Multiclass Traffic Assignment Problem with Flow-Dependent Passenger Car Equivalent Value of Trucks

Abstract

This paper develops and analyzes a multiclass traffic assignment model considering the flow-dependent passenger car equivalent (PCE) value of trucks based on the latest Highway Capacity Manual (HCM, 6th edition) and explores the properties of the proposed model to provide guidance on related planning applications. HCM discrete values of truck PCEs are fitted by power functions for combinations of link grades and lengths, which have been found to produce high coefficients of determination (R²) in all cases. With the established fitting functions, the multiclass traffic assignment problem is formulated as a variational inequality problem and solved by an efficient method. The equilibrium link flow distribution is proved to exist but may not be unique. Numerical examples and discussions are presented to demonstrate the variance of the link flow distributions and the effect of such nonuniqueness on traffic planning applications. Several approaches are then provided to obtain the best range of solutions according to a congestion pricing design problem.

Get full access to this article

View all access options for this article.

References

Bureau of Transportation Statistics, U.S. Department of Transportation, Washington, D.C. Freight Facts, 2015. http://www.rita.dot.gov/bts/sites/rita.dot.gov.bts/files/data_and_statistics/by_subject/freight/freight_facts_2015/chapter3/table3_3. Accessed July 4, 2016.

Bureau of Transportation Statistics. U.S. Department of Transportation, Washington, D.C. Commodity Flow Survey. http://www.bts.gov/publications/commodity_flow_survey. Accessed July 4, 2016.

Statista. ATA’s U.S. Truck Freight Trend from December 2009 to December 2013. http://www.statista.com/statistics/255252/us-truck-freight-trend/. Accessed July 4, 2016.

Yang

Multiple Equilibrium Behaviors and Advanced Traveler Information Systems with Endogenous Market Penetration. Transportation Research Part B: Methodological, Vol. 32, No. 3, 1998, pp. 205–218. https://doi.org/10.1016/S0191-2615(97)00025-8.

Yang

, and Meng

. Modeling User Adoption of Advanced Traveler Information Systems: Dynamic Evolution and Stationary Equilibrium. Transportation Research Part A: Policy and Practice, Vol. 35, No. 10, 2001, pp. 895–912. https://doi.org/10.1016/S0965-8564(00)00030-6.

Huang

H. J.

, and Li

Z. C.

. A Multiclass, Multicriteria Logit-Based Traffic Equilibrium Assignment Model Under ATIS. European Journal of Operational Research, Vol. 176, No. 3, 2007, pp. 1464–1477. https://doi.org/10.1016/j.ejor.2005.09.035.

Dafermos

S. C.

The Traffic Assignment Problem for Multiclass-User Transportation Networks. Transportation Science, Vol. 6, No. 1, 1972, pp. 73–87. https://doi.org/10.1287/trsc.6.1.73.

Daganzo

C. F.

Stochastic Network Equilibrium with Multiple Vehicle Types and Asymmetric, Indefinite Link Cost Jacobians. Transportation Science, Vol. 17, No. 3, 1983, pp. 282–300. https://doi.org/10.1287/trsc.17.3.282.

Mahmassani

H. S.

, and Mouskos

K. C.

. Some Numerical Results on the Diagonalization Algorithm for Network Assignment with Asymmetric Interactions Between Cars and Trucks. Transportation Research Part B: Methodological, Vol. 22, No. 4, 1988, pp. 275–290. https://doi.org/10.1016/0191-2615(88)90004-5.

10.

J. H.

, Florian

, and He

. An Algorithm for Multi-Class Network Equilibrium Problem in PCE of Trucks: Application to the SCAG Travel Demand Model. Transportmetrica, Vol. 2, No. 1, 2006, pp. 1–9. https://doi.org/10.1080/18128600608685656.

11.

Noriega

, and Florian

M. A.

. Algorithmic Approaches for Asymmetric Multi-Class Network Equilibrium Problems with Different Class Delay Relationships. CIRRELT. 2007. www.inroglobal.com/assets/pres-pap/international/ieug07/CIRRELT-2007-30.pdf. Accessed June 5, 2016.

12.

Ryu

, Chen

, and Choi

. Solving the Stochastic Multi-Class Traffic Assignment Problem with Asymmetric Interactions, Route Overlapping, and Vehicle Restrictions. Journal of Advanced Transportation, Vol. 50, No. 2, 2016, pp. 255–270. https://doi.org/10.1002/atr.1313.

13.

Huber

M. J.

Estimation of Passenger-Car Equivalents of Trucks in Traffic Stream. Transportation Research Record, No. 869, 1982, pp. 60–70.

14.

Meyer Mohaddes Associates, Inc. Heavy Duty Truck Model and VMT Estimation. Southern California Association of Governments, Los Angeles, 1999.

15.

Highway Capacity Manual. TRB, National Research Council, Washington, D.C., 2000.

16.

Highway Capacity Manual 2010. Transportation Research Board of the National Academies, Washington, D.C., 2010.

17.

List

G. F.

, Yang

, and Rouphail

N. M.

. On the Treatment of Trucks for Analysis of Freeway Capacity. Transportation Research Record: Journal of the Transportation Research Board, No. 2483, 2015, pp. 120–129. https://doi.org/10.3141/2483-14.

18.

Drakopoulos

, and Dehman

. Field-Derived Freeway Passenger Car Equivalents for Congested Conditions. Transportation Research Record: Journal of the Transportation Research Board, No. 2483, 2015, pp. 111–119. https://doi.org/10.3141/2483-13.

19.

Special Report 87: Highway Capacity Manual. HRB, National Research Council, Washington, D.C., 1965.

20.

Reilly

, and Seifert

. Truck Equivalency. Highway Research Record, No. 289, HRB, National Research Council, Washington, D.C., 1969, pp. 25–37.

21.

Linzer

E. M.

, Roess

R. P.

, and McShane

W. R.

. Effects of Trucks, Buses and Recreational Vehicles on Freeway Capacity and Service Volume. Transportation Research Record, No. 699, 1979, pp. 17–25.

22.

Sumner

, Hill

, and Shapiro

. Segment Passenger Car Equivalent Values for Cost Allocation on Urban Arterial Roads. Transportation Research Part A: General, Vol. 18, No. 5–6, 1984, pp. 399–406. https://doi.org/10.1016/0191-2607(84)90014-1.

23.

Special Report 209: Highway Capacity Manual, 3rd ed. (1997 update). TRB, National Research Council, Washington, D.C., 1998.

24.

Elefteriadou

, Torbic

, and Webster

. Development of Passenger Car Equivalents for Freeways, Two-Lane Highways, and Arterials. Transportation Research Record: Journal of the Transportation Research Board, No. 1572, 1997, pp. 51–58. https://doi.org/10.3141/1572-07.

25.

Webster

, and Elefteriadou

. A Simulation Study of Truck Passenger Car Equivalents (PCE) on Basic Freeway Sections. Transportation Research Part B: Methodological, Vol. 33, No. 5, 1999, pp. 323–336. https://doi.org/10.1016/S0965-8564(98)00036-6.

26.

Dowling

, List

, Yang

, Witzke

, and Flannery

. National Cooperative Freight Research Program (NCFRP) Report 31: Incorporating Truck Analysis into the Highway Capacity Manual. Transportation Research Board, Washington, D.C., 2014. https://doi.org/10.17226/22311.

27.

List

G. F.

, Yang

, and Rouphail

N. M.

. National Cooperative Freight Research Program (NCFRP) Report 41: Incorporating Truck Analysis into the Highway Capacity Manual. PCE Values for Single Grades. Transportation Research Board, Washington, D.C., 2014.

28.

Florian

, and Spiess

. On Binary Mode Choice/Assignment Models. Transportation Science, Vol. 17, No. 1, 1983, pp. 32–47. https://doi.org/10.1287/trsc.17.1.32.

29.

Bliemer

M. C.

, and Bovy

P. H.

. Quasi-Variational Inequality Formulation of the Multiclass Dynamic Traffic Assignment Problem. Transportation Research Part B: Methodological, Vol. 37, No. 6, 2003, pp. 501–519. https://doi.org/10.1016/S0191-2615(02)00025-5.

30.

Harker

P. T.

, and Pang

J.-S.

. Finite-Dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms and Applications. Mathematical Programming, Vol. 48, No. 1–3, 1990, pp. 161–220. https://doi.org/10.1007/BF01582255.

31.

Aghassi

, Bertsimas

, and Perakis

. Solving Asymmetric Variational Inequalities via Convex Optimization. Operations Research Letters, Vol. 34, No. 5, 2006, pp. 481–490. https://doi.org/10.1016/j.orl.2005.09.006.

32.

Chen

, He

, and Yin

. Optimal Deployment of Charging Lanes for Electric Vehicles in Transportation Networks. Transportation Research Part B: Methodological, Vol. 91, 2016, pp. 344–365. https://doi.org/10.1016/j.trb.2016.05.018.

33.

Luo

Z. Q.

, Pang

J.-S.

, and Ralph

. Mathematical Programs with Equilibrium Constraints. Cambridge University Press, New York, 1996. https://doi.org/10.1017/CBO9780511983658.

34.

Fletcher

, and Leyffer

. Solving Mathematical Programs with Complementarity Constraints as Nonlinear Programs. Optimization Methods and Software, Vol. 19, No. 1, 2004, pp. 15–40. https://doi.org/10.1080/10556780410001654241.

35.

Lawphongpanich

, and Yin

. Solving the Pareto-Improving Toll Problem via Manifold Suboptimization. Transportation Research Part C: Emerging Technologies, Vol. 18, No. 2, 2010, pp. 234–246. https://doi.org/10.1016/j.trc.2009.08.006.

36.

Ben-Tal

, and Nemirovski

. Robust Optimization—Methodology and Applications. Mathematical Programming, Series B, No. 92, 2002, pp. 453–380. https://doi.org/10.1007/s101070100286.

37.

Bertsimas

, and Sim

. Robust Discrete Optimization and Network Flows. Mathematical Programming, Vol. 98, No. 1–3, 2003, pp. 49–71. https://doi.org/10.1007/s10107-003-0396-4.

38.

Lou

, Yin

, and Lawphongpanich

. Robust Congestion Pricing Under Boundedly Rational User Equilibrium. Transportation Research Part B: Methodological, Vol. 44, No. 1, 2010, pp. 15–28. https://doi.org/10.1016/j.trb.2009.06.004.

39.

Ban

X. J.

, Lu

, Ferris

, and Liu

H. X.

. Risk Averse Second Best Toll Pricing. In Transportation and Traffic Theory 2009: Golden Jubilee ( Lam

W. H. K.

, Wong

S. C.

, and Lo

H. K.

, eds.), Springer, 2009, pp. 197–218.

40.

Ban

X. J.

, Ferris

, Tang

, and Lu

. Risk-Neutral Second Best Toll Pricing. Transportation Research Part B: Methodological, Vol. 48, 2013, pp. 67–87. https://doi.org/10.1016/j.trb.2012.11.003.

41.

Polak

, and Royset

. On the Use of Augmented Lagrangians in the Solution of Generalized Semi-Infinite Min–Max Problems. Computational Optimization and Applications, Vol. 31, No. 2, 2005, pp. 173–192. https://doi.org/10.1007/s10589-005-2179-8.

42.

Still

Generalized Semi-Infinite Programming: Theory and Methods. European Journal of Operational Research, Vol. 119, No. 2, 1999, pp. 301–313. https://doi.org/10.1016/S0377-2217(99)00132-0.

43.

Lawphongpanich

, and Hearn

D. W.

. An MPEC Approach to Second-Best Toll Pricing. Mathematical Programming B, Vol. 101, No. 1, 2004, pp. 33–55. https://doi.org/10.1007/s10107-004-0536-5.

44.

Yin

, and Lawphongpanich

. A Robust Approach to the Continuous Network Design Problem with Demand Uncertainty. In Proceedings of 17th International Symposium on Transportation and Traffic Theory ( Allsop

R. E.

, Bell

M. G. H.

, and Heydecker

B. G.

, eds.), Elsevier, 2007, pp. 111–126.

45.

Akamatsu

Decomposition of Path Choice Entropy in General Transport Networks. Transportation Science, Vol. 31, No. 4, 1997, pp. 349–362. https://doi.org/10.1287/trsc.31.4.349.

46.

Rossi

T. F.

, McNeil

, and Hendrickson

. Entropy Model for Consistent Impact-Free Assessment. Journal of Urban Planning and Development, Vol. 115, No. 2, 1989, pp. 51–63. https://doi.org/10.1061/(ASCE)0733-9488(1989)115:2(51).