, Volume 46, Issue 3, pp 647–669 | Cite as

Activity-based trip chaining behavior analysis in the network under the parking fee scheme

  • Ge Gao
  • Huijun SunEmail author
  • Jianjun Wu


In this paper, we incorporate activity-based trip chaining behavior into the network equilibrium analysis. An integrated model which combines Beckman-type congestion link terms and entropy-type logit demand terms is proposed to describe the traveler behavior. The convexity and equivalency conditions of the model are discussed. Based on the integrated model, a bi-level model is designed to maximize the social welfare by appropriate parking fee. Also, an expanded network is developed to eliminate the non-additivity of the utilities of activities and travelling in the original network. Then, the Simulated Annealing (SA) method is used to solve the proposed bi-level model. Numerical examples are presented to examine the model’s availability and effects of the parking fee scheme on traveler behavior and social welfare. Results show that the model is effective in describing the trip chaining behavior in the network.


Activity location Parking fees Social welfare Trip chain 



The authors would like to thank the two anonymous reviewers for the constructive comments and suggestions. This paper is partly supported by the NSFC (71621001) and the China National Funds for Distinguished Young Scientists (71525002).

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. Anderson, S.P., Palma, A.D.: The economics of on-street parking: road congestion and driver search number. JEL. Classificaiton: R41, H23, D62 (2002)Google Scholar
  2. Antipova, A., Wang, F.H.: Land use impacts on trip-chaining propensity for workers and non-workers in Baton Rouge, Louisiana. Ann. GIS 16(3), 141–154 (2010)Google Scholar
  3. Arnott, R., Inci, E.: An integrated model of downtown parking and traffic congestion. J. Unban Econ. 60, 418–442 (2006)Google Scholar
  4. Bard, J.F.: Some properties of the bilevel programming. J. Optim. Theory Appl. 68, 371–378 (1991)Google Scholar
  5. Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation, Cowles Commission Monograph. Yale University Press, New Haven (1956)Google Scholar
  6. Bekhor, S., Ben-Akiva, M., Ramming, S.: Adaptation of logit kernel to route choice situation. Transp. Res. Rec. 1805, 78–85 (2002)Google Scholar
  7. Bell, M.G.H.: A game theory approach to measuring the performance reliability of transport networks. Transp. Res. B 34(6), 533–545 (2000)Google Scholar
  8. Ben-Ayed, O., Blair, O.: Computational difficulty of bi-level linear programming. Oper. Res. 38, 556–560 (1990)Google Scholar
  9. Ben-Akiva, M., Bierlaire, M.: Discrete choice methods and their applications to short term travel decisions. In: Hall, R.W. (ed.) Handbook of Transportation Science, pp. 5–34. Kluwer Publishers, Norwell (1999)Google Scholar
  10. Bentley, G., Bruce, A., Jones, D.: Intra-urban Journeys and Activity Linkages. Soc. Econ. Plan. Sci. 11, 213–220 (1977)Google Scholar
  11. Bhat, C.R.: An analysis of evening commutes stop-making behavior using repeated choice observations from a multi-day survey. Transp. Res. B 33(6), 495–510 (1999)Google Scholar
  12. Bhat, C.R., Misra, R.: Discretionary activity time allocation of individuals between in-home and out-of-home and between weekdays and weekends. Transportation 26(2), 193–209 (1999)Google Scholar
  13. Bhat, C.R., Singh, S.K.: A comprehensive daily activity-travel generation model system for workers. Transp. Res. A 34(1), 1–22 (2000)Google Scholar
  14. Bonsall, P., Young, W.: Is there a case for replacing parking charges by road user charges? Transp. Policy 17(5), 323–334 (2010)Google Scholar
  15. Brunow, S., Gründer, M.: The impact of activity chaining on the duration of daily activities. Transportation 40, 981–1001 (2013)Google Scholar
  16. Button, K.: The political economy of parking charges in ‘first’ and ‘second-best’ worlds. Transp. Policy 13(6), 470–478 (2006)Google Scholar
  17. Cascetta, E., Nuzzolo, A., Russo, F., Vitetta, A.: A modified logit route choice model overcoming path overlapping problems: specification and some calibration results for interurban networks. In: Lesort, J.B. (ed.) Proceedings of the International Symposium on Transportation and Traffic Theory, Lyon, France, pp. 697–711. Pergman, Oxford (1996)Google Scholar
  18. Chapin, J.: Human Activity Patterns in the City. Wiley, New York (1974)Google Scholar
  19. Chu, Y.: Empirical analysis of commute stop-making behavior. Transp. Res. Rec. 1831, 106–113 (2003)Google Scholar
  20. Currie, G., Delbosc, A.: Exploring the trip chaining behavior of public transport users in Melbourne. Transp. Policy 18, 204–210 (2011)Google Scholar
  21. Cullen, I., Godson, V.: Urban Networks: The Structure of Activily Patterns. Pergamon Press, Oxford (1975)Google Scholar
  22. Daganzo, C.F., Sheffi, Y.: On stochastic models of traffic assignment. Transp. Sci. 11(3), 253–274 (1977)Google Scholar
  23. Dekkers, A., Aarts, E.: Global optimization and simulated annealing. Math. Program. 50, 367–393 (1991)Google Scholar
  24. Dial, R.B.: A probabilistic multipath traffic assignment model which obviates path enumeration. Transp. Res. 5, 83–111 (1971)Google Scholar
  25. Evans, S.P.: A relationship between the gravity model for trip distribution and the transportation problem in linear programming. Transp. Res. 7, 39–61 (1973)Google Scholar
  26. Friesz, T.L., Bernstein, D., Smith, T.E., Tobin, R.L., Wie, B.W.: A variational inequality formulation of the dynamic network user equilibrium problem. Oper. Res. 41(1), 179–191 (1993)Google Scholar
  27. Friesz, T.L., Tobin, R.L., Cho, H.J., Mehta, N.J.: Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints. Math. Program. 48, 265–284 (1990)Google Scholar
  28. Fu, X., Lam, W.H.K.: A network equilibrium approach for modelling activity travel pattern scheduling problems in multi-modal transit networks with uncertainty. Transportation 41, 37–55 (2014)Google Scholar
  29. Gao, Z.Y., Song, Y.F.: A reserve capacity model of optimal signal control with user-equilibrium route choice. Transp. Res. B 36(4), 313–323 (2002)Google Scholar
  30. Glazer, A., Niskanen, E.: Parking fees and congestion. Reg. Sci. Urban Econ. 22(2), 123–132 (1992)Google Scholar
  31. Golob, T.F.: A simultaneous model of household activity participation and trip chain generation. Transp. Res. B 34(5), 355–376 (2000)Google Scholar
  32. Hamdouch, Y., Marcotte, P., Nguyen, S.A.: A strategic model for dynamic traffic assignment. Netw. Spat. Econ. 4(3), 291–315 (2004)Google Scholar
  33. Harding, C., Miller, E.J., Patterson, Z., Axhausen, K.W.: Multiple purpose tours and efficient trip chaining: an analysis of the effects of land use and transit on travel behavior in Switzerland. Transp. Res. Rec. 15, 4551 (2015)Google Scholar
  34. Hess, D.B. The effect of free parking on commuter mode choice: evidence from travel diary data. In: The 80th Annual TRB Meeting (2001)Google Scholar
  35. Higuchi, T., Shimamoto, H., Uno, N., Shiomi, Y.: A trip-chain based combined mode and route choice network equilibrium model considering common lines problem in transit assignment model. Procedia Soc. Behav. Sci. 20, 354–363 (2011)Google Scholar
  36. Hine, J., Kamruzzaman, M., Blair, N.: Weekly activity-travel behaviour in rural Northern Ireland: differences by context and socio-demographic. Transportation 39(1), 175–195 (2012)Google Scholar
  37. Islam, M.T., Habib, K.M.N.: Unraveling the relationship between trip chaining and mode choice: evidence from a multi-week travel diary. Transp. Plan. Technol. 35(4), 409–426 (2012)Google Scholar
  38. Jang, T.Y.: Causal relationship among travel mode, activity, and travel patterns. J. Transp. Eng. 1, 16–22 (2003)Google Scholar
  39. Joh, C.H., Arentze, T., Timmermans, H.: Activity-travel scheduling and rescheduling decision processes -empirical estimation of aurora model. Transp. Res. Rec. 1898, 10–18 (2004)Google Scholar
  40. Kuppam, A.R., Pendyala, R.M.: A structural equations analysis of commuters’ activity and travel patterns. Transportation 28, 33–54 (2001)Google Scholar
  41. Lee, Y., Hickman, M., Washington, S.: Household type and structure, time-use pattern, and trip-chaining behavior. Transp. Res. A 41, 1004–1020 (2007)Google Scholar
  42. Lo, H., Yip, C., Wan, K.: Modeling transfer and non-linear fare structure in multi-modal network. Transp. Res. B 37(2), 149–170 (2003)Google Scholar
  43. Lu, X.L., Pas, E.I.: Socio-demographics, activity participation, and travel behavior. Transp. Res. A 33(1), 1–18 (1999)Google Scholar
  44. MacLennan, C.: Parking and traffic demand, the policy background, In: TRL Parking Seminar and Parking Control in the 90 s, pp. 125–128 (1993)Google Scholar
  45. Ma, J., Mitchell, G., Heppenstall, A.: Daily travel behaviour in Beijing, China: an analysis of workers’ trip chains, and the role of socio-demographics and urban form. Habitat Int. 43, 263–273 (2014)Google Scholar
  46. Marsden, G.: The evidence base for parking policies—a review. Transp. Policy 13(6), 2006 (2006)Google Scholar
  47. Maruyama, T., Harata, N.: Incorporating trip-chaining behavior into network equilibrium analysis. Transp. Res. Rec. 1921, 11–18 (2005)Google Scholar
  48. Maruyama, T., Sumalee, A.: Efficiency and equity comparison of cordon- and area-based road pricing schemes using a trip-chain equilibrium model. Transp. Res. A 41, 655–671 (2007)Google Scholar
  49. Meng, Q., Yang, H.: Benefit distribution and equity in road network design. Transp. Res. B 36, 19–35 (2002)Google Scholar
  50. Ottosson, D., Chen, C., Wang, T., Lin, H.: The sensitivity of on-street parking demand in response to price charge: a case study in Seattle, WA. Transp. Policy. 25, 222–232 (2013)Google Scholar
  51. Paleti, R., Vovsha, P., Vyas, G., Anderson, R., Giaimo, R.: Activity sequencing, location, and formation of individual non-mandatory tours: application to the activity-based models for Columbus, Cincinnati, and Cleveland OH. Transportation 44, 615–640 (2017)Google Scholar
  52. Prashker, J.N., Bekhor, S.: Investigation of stochastic network loading procedures. Transp. Res. Rec. 1645, 94–102 (1998)Google Scholar
  53. Pravinvongvuth, S., Chen, A.: Adaptation of the paired combinatorial logit model to the route choice problem. Transportmetrica 1(3), 223–240 (2005)Google Scholar
  54. Romeijin, H.E., Smith, R.L.: Simulated annealing for constrained global optimization. J. Glob. Optimum. 5, 101–126 (1994)Google Scholar
  55. Roth, G.J.: Paying for Parking. The institute of Economic Affairs, London (1965)Google Scholar
  56. Scheiner, J., Holz-Rau, C.: Women’s complex daily lives: a gendered look at trip chaining and activity pattern entropy in Germany. Transportation 44, 117–138 (2017)Google Scholar
  57. Schmöcker, J.D., Su, F., Noland, R.B.: An analysis of trip chaining among older London residents. Transportation 37(1), 105–123 (2010)Google Scholar
  58. Scott, D.M., Kanaroglou, P.S.: An activity-episode generation model that captures interactions between household heads: development and empirical analysis. Transp. Res. B 36(10), 875–896 (2002)Google Scholar
  59. Sheffi, Y.: Urban transportation networks-equilibrium analysis with mathematical programming methods. Prentice-hall, Englewood Cliffs (1985)Google Scholar
  60. Shiftan, Y.: Practical approach to model trip chaining. Transp. Res. Rec. 1645, 17–23 (1998)Google Scholar
  61. Shoup, D.: The trouble with minimum parking requirements. Transp. Res. A 8(2), 115–124 (1999)Google Scholar
  62. Small, K.A., Rosen, H.S.: Applied welfare economics with discrete choice models. Econometrica 49, 105–130 (1981)Google Scholar
  63. Timmermans, H., Arentze, T., Joh, C.H.: Modeling effects of anticipated time pressure on execution of activity programs. Transp. Res. Rec. 1752, 8–15 (2001)Google Scholar
  64. Wallace, B., Barnes, J., Rutherford, G.S.: Evaluating the effects of traveler and trip characteristics on trip chaining, with implications for transportation demand management strategies. Transp. Res. Rec. 1718, 97–106 (2000)Google Scholar
  65. Wardrop, J.G.: Some theoretical aspects of road traffic research. Proc. Inst. Civil Eng. II 1, 325–378 (1952)Google Scholar
  66. Williams, H.C.W.L.: On the formation of travel demand models and economic evaluation measures of user benefits. Environ. Plan. A 9, 285–344 (1977)Google Scholar
  67. Yamamoto, T., Kitamura, R.: An analysis of time allocation to in-home and out-of-home discretionary activities across working days and non-working days. Transportation 26(2), 211–230 (1999)Google Scholar
  68. Yang, H.: System optimum, stochastic user system optimum, stochastic user. Transp. Sci. 33(4), 354–360 (1999)Google Scholar
  69. Yang, H., Zhang, X.N.: Multiclass network toll design problem with social and spatial equity constraints. J. Transp. Eng. 128, 420–428 (2002)Google Scholar
  70. Yu, X., Chuan, J.: Research on the interdependencies between commute mode choice and trip chaining behavior. In: The 20th International Conference on Management Science and Engineering, pp. 2042–2046 (2013)Google Scholar
  71. Zhao, J.B., Wang, J., Deng, W.: Exploring bike-sharing travel time and trip chain by gender and day of the week. Transp. Res. C 58, 251–264 (2015)Google Scholar
  72. Zhou, Z., Chen, A., Bekhor, S.: C-logit stochastic user equilibrium model: formulations and solution algorithm. Transportmetrica 8(1), 17–41 (2012)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Key Laboratory of Urban Transportation Complex Systems Theory and Technology of Ministry of EducationBeijing Jiaotong UniversityBeijingChina

Personalised recommendations