The VLDB Journal

, Volume 27, Issue 3, pp 321–345 | Cite as

Go slow to go fast: minimal on-road time route scheduling with parking facilities using historical trajectory

  • Lei Li
  • Kai Zheng
  • Sibo Wang
  • Wen Hua
  • Xiaofang Zhou
Regular Paper


For thousands of years, people have been innovating new technologies to make their travel faster, the latest of which is GPS technology that is used by millions of drivers every day. The routes recommended by a GPS device are computed by path planning algorithms (e.g., fastest path algorithm), which aim to minimize a certain objective function (e.g., travel time) under the current traffic condition. When the objective is to arrive the destination as early as possible, waiting during travel is not an option as it will only increase the total travel time due to the First-In-First-Out property of most road networks. However, some businesses such as logistics companies are more interested in optimizing the actual on-road time of their vehicles (i.e., while the engine is running) since it is directly related to the operational cost. At the same time, the drivers’ trajectories, which can reveal the traffic conditions on the roads, are also collected by various service providers. Compared to the existing speed profile generation methods, which mainly rely on traffic monitor systems, the trajectory-based method can cover a much larger space and is much cheaper and flexible to obtain. This paper proposes a system, which has an online component and an offline component, to solve the minimal on-road time problem using the trajectories. The online query answering component studies how parking facilities along the route can be leveraged to avoid predicted traffic jam and eventually reduce the drivers’ on-road time, while the offline component solves how to generate speed profiles of a road network from historical trajectories. The challenging part of the routing problem of the online component lies in the computational complexity when determining if it is beneficial to wait on specific parking places and the time of waiting to maximize the benefit. To cope with this challenging problem, we propose two efficient algorithms using minimum on-road travel cost function to answer the query. We further introduce several approximation methods to speed up the query answering, with an error bound guaranteed. The offline speed profile generation component makes use of historical trajectories to provide the traveling time for the online component. Extensive experiments show that our method is more efficient and accurate than baseline approaches extended from the existing path planning algorithms, and our speed profile is accurate and space efficient.


Road network Shortest path Trajectory 



This research is partially supported by Natural Science Foundation of China (Grant Nos. 61232006, 61502324 and 61532018) and the Australian Research Council (LP130100164 and DP170101172).


  1. 1.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Goldberg, A.V., Harrelson, C.: Computing the shortest path: a search meets graph theory. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 156–165. Society for Industrial and Applied Mathematics (2005)Google Scholar
  3. 3.
    Wu, L., Xiao, X., Deng, D., Cong, G., Zhu, A.D., Zhou, S.: Shortest path and distance queries on road networks: an experimental evaluation. Proc. VLDB Endow. 5(5), 406–417 (2012)CrossRefGoogle Scholar
  4. 4.
    Kanoulas, E., Du, Y., Xia, T., Zhang, D.: Finding fastest paths on a road network with speed patterns. In: Proceedings of the 22nd International Conference on Data Engineering, ICDE’06, p. 10. IEEE (2006)Google Scholar
  5. 5.
    Ding, B., Yu, J.X., Qin, L.: Finding time-dependent shortest paths over large graphs. In: Proceedings of the 11th International Conference on Extending Database Technology: Advances in Database Technology, pp. 205–216. ACM (2008)Google Scholar
  6. 6.
    Chabini, I.: Discrete dynamic shortest path problems in transportation applications: complexity and algorithms with optimal run time. Transp. Res. Rec. J. Transp. Res. Board 1645, 170–175 (1998)CrossRefGoogle Scholar
  7. 7.
    Orda, A., Rom, R.: Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. J. ACM (JACM) 37(3), 607–625 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Demiryurek, U., Banaei-Kashani, F., Shahabi, C., Ranganathan, A.: Online computation of fastest path in time-dependent spatial networks. In: Pfoser, D., et al. (eds.) Advances in spatial and temporal databases, pp. 92–111. Springer, Berlin (2011)CrossRefGoogle Scholar
  9. 9.
    Cai, X., Kloks, T., Wong, C.: Time-varying shortest path problems with constraints. Networks 29(3), 141–150 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Dreyfus, S.E.: An appraisal of some shortest-path algorithms. Oper. Res. 17(3), 395–412 (1969)CrossRefzbMATHGoogle Scholar
  11. 11.
    Demiryurek, U., Pan, B., Banaei-Kashani, F., Shahabi, C.: Towards modeling the traffic data on road networks. In: Proceedings of the Second International Workshop on Computational Transportation Science, pp. 13–18. ACM (2009)Google Scholar
  12. 12.
    Zheng, B., Su, H., Hua, W., Zheng, K., Zhou, X., Li, G.: Efficient clue-based route search on road networks. IEEE Trans. Knowl. Data Eng. 29, 1846 (2017)CrossRefGoogle Scholar
  13. 13.
    Li, L., Hua, W., Du, X., Zhou, X.: Minimal on-road time route scheduling on time-dependent graphs. Proc. VLDB Endow. 10(11), 1274–1285 (2017)CrossRefGoogle Scholar
  14. 14.
    Cooke, K.L., Halsey, E.: The shortest route through a network with time-dependent internodal transit times. J. Math. Anal. Appl. 14(3), 493–498 (1966)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Geisberger, R.: Contraction of timetable networks with realistic transfers. In: Festa, P. (ed.) Experimental algorithms, pp. 71–82. Springer, Berlin (2010)CrossRefGoogle Scholar
  16. 16.
    Wu, H., Cheng, J., Huang, S., Ke, Y., Lu, Y., Xu, Y.: Path problems in temporal graphs. Proc. VLDB Endow. 7(9), 721–732 (2014)CrossRefGoogle Scholar
  17. 17.
    Wang, S., Lin, W., Yang, Y., Xiao, X., Zhou, S.: Efficient route planning on public transportation networks: a labelling approach. In: Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, pp. 967–982. ACM (2015)Google Scholar
  18. 18.
    Halpern, J.: Shortest route with time dependent length of edges and limited delay possibilities in nodes. Z. Oper. Res. 21(3), 117–124 (1977)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Orda, A., Rom, R.: Minimum weight paths in time-dependent networks. Networks 21(3), 295–319 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Foschini, L., Hershberger, J., Suri, S.: On the complexity of time-dependent shortest paths. Algorithmica 68(4), 1075–1097 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Cai, X., Kloks, T., Wong, C.: Shortest path problems with time constraints. In: International Symposium on Mathematical Foundations of Computer Science, pp. 255–266. Springer (1996)Google Scholar
  22. 22.
    Batz, G.V., Delling, D., Sanders, P., Vetter, C.: Time-dependent contraction hierarchies. In: Proceedings of the Meeting on Algorithm Engineering and Experiments, pp. 97–105. Society for Industrial and Applied Mathematics (2009)Google Scholar
  23. 23.
    Delling, D.: Time-dependent sharc-routing. Algorithmica 60(1), 60–94 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Li, L., Zhou, X., Zheng, K.: Finding least on-road travel time on road network. In: Australasian Database Conference, pp. 137–149. Springer (2016)Google Scholar
  25. 25.
    Yang, Y., Gao, H., Yu, J.X., Li, J.: Finding the cost-optimal path with time constraint over time-dependent graphs. Proc. VLDB Endow. 7(9), 673–684 (2014)CrossRefGoogle Scholar
  26. 26.
    Adler, J.D., Mirchandani, P.B., Xue, G., Xia, M.: The electric vehicle shortest-walk problem with battery exchanges. Netw. Spat. Econ. 16(1), 155–173 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Ichimori, T., Ishii, H., Nishida, T.: Routing a vehicle with the limitation of fuel. J. Oper. Res. Soc. Jpn. 24(3), 277–281 (1981)CrossRefzbMATHGoogle Scholar
  28. 28.
    Xiao, Y., Thulasiraman, K., Xue, G., Jüttner, A.: The constrained shortest path problem: algorithmic approaches and an algebraic study with generalization. AKCE Int. J. Graphs Comb. 2(2), 63–86 (2005)MathSciNetzbMATHGoogle Scholar
  29. 29.
    Wang, S., Xiao, X., Yang, Y., Lin, W.: Effective indexing for approximate constrained shortest path queries on large road networks. Proc. VLDB Endow. 10(2), 61–72 (2016)CrossRefGoogle Scholar
  30. 30.
    Blokh, D., Gutin, G.: An approximate algorithm for combinatorial optimization problems with two parameters. Australas. J. Comb. 14, 157–164 (1996)MathSciNetzbMATHGoogle Scholar
  31. 31.
    Juttner, A., Szviatovski, B., Mécs, I., Rajkó, Z.: Lagrange relaxation based method for the QoS routing problem. In: Proceedings of the Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies, INFOCOM 2001, vol. 2, pp. 859–868. IEEE (2001)Google Scholar
  32. 32.
    Tong, Y., Wang, L., Zhou, Z., Ding, B., Chen, L., Ye, J., Xu, K.: Flexible online task assignment in real-time spatial data. Proc. VLDB Endow. 10(11), 1334–1345 (2017)CrossRefGoogle Scholar
  33. 33.
    Tong, Y., Chen, Y., Zhou, Z., Chen, L., Wang, J., Yang, Q., Ye, J., Lv, W.: The simpler the better: a unified approach to predicting original taxi demands based on large-scale online platforms. In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1653–1662. ACM (2017)Google Scholar
  34. 34.
    Dai, J., Yang, B., Guo, C., Jensen, C.S., Hu, J.: Path cost distribution estimation using trajectory data. PVLDB 10(3), 85–96 (2016)Google Scholar
  35. 35.
    Bakalov, P., Hoel, E., Heng, W.-L.: Time dependent transportation network models. In: 2015 IEEE 31st International Conference on Data Engineering (ICDE), pp. 1364–1375. IEEE (2015)Google Scholar
  36. 36.
    Yang, B., Guo, C., Jensen, C.S.: Travel cost inference from sparse, spatio temporally correlated time series using Markov models. Proc. VLDB Endow. 6(9), 769–780 (2013)CrossRefGoogle Scholar
  37. 37.
    Shang, J., Zheng, Y., Tong, W., Chang, E., Yu, Y.: Inferring gas consumption and pollution emission of vehicles throughout a city. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1027–1036. ACM (2014)Google Scholar
  38. 38.
    Xin, X., Lu, C., Wang, Y., Huang, H.: Forecasting collector road speeds under high percentage of missing data. In: AAAI, pp. 1917–1923 (2015)Google Scholar
  39. 39.
    Asif, M.T., Mitrovic, N., Garg, L., Dauwels, J., Jaillet, P.: Low-dimensional models for missing data imputation in road networks. In: 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3527–3531. IEEE (2013)Google Scholar
  40. 40.
    Shan, Z., Zhao, D., Xia, Y.: Urban road traffic speed estimation for missing probe vehicle data based on multiple linear regression model. In: 16th International IEEE Conference on Intelligent Transportation Systems-(ITSC), pp. 118–123. IEEE (2013)Google Scholar
  41. 41.
    Widhalm, P., Piff, M., Brändle, N., Koller, H., Reinthaler, M.: Robust road link speed estimates for sparse or missing probe vehicle data. In: 15th International IEEE Conference on Intelligent Transportation Systems (ITSC), pp. 1693–1697. IEEE (2012)Google Scholar
  42. 42.
    Guo, C., Jensen, C.S., Yang, B.: Towards total traffic awareness. SIGMOD Rec. 43(3), 18–23 (2014)CrossRefGoogle Scholar
  43. 43.
    Guo, C., Yang, B., Andersen, O., Jensen, C.S., Torp, K.: Ecomark 2.0: empowering eco-routing with vehicular environmental models and actual vehicle fuel consumption data. GeoInformatica 19(3), 567–599 (2015)CrossRefGoogle Scholar
  44. 44.
    Idé, T., Sugiyama, M.: Trajectory regression on road networks. In: AAAI (2011)Google Scholar
  45. 45.
    Zheng, J., Ni, L.M.: Time-dependent trajectory regression on road networks via multi-task learning. In: AAAI (2013)Google Scholar
  46. 46.
    Yang, B., Kaul, M., Jensen, C.S.: Using incomplete information for complete weight annotation of road networks. IEEE Trans. Knowl. Data Eng. 26(5), 1267–1279 (2014)CrossRefGoogle Scholar
  47. 47.
    Zhang, J., Zheng, Y., Qi, D.: Deep spatio-temporal residual networks for citywide crowd flows prediction. In: AAAI, pp. 1655–1661 (2017)Google Scholar
  48. 48.
    Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM (JACM) 34(3), 596–615 (1987)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Lou, Y., Zhang, C., Zheng, Y., Xie, X., Wang, W., Huang, Y.: Map-matching for low-sampling-rate GPS trajectories. In: Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pp. 352–361. ACM (2009)Google Scholar
  50. 50.
    Yuan, J., Zheng, Y., Zhang, C., Xie, X., Sun, G.-Z.: An interactive-voting based map matching algorithm. In: Proceedings of the 2010 Eleventh International Conference on Mobile Data Management, pp. 43–52. IEEE Computer Society (2010)Google Scholar
  51. 51.
    Quddus, M.A., Ochieng, W.Y., Noland, R.B.: Current map-matching algorithms for transport applications: state-of-the art and future research directions. Transp. Res. Part C Emerg. Technol. 15(5), 312–328 (2007)CrossRefGoogle Scholar
  52. 52.
    Cox, D.R.: The regression analysis of binary sequences. J. R. Stat. Soc. Ser. B (Methodol.) 1, 215–242 (1958)MathSciNetzbMATHGoogle Scholar
  53. 53.
    Seal, H.L.: The Historical Development of the Gauss Linear Model. Yale University, New Haven (1968)zbMATHGoogle Scholar
  54. 54.
    Shatkay, H., Zdonik, S.B.: Approximate queries and representations for large data sequences. In: Proceedings of the Twelfth International Conference on Data Engineering, pp. 536–545. IEEE (1996)Google Scholar
  55. 55.
    Keogh, E., Chu, S., Hart, D., Pazzani, M.: Segmenting time series: a survey and novel approach. Data Min. Time Ser. Databases 57, 1–22 (2004)CrossRefGoogle Scholar
  56. 56.
    Esling, P., Agon, C.: Time-series data mining. ACM Comput. Surv. (CSUR) 45(1), 12 (2012)CrossRefzbMATHGoogle Scholar
  57. 57.
    Li, C.-S., Yu, P.S., Castelli, V.: Malm: A framework for mining sequence database at multiple abstraction levels. In: Proceedings of the Seventh International Conference on Information and Knowledge Management, pp. 267–272. ACM (1998)Google Scholar
  58. 58.
    Keogh, E .J., Pazzani, M .J.: An enhanced representation of time series which allows fast and accurate classification, clustering and relevance feedback. KDD 98, 239–243 (1998)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of ITEEUniversity of QueenslandBrisbaneAustralia
  2. 2.School of Computer Science and EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina
  3. 3.School of Computer Science and TechnologySoochow UniversitySuzhouChina

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