Abstract
This paper proposes a new activity-based transit assignment model for investigating the scheduling (or timetabling) problem of transit services in multi-modal transit networks. The proposed model can be used to generate the short-term and long-term timetables of multimodal transit lines for transit operations and service planning purposes. The interaction between transit timetables and passenger activity-travel scheduling behaviors is captured by the proposed model, as the activity and travel choices of transit passengers are considered explicitly in terms of departure time choice, activity/trip chain choices, activity duration choice, transit line and mode choices. A heuristic solution algorithm which combines the Hooke–Jeeves method and an iterative supply–demand equilibrium approach is developed to solve the proposed model. Two numerical examples are presented to illustrate the differences between the activity-based approach and the traditional trip-based method, together with comparison on the effects of optimal timetables with even and uneven headways. It is shown that the passenger travel scheduling pattern derived from the activity-based approach is significantly different from that obtained by the trip-based method, and that a demand-sensitive (with uneven headway) timetable is more efficient than an even-headway timetable.






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References
Ashiru, O., Polak, J.W., Noland, R.B.: Utility of schedules: theoretical model of departure-time choice and activity-time allocation with application to individual activity schedules. Transp. Res. Rec. 1894, 84–98 (2004)
Arentze, T.A., Timmermans, H.J.P.: A need-based model of multi-day, multi-person activity generation. Transp. Res. Part B 43(2), 251–265 (2009)
Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming: Theory and Algorithms. Wiley, Hoboken, New Jersey (2006)
Ben-Akiva, M., Lerman, S.R.: Discrete Choice Analysis: Theory and Application to Travel Demand. MIT Press, Cambridge, MA (1985)
Caprara, A., Fischetti, M., Toth, P.: Modeling and solving the train timetabling problem. Oper. Res. 50(5), 851–861 (2002)
Ceder, A.: Methods for creating bus timetables. Transp. Res. Part A 21(1), 59–83 (1986)
Ceder, A.: Public transport timetabling and vehicle scheduling. In: Lam, W.H.K., Bell, M.G.H., (eds.) Advanced Modeling for Transit Operations and Service Planning, pp. 31–57. Pergamon, Oxford (2003)
Chen, C.H., Yan, S., Tseng, C.H.: Inter-city bus scheduling for allied carriers. Transportmetrica 6(3), 161–185 (2010)
Crisalli, U., Rosati, L.: DY-RT: a tool for schedule-based planning of regional transit networks. In: Wilson, N.H.M., Nuzzolo, A. (eds.) Schedule-Based Dynamic Transit Modeling: Theory and Applications, pp. 135–158. Kluwer Academic Publishers, The Netherland (2004)
De Cea, J., Fernandez, E.: Transit assignment for congested public transport system: an equilibrium model. Transp. Sci. 27(2), 133–147 (1993)
De Palma, A., Lindsey, R.: Optimal timetables for public transportation. Transp. Res. Part B 35(8), 789–813 (2001)
Ettema, D., Timmermans, H.J.P.: Activity-Based Approaches to Travel Analysis. Oxford, Pergamon (1997)
Ettema, D., Timmermans, H.J.P.: Modeling departure time choice in the context of activity scheduling behavior. Transp. Res. Rec. 1831, 39–46 (2003)
Granas, A., Dugundji, J.: Fixed Point Theory. New York, Springer (2003)
Habib, K.M.N., Miller, E.J.: Modelling activity generation: a utility-based model for activity-agenda formulation. Transportmetrica 5(1), 3–23 (2009)
Hensher, D.A.: Some insights into the key influences on trip-chaining activity and public transport use of seniors and the elderly. Int. J. Sustain. Transp. 1(1), 53–68 (2007)
Huang, H.J., Li, Z.C., Lam, W.H.K., Wong, S.C.: A time-dependent activity and travel choice model with multiple parking options. In: Mahmassani, H. (ed.) Transportation and Traffic Theory, pp. 717–739. Elsevier, Oxford (2005)
Joh, C.H., Arentze, T.A., Timmermans, H.J.P.: Modeling individuals’ activity-travel rescheduling heuristics: Theory and numerical experiments. Transp. Res. Rec. 1807, 16–25 (2002)
Jones, P.M., Koppelman, F.S., Orfeuil, J.P.: Activity analysis: state of the art and future directions. In: Jones, P. (ed.) Developments in Dynamic and Activity-Based Approaches to Travel Analysis, pp. 34–55. Avebury, Aldershot, England (1990)
Kitamura, R.: An evaluation of activity-based travel analysis. Transportation 15(1), 9–34 (1988)
Kurauchi, F., Bell, M.G.H., Schmöcker, J.-D.: Capacity constrained transit assignment with common lines. J. Math. Model. Algorithm 2(4), 309–327 (2003)
Lam, W.H.K., Gao, Z.Y., Chan, K.S., Yang, H.: A stochastic user equilibrium assignment model for congested transit networks. Transp. Res. Part B 33(5), 351–368 (1999)
Lam, W.H.K., Zhou, J., Sheng, Z.: A capacity restraint transit assignment with elastic line frequency. Transp. Res. Part B 36(10), 919–938 (2002)
Lam, W.H.K., Yin, Y.: An activity-based time-dependent traffic assignment model. Transp. Res. Part B 35(6), 549–574 (2001)
Lam, W.H.K., Huang, H.J.: A combined activity/travel choice model for congested road networks with queues. Transportation 29(1), 5–29 (2002)
Li, Z.C., Lam, W.H.K., Wong, S.C.: The optimal transit fare structure under different market regimes with uncertainty in the network. Netw. Spat. Econ. 9(2), 191–216 (2009)
Lo, H.K., Yip, C.W., Wan, K.H.: Modeling transfer and non-linear fare structure in multi-modal network. Transp. Res. Part B 37(2), 149–170 (2003)
Luo, Z.Q., Pang, J.S., Ralph, D.: Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge (1996)
Magnanti, T.L., Perakis, G.: Computing fixed points by averaging. In: Gendreau, M., Marcotte, P. (eds.) Transportation and Network Analysis: Current Trends, pp. 181–198. Kluwer Academic Publishers, Netherlands (2002)
Maruyama, T., Sumalee, A.: Efficiency and equity comparison of cordon- and area-based road pricing schemes using a trip-chain equilibrium model. Transp. Res. Part A 41(7), 655–671 (2007)
Nuzzolo, A., Russo, F., Crisalli, U.: A doubly dynamic schedule-based assignment model for transit networks. Transp. Sci. 35(3), 268–285 (2001)
Pendyala, R.M., Yamamoto, T., Kitamura, R.: On the formulation of time-space prisms to model constraints on personal activity-travel engagement. Transportation 29(1), 73–94 (2002)
Poon, M.H., Wong, S.C., Tong, C.O.: A dynamic schedule-based model for congested transit networks. Transp. Res. Part B 38(4), 343–368 (2004)
Ramadurai, G., Ukkusuri, S.: Dynamic user equilibrium model for combined activity-travel choices using activity-travel super network representation. Netw. Spat. Econ. 10(2), 273–292 (2010)
Schmöcker, J.-D., Bell, M.G.H., Kurauchi, F.: A quasi-dynamic capacity constrained frequency-based transit assignment model. Transp. Res. Part B 42(10), 925–945 (2008)
Sumalee, A., Tan, Z.J., Lam, W.H.K.: Dynamic stochastic transit assignment with explicit seat allocation model. Transp. Res. Part B 43(8–9), 895–912 (2009)
Timmermans, H.J.P.: Progress in Activity-Based Analysis. Elsevier, Amsterdam (2005)
Tong, C.O., Wong, S.C.: A stochastic transit assignment model using a dynamic schedule-based network. Transp. Res. Part B 33(2), 107–121 (1999)
Tong, C.O., Wong, S.C., Poon, M.H., Tan, M.C.: A scheduled based dynamic transit network model––recent advances and prospective future research. J. Adv. Transp. 35(2), 175–195 (2001)
Uchida, K., Sumalee, A., Watling, D.P., Connors, R.: A study on optimal frequency design problem for multi-modal network using probit-based user equilibrium assignment. Transp. Res. Rec. 1923, 236–245 (2005)
Wong, S.C., Tong, C.O.: Estimation of time-dependent origin–destination matrices and transit networks. Transp. Res. Part B 32(1), 35–48 (1998)
Wu, J.H., Florian, M., Marcotte, P.: Transit equilibrium assignment: a model and solution algorithm. Transp. Sci. 28(3), 193–203 (1994)
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)
Yamamoto, T., Fujii, S., Kitamura, R., Yoshida, H.: Analysis of time allocation, departure time, and route choice behavior under congestion pricing. Transp. Res. Rec. 1725, 95–101 (2000)
Zhang, X., Yang, H., Huang, H.J., Zhang, M.: Integrated scheduling of daily work activities and morning-evening commutes with bottleneck congestion. Transp. Res. Part A 39(1), 41–60 (2005)
Zhang, J.Y., Kuwano, M., Lee, B., Fujiwara, A.: Modeling household discrete choice behavior incorporating heterogeneous group decision-making mechanisms. Transp. Res. Part B 43(2), 230–250 (2009)
Zhao, F., Zeng, X.G.: Optimization of transit route network, vehicle headways and timetables for large-scale transit networks. Eur. J. Oper. Res. 186(2), 841–855 (2008)
Acknowledgements
The authors would like to thank the guest editors and three anonymous referees for their helpful comments and constructive suggestions on an earlier version of the manuscript. The work described in this paper was jointly supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region (PolyU 5215/09E), the Research Committee of the Hong Kong Polytechnic University (G-YX1V), the National Natural Science Foundation of China (70971045), the Foundation for the Author of National Excellent Doctoral Dissertation of China (200963), the University Research Committee of the University of Hong Kong (10400582/00002771), and the Program for New Century Excellent Talents in University of China (NCET-10-0385).
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Li, ZC., Lam, W.H.K., Wong, S.C. et al. An activity-based approach for scheduling multimodal transit services. Transportation 37, 751–774 (2010). https://doi.org/10.1007/s11116-010-9291-z
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DOI: https://doi.org/10.1007/s11116-010-9291-z

