 36, No. 9, 2002, pp. 779–798.
8.
ChuC., and TsaiJ.Road Pricing Models with Maintenance Cost. Transportation, Vol. 31, No. 4, 2004, pp. 457–477.
9.
YinY., and YangH.Optimal Tolls with a Multiclass, Bicriterion Traffic Network Equilibrium. In Transportation Research Record: Journal of the Transportation Research Board, No. 1882, Transportation Research Board of the National Academies, Washington, D.C., 2004, pp. 45–52.
10.
YingJ.Sensitivity Analysis Based Method for Optimal Road Network Pricing. Annals of Operations Research, Vol. 133, No. 1-4, 2005, pp. 303–317.
11.
ZhaoY., and KockelmanK.On-Line Marginal-Cost Pricing Across Networks: Incorporating Heterogeneous Users and Stochastic Equilibria. Transportation Research B, Vol. 40, No. 5, 2006, pp. 424–435.
12.
ZhangX., YangH., and HuangH.Multiclass Multicriteria Mixed Equilibrium on Networks and Uniform Link Tolls for System Optimum. European Journal of Operational Research, Vol. 189, No. 1, 2008, pp. 146–158.
13.
DongJ.Anticipatory Traveler Information and Pricing for Real-Time Traffic Management. PhD dissertation. Northwestern University, Evanston, Ill., 2009.
14.
KidoT., and MasudaY.Second-Best Congestion Pricing and User Heterogeneity in Static Transportation Networks. Journal of the Operations Research Society of Japan, Vol. 53, No. 2, 2010, pp. 157–171.
15.
DongJ., MahmassaniH., ErdoganS., and LuC.State-Dependent Pricing for Real-Time Freeway Management: Anticipatory Versus Reactive Strategies. Transportation Research C, Vol. 19, No. 4, 2011, pp. 644–657.
16.
TsekerisT., and VossS.Design and Evaluation of Road Pricing: State-of-the-Art and Methodological Advances. Netnomics, Vol. 10, No. 1, 2009, pp. 5–52.
17.
BergendorffP., HearnD., and RamanaM.Congestion Toll Pricing of Traffic Networks. In Network Optimization (PardalosP., HearnD., and HagerW., eds.), Springer-Verlag, Berlin, 1997, pp. 51–71.
18.
YangH., and BellM.Traffic restraint, road pricing, and network equilibrium. Transportation Research B, Vol. 31, No. 4, 1997, pp. 303–314.
19.
JoksimovicD., BliemerM. C. J., and BovyP. H. L.Optimal Toll Design Problem in Dynamic Traffic Networks with Joint Route and Departure Time Choice. In Transportation Research Record: Journal of the Transportation Research Board, No. 1923, Transportation Research Board of National Academies, Washington, D.C., 2005, pp. 61–72.
20.
LarssonT., and PatrikssonM.Side Constrained Traffic Assignment Models—Traffic Management Through Link Toll. In Equilibrium and Advanced Transportation Modeling (MarcotteP., and NguyenS., eds.), Kluwer Academic Publishers, New York, 1998, pp. 125–151.
21.
HearnD., and YilidirimM.A Toll Pricing Framework for Traffic Assignment Problems with Elastic Demand. In Transportation and Network Analysis: Current Trends (GendreauM., and MarcotteP., eds.), Kluwer Academic Publishers, New York, 2002, pp. 135–145.
22.
VerhoefE.Second-Best Congestion Pricing in General Static Transportation Networks with Elastic Demands. Regional Science and Urban Economics, Vol. 32, No. 3, 2002, pp. 281–310.
23.
LabbeM., MarcotteP., and SavardG.A Bilevel Model of Taxation and Its Application to Optimal Highway Pricing. Management Science, Vol. 44, No. 12, 1998, pp. 1608–1622.
24.
RochS., SavardG., and MarcotteP.An Approximation Algorithm for Stackelberg Network Pricing. Networks, Vol. 46, No. 1, 2005, pp. 57–67.
25.
PatrikssonM., and RockafellarR.A Mathematical Model and Descent Algorithm for Bilevel Traffic Management. Transportation Science, Vol. 36, No. 3, 2002, pp. 271–291.
26.
LawphongpanichS., and HearnD.An MPEC Approach to Second-Best Toll Pricing. Mathematical Programming, Vol. 101, No. 1, 2004, pp. 33–55.
27.
DussaultJ., MarcotteP., RochS., and SavardG.A Smoothing Heuristic for a Bilevel Pricing Program. European Journal of Operation Research, Vol. 174, No. 3, 2006, pp. 1396–1413.
28.
ChiouW.An Optimal Scheme for Toll Pricing Problem. Applied Mathematics and Computation, Vol. 182, No. 2, 2006, pp. 1127–1136.
29.
BraidR.Uniform Versus Peak-Load Pricing of a Bottleneck with Elastic Demand. Journal of Urban Economics, Vol. 26, 1989, pp. 320–327.
30.
ArnottR., De PalmaA., and LindseyR.Departure Time and Route Choice for the Morning Commute. Transportation Research Part B, Vol. 24, 1990, pp. 209–228.
31.
VickreyW.Optimization of Traffic and Facilities. Journal of Transport Economics and Policy, Vol. 1, 1967, pp. 123–136.
32.
Ben AkivaM., De PalmaA., and KanaroglouP.Dynamic Model of Peak Period Traffic Congestion with Elastic Arrival Rates. Transportation Science, Vol. 20, 1986, pp. 164–181.
33.
MunS.Traffic Jams and the Congestion Toll. Transportation Research B, Vol. 28, 1994, pp. 365–375.
34.
CareyM., and SrinivasanA.Externalities, Average and Marginal Costs, and Tolls on Congested Networks with Time-Varying Flows. Operations Research, Vol. 41, 1993, pp. 217–231.
35.
YangH., and HuangH.Analysis of Time-Varying Pricing of a Bottleneck with Elastic Demand Using Optimal Control Theory. Transportation Research B, Vol. 31, 1997, pp. 425–440.
36.
YangH., and MengQ.Departure Time Route Choice and Congestion Toll in a Queuing Network with Elastic Demand. Transportation Research B, Vol. 32, 1998, pp. 247–260.
37.
WieB., and TobinR.Dynamic Congestion Pricing Models for General Traffic Networks. Transportation Record Part B, Vol. 32, 1998, pp. 313–327.
38.
MayA. D., and MilneD. S.Effects of Alternative Road Pricing Systems on Network Performance. Transportation Research A, Vol. 34, 2000, pp. 407–436.
39.
ChangM., and HsuehC.A Dynamic Road Pricing Model for Freeway Electronic Toll Collection Systems Under Build-Operate-Transfer Arrangements. Transportation Planning and Technology, Vol. 29, No. 2, 2006, pp. 91–104.
GreenshieldsB. D., BibbinsJ. R., ChanningW. S., and MillerH. H.A Study of Traffic Capacity. Highway Research Board Proceedings, Vol. 14, Part 1, 1935, pp. 448–477.
42.
EtemadniaH., AbdelghanyK., and HaririH.Towards an Autonomic Architecture for Real-Time Traffic Network Management. Journal of Intelligent Transportation Systems, Vol. 16, No. 2, 2012, pp. 45–59.
43.
BazaraaM., SheraliH., and ShettyC.Nonlinear Programming: Theory and Algorithms.John Wiley & Sons, New York, 2006.
