Abstract
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.
Similar content being viewed by others
References
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)
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)
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)
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)
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)
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)
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)
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)
Cai, X., Kloks, T., Wong, C.: Time-varying shortest path problems with constraints. Networks 29(3), 141–150 (1997)
Dreyfus, S.E.: An appraisal of some shortest-path algorithms. Oper. Res. 17(3), 395–412 (1969)
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)
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)
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)
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)
Geisberger, R.: Contraction of timetable networks with realistic transfers. In: Festa, P. (ed.) Experimental algorithms, pp. 71–82. Springer, Berlin (2010)
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)
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)
Halpern, J.: Shortest route with time dependent length of edges and limited delay possibilities in nodes. Z. Oper. Res. 21(3), 117–124 (1977)
Orda, A., Rom, R.: Minimum weight paths in time-dependent networks. Networks 21(3), 295–319 (1991)
Foschini, L., Hershberger, J., Suri, S.: On the complexity of time-dependent shortest paths. Algorithmica 68(4), 1075–1097 (2014)
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)
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)
Delling, D.: Time-dependent sharc-routing. Algorithmica 60(1), 60–94 (2011)
Li, L., Zhou, X., Zheng, K.: Finding least on-road travel time on road network. In: Australasian Database Conference, pp. 137–149. Springer (2016)
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)
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)
Ichimori, T., Ishii, H., Nishida, T.: Routing a vehicle with the limitation of fuel. J. Oper. Res. Soc. Jpn. 24(3), 277–281 (1981)
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)
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)
Blokh, D., Gutin, G.: An approximate algorithm for combinatorial optimization problems with two parameters. Australas. J. Comb. 14, 157–164 (1996)
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)
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)
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)
Dai, J., Yang, B., Guo, C., Jensen, C.S., Hu, J.: Path cost distribution estimation using trajectory data. PVLDB 10(3), 85–96 (2016)
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)
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)
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)
Xin, X., Lu, C., Wang, Y., Huang, H.: Forecasting collector road speeds under high percentage of missing data. In: AAAI, pp. 1917–1923 (2015)
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)
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)
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)
Guo, C., Jensen, C.S., Yang, B.: Towards total traffic awareness. SIGMOD Rec. 43(3), 18–23 (2014)
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)
Idé, T., Sugiyama, M.: Trajectory regression on road networks. In: AAAI (2011)
Zheng, J., Ni, L.M.: Time-dependent trajectory regression on road networks via multi-task learning. In: AAAI (2013)
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)
Zhang, J., Zheng, Y., Qi, D.: Deep spatio-temporal residual networks for citywide crowd flows prediction. In: AAAI, pp. 1655–1661 (2017)
Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM (JACM) 34(3), 596–615 (1987)
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)
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)
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)
Cox, D.R.: The regression analysis of binary sequences. J. R. Stat. Soc. Ser. B (Methodol.) 1, 215–242 (1958)
Seal, H.L.: The Historical Development of the Gauss Linear Model. Yale University, New Haven (1968)
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)
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)
Esling, P., Agon, C.: Time-series data mining. ACM Comput. Surv. (CSUR) 45(1), 12 (2012)
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)
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)
Acknowledgements
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).
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Li, L., Zheng, K., Wang, S. et al. Go slow to go fast: minimal on-road time route scheduling with parking facilities using historical trajectory. The VLDB Journal 27, 321–345 (2018). https://doi.org/10.1007/s00778-018-0499-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00778-018-0499-4