# Shortest Path Routing in Transportation Networks with Time-Dependent Road Speeds

### Costas Constantinou, Georgios Ellinas, Christos Panayiotou, Marios Polycarpou

#### Abstract

This paper deals with the subject of shortest (in terms of traveling time) path routing in transportation networks, where the speed in the network’s roads is a function of the time interval. These networks are encountered in practice when the roads’ speed has been measured for several time instants during a large period of time (e.g., an entire year). In this way, time-dependent speed patterns can be derived for the network’s roads, that constitute an estimation of the network’s future behavior. For shortest path routing in these networks, the traveling time on the network’s roads must be calculated according to the time instant of departure. Conventional approaches perform this calculation under the assumption that the road’s speed has a constant (possibly distinct) value inside each time interval. In the work presented here, the assumption that the road’s speed is linear (possibly distinct) function of time inside each time interval, is considered. Under this assumption, a procedure is proposed that derives the traveling time on the network’s roads according to the time instant of departure. It is combined with Dijkstra’s algorithm, resulting in a practically applicable algorithm for optimal shortest path routing for the type of networks investigated in this work.

#### References

- Ahuja, R. K., Magnanti, T. L., and Orlin, J. B. (1993). Network flows: theory, algorithms, and applications. Prentice-Hall, Inc., Upper Saddle River, NJ, USA.
- Batz, G. V., Geisberger, R., Sanders, P., and Vetter, C. (2013). Minimum time-dependent travel times with contraction hierarchies. J. Exp. Algorithmics, 18:1.4:1.1-1.4:1.43.
- Chabini, I. (1998). Discrete dynamic shortest path problems in transportation applications: Complexity and algorithms with optimal run time. Transportation Research Records, 1645:170-175.
- Chabini, I. and Lan, S. (2002). Adaptations of the A* algorithm for the computation of fastest paths in deterministic discrete-time dynamic networks. Trans. Intell. Transport. Sys., 3(1):60-74.
- Cooke, K. and Halsey, E. (1966). The shortest route through a network with time-dependent internodal transit times. Journal of Mathematical Analysis and Applications, 14(3):493-498.
- Delling, D. (2011). Time-dependent sharc-routing. Algorithmica, 60(1):60-94.
- Delling, D. and Nannicini, G. (2012). Core routing on dynamic time-dependent road networks. INFORMS J. on Computing, 24(2):187-201.
- Delling, D., Sanders, P., Schultes, D., and Wagner, D. (2009). Algorithmics of large and complex networks. chapter Engineering Route Planning Algorithms, pages 117-139. Springer-Verlag, Berlin, Heidelberg.
- Delling, D. and Wagner, D. (2009). Time-dependent route planning. In Ahuja, R., Mhring, R., and Zaroliagis, C., editors, Robust and Online Large-Scale Optimization, volume 5868 of Lecture Notes in Computer Science, pages 207-230. Springer Berlin Heidelberg.
- Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1:269-271. 10.1007/BF01386390.
- Ding, B., Yu, J. X., and Qin, L. (2008). Finding timedependent shortest paths over large graphs. In Proceedings of the 11th International Conference on Extending Database Technology: Advances in Database Technology, EDBT 7808, pages 205-216, New York, NY, USA. ACM.
- Fredman, M. L. and Tarjan, R. E. (1987). Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM, 34(3):596-615.
- May, A. D. (1990). Traffic flow fundamentals . Prentice Hall.
- Nannicini, G., Delling, D., Schultes, D., and Liberti, L. (2012). Bidirectional A* search on time-dependent road networks. Networks, 59(2):240-251.
- Sung, K., Bell, M. G., Seong, M., and Park, S. (2000). Shortest paths in a network with time-dependent flow speeds. European Journal of Operational Research, 121(1):32-39.

#### Paper Citation

#### in Harvard Style

Constantinou C., Ellinas G., Panayiotou C. and Polycarpou M. (2016). **Shortest Path Routing in Transportation Networks with Time-Dependent Road Speeds** . In *Proceedings of the International Conference on Vehicle Technology and Intelligent Transport Systems - Volume 1: VEHITS,* ISBN 978-989-758-185-4, pages 91-98. DOI: 10.5220/0005807000910098

#### in Bibtex Style

@conference{vehits16,

author={Costas Constantinou and Georgios Ellinas and Christos Panayiotou and Marios Polycarpou},

title={Shortest Path Routing in Transportation Networks with Time-Dependent Road Speeds},

booktitle={Proceedings of the International Conference on Vehicle Technology and Intelligent Transport Systems - Volume 1: VEHITS,},

year={2016},

pages={91-98},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005807000910098},

isbn={978-989-758-185-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Vehicle Technology and Intelligent Transport Systems - Volume 1: VEHITS,

TI - Shortest Path Routing in Transportation Networks with Time-Dependent Road Speeds

SN - 978-989-758-185-4

AU - Constantinou C.

AU - Ellinas G.

AU - Panayiotou C.

AU - Polycarpou M.

PY - 2016

SP - 91

EP - 98

DO - 10.5220/0005807000910098