Synchronized timetables for bus rapid transit networks in small and large cities

Document Type : Article


1 Department of Industrial Engineering, Urmia University, Urmia, Iran.

2 Toos Institute of Higher Education, Mashhad, Iran

3 Department of Management Studies, Indian Institute of Technology Delhi, New Delhi, India


The quality of public transportation service has major effects on people’s quality of life. During frequency and timetable setting, synchronization is a very important and complicated issue which can directly influence the utility and attractiveness of the system. In this paper, a mixed-integer nonlinear programming model is proposed that aims at setting timetables on a bus transit network with the maximum synchronization and the minimum number of fleet size. The proposed model is shown to be applicable for both small and large-scale transit networks by employing it for setting timetables on two samples of both sizes. As an illustrative example, a simple version of the model is coded and run in GAMS Software and a completely reasonable timetable is obtained. As the second example, the proposed model is used to set timetables on Tehran BRT networks through the genetic algorithm; then the NSGA-II is used to obtain the Pareto optimal solutions of the problem for five different scenarios. The Pareto optimal solutions are used to draw the Pareto optimal fronts which act as an essential decision making tool. The overall results show that the proposed model is efficient enough to be employed setting timetables on transit networks with different sizes.


Main Subjects

1. Liu, T., Ceder, A., Ma, J., and Guan, W. Synchronizing
public transport transfers by using intervehicle
communication scheme: Case study", Transportation
Research Record: Journal of the Transportation Research
Board, 2417(1), pp. 78{91 (2014).
2. Ceder, A. Public transit planning and operation:
Theory, modeling and practice", In Elsevier,
Butterworth-Heinemann, Oxford, UK (2007).
3. Desaulniers, G. and Hickman, M.D. Public transit",
Handbooks in Operations Research and Management
Science, 14, pp. 69{127 (2007).
4. Guihaire, V. and Hao, J.K. Transit network design
and scheduling: A global review", Transportation
Research Part A: Policy and Practice, 42(10), pp.
1251{1273 (2008).
5. Wu, Y., Yang, H., Tang, J., and Yu, Y. Multiobjective
re-synchronizing of bus timetable: Model,
complexity and solution", Transportation Research
Part C: Emerging Technologies, 67, pp. 149{168
6. Ibarra-Rojas, O.J., Delgado, F., Giesen, R., and
Mu~noz, J.C. Planning, operation, and control of bus
transport systems: A literature review", Transportation
Research Part B: Methodological, 77, pp. 38{75
7. Wu, Y., Tang, J., Yu, Y., and Pan, Z. A stochastic
optimization model for transit network timetable design
to mitigate the randomness of traveling time by
adding slack time", Transportation Research Part C:
Emerging Technologies, 52, pp. 15{31 (2015).
8. Ibarra-Rojas, O.J., Lopez-Irarragorri, F., and Rios-
Solis, Y.A. Multiperiod bus timetabling", Transportation
Science, 50(3), pp. 805{822 (2015).
9. Nagatani, T. Nonlinear-map model for bus schedule
in capacity-controlled transportation", Applied Mathematical
Modelling, 37(4), pp. 1823{1835 (2013).
10. Gershenson, C. and Pineda, L.A. Why does public
transport not arrive on time? The pervasiveness of
equal headway instability", PloS One, 4(10), e7292
11. Petersen, H.L., Larsen, A., Madsen, O.B., Petersen,
B., and Ropke, S. The simultaneous vehicle scheduling
and passenger service problem", Transportation
Science, 47(4), pp. 603{616 (2012).
12. Kang, L. and Zhu, X. A simulated annealing algorithm
for rst train transfer problem in urban railway
networks", Applied Mathematical Modelling, 40(1), pp.
419{435 (2016).
13. Guo, X., Wu, J., Sun, H., Liu, R., and Gao, Z.
Timetable coordination of rst trains in urban railway
network: A case study of Beijing", Applied Mathematical
Modelling, 40(17), pp. 8048{8066 (2016).
14. Ceder, A., Golany, B., and Tal, O. Creating bus
timetables with maximal synchronization", Transportation
Research Part A: Policy and Practice,
35(10), pp. 913{928 (2001).
15. Eranki, A. A model to create bus timetables to attain
maximum synchronization considering waiting times
at transfer stops", Master Thesis, University of South
Florida (2004).
16. Currie, G. and Bromley, L. Developing measures of
public transport schedule coordination quality", 28th
Australasian Transport Research Forum (2005).
17. Quak, C.B. Bus line planning", Master Thesis, TU
Delft (2003).
18. Ibarra-Rojas, O.J. and Rios-Solis, Y.A. Integrating
synchronization bus timetabling and single-depot
single-type vehicle scheduling", ORP3 Meeting, Cadiz,
Spain (2011).
19. Shafahi, Y. and Khani, A. A practical model for
transfer optimization in a transit network: Model
formulations and solutions", Transportation Research
Part A: Policy and Practice, 44(6), pp. 377{389
20. Cevallos, F. and Zhao, F. Minimizing transfer times
in public transit network with genetic algorithm",
Transportation Research Record: Journal of the Transportation
Research Board, 1971(1), pp. 74{79 (2006).
21. Jansen, L.N., Pedersen, M.B., and Nielsen, O.A. Minimizing
passenger transfer times in public transport
timetables", Proceedings of the Seventh Conference of
the Hong Kong Society for Transportation Studies:
Transportation in the Information Age, Hong Kong,
China, pp. 229{239 (2002).
22. Chakroborty, P., Deb, K., and Subrahmanyam, P.S.
Optimal scheduling of urban transit systems using
genetic algorithms", Journal of Transportation Engineering,
121(6), pp. 544{553 (1995).
23. Chakroborty, P., Deb, K., and Porwal, H. A genetic
algorithm based procedure for optimal transit systems
scheduling", Proceedings of the Fifth International
Conference on Computers in Urban Planning and
Urban Management, Mumbai, India, pp. 330{0341
24. Daduna, J.R. and VoB, S. Practical experiences in
schedule synchronization", In Computer-Aided Transit
Scheduling, Lecture Notes in Economics and Mathe490
Sh. Ataeian et al./Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 477{491
matical Systems, Springer, Berlin, Heidelberg, 430, pp.
39{55 (1995).
25. Gao, Z., Sun, H., and Shan, L.L. A continuous
equilibrium network design model and algorithm for
transit systems", Transportation Research Part B:
Methodological, 38(3), pp. 235{250 (2004).
26. Bookbinder, J. and Desilets, A. Transfer optimization
in a transit network", Transportation Science, 26(2),
pp. 106{118 (1992).
27. Ting, C.J. and Schonfeld, P. Schedule coordination
in a multiple hub transit network", Journal of Urban
Planning and Development, 131(2), pp. 112{124
28. Knoppers, P. and Muller, T. Optimized transfer
opportunities in public transport", Transportation Science,
29(1), pp. 101{105 (1995).
29. Yu, B., Yang, Z., Cheng, C., and Liu, C. Optimizing
bus transit network with parallel ant colony
algorithm", Proceedings of the Eastern Asia Society for
Transportation Studies, 5(1), pp. 374{389 (2005).
30. Poorzahedy, H. and Abulghasemi, F. Application of
ant system to network design problem", Transportation,
32(3), pp. 251{273 (2005).
31. Yang, Z.Z., Yu, B., and Cheng, C.T. A parallel
ant colony algorithm for bus network optimization",
Computer-Aided Civil and Infrastructure Engineering,
22(1), pp. 44{55 (2007).
32. Peng, K. and Shen, Y. A variable iterated greedy
algorithm based on grey relational analysis for crew
scheduling", Scientia Iranica, Transactions E, Industrial
Engineering, 25(2), pp. 831{840 (2018).
33. Fleurent, C., Lessard, R., and Seguin, L. August.
transit timetable synchronization: Evaluation and
optimization", Proceedings of the 9th International
Conference on Computer-Aided Scheduling of Public
Transport, San Diego, US, pp. 9{11 (2004).
34. Castelli, L., Pesenti, R., and Ukovich, W. Scheduling
multimodal transportation systems", European Journal
of Operational Research, 155(3), pp. 603{615
35. Rapp, M.H. and Gehner, C.D. Transfer optimization
in an interactive graphic system for transit planning",
No. Intrm Rpt., pp. 27{33 (1967).
36. Deb, K. and Chakroborty, P. Time scheduling of transit
systems with transfer considerations using genetic
algorithms", Evolutionary Computation, 6(1), pp.1{24
37. Chakroborty, P., Deb, K., and Sharma, R.K. Optimal

eet size distribution and scheduling of urban transit
systems using genetic algorithms", Transportation
Planning and Technology, 24(3), pp. 209{226 (2001).
38. Ngamchai, S. and Lovell, D.J. Optimal time transfer
in bus transit route network design using a genetic
algorithm", Journal of Transportation Engineering,
129(5), pp. 510{521 (2003).
39. Pattnaik, S.B., Mohan, S., and Tom, V.M. Urban bus
transit route network design using genetic algorithm",
Journal of Transportation Engineering, 124(4), pp.
368{375 (1998).
40. Chien, S., Yang, Z., and Hou, E. Genetic algorithm
approach for transit route planning and design", Journal
of Transportation Engineering, 127(3), pp. 200{
207 (2001).
41. Bielli, M., Caramia, M., and Carotenuto, P. Genetic
algorithms in bus network optimization", Transportation
Research Part C, 10(1), pp. 19{34 (2002).
42. Chakroborty, P. and Dwivedi, T. Optimal route
network design for transit systems using genetic algorithms",
Engineering Optimization, 34(1), pp. 83{100
43. Tom, V.M. and Mohan, S. Transit route network design
using frequency coded genetic algorithm", Journal
of Transportation Engineering, 129(2), pp. 186{195
44. Kuan, S.N., Ong, H.L., and Ng, K.M. Solving the
feeder bus network design problem by genetic algorithms
and ant colony optimization", Advances in
Engineering Software, 37(6), pp. 351{359 (2006).
45. Agrawal, J. and Mathew, T.V. Transit route network
design using parallel genetic algorithm", Journal of
Computing in Civil Engineering, 18(3), pp. 248{256
46. Fan, W. and Machemehl, R. Optimal transit route
network design problem with variable transit demand:
genetic algorithm approach", Journal of Transportation
Engineering, 132(1), pp. 40{51(2006).
47. Zhao, F. and Zeng, X. Simulated annealing-genetic
algorithm for transit network optimization", Journal
of Computing in Civil Engineering, 20(1), pp. 57{68
48. Ibarra-Rojas, O.J. and Rios, Y. Synchronization of
bus timetabling", Transportation Research Part B:
Methodological, 46(5), pp. 599{614 (2012).
49. Abraham, A. and Jain, L. Evolutionary multi objective
optimization", In Evolutionary Multi Objective
Optimization, Abraham, A., Jain, L., and Goldberg,
R., Eds., pp. 1{6, Springer, London, UK (2005).
50. Holland, J.H., Adaptation in Natural and Arti cial
Systems: An Introductory Analysis with Applications
to Biology, Control, and Arti cial Intelligence, MIT
press, Cambridge, MA (1992).
51. Amiripour, S.M., Ceder, A.A., and Mohaymany, A.S.
Designing large-scale bus network with seasonal variations
of demand", Transportation Research Part C:
Emerging Technologies, 48, pp. 322{338 (2014).
52. Deb, K., Pratap, A., Agarwal, S., and Meyarivan,
T.A.M.T. A fast and elitist multi objective genetic
Sh. Ataeian et al./Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 477{491 491
algorithm: NSGA-II", IEEE Transactions on Evolutionary
Computation, 6(2), pp. 182{197 (2002).
53. Habibnejad-Ledari, H., Rabbani, M., and Ghorbani-
Kutenaie, N. Solving a multi-objective model toward
home care sta planning considering cross-training and
sta 's preferences by NSGA-II and NRGA", Scientia
Iranica, 26(5), pp. 2919{2935 (2019).