TEST: Modelling Occupancy-Queue Relation using Gaussian Process

Jan Prikryl


One of the key indicators of the quality of service for urban transportation
control (UTC) systems is the queue length. Even in unsaturated conditions,
longer queues indicate longer travel delays and higher fuel consumption.
With the exception of some expensive surveillance equipment, the queue length
itself cannot be measured automatically, and manual measurement is both
impractical and costly in a long term scenario. Hence, many mathematical models
that express the queue length as a function of detector measurements are used
in engineering practice, ranging from simple to elaborate ones.  The method
proposed in this paper makes use of detector time-occupancy, a complementary
quantity to vehicle count, provided by most of the traffic detectors at no cost
and disregarded by majority of existing approaches for various reasons. Our model
is designed as a complement to existing methods. It is based on Gaussian-process
(GP) model of the occupancy-queue relationship, it can handle data uncertainties,
and it provides more information about the quality of the queue length prediction.


queue estimation; uncertainty; traffic model; Gaussian process


AKCELIK, R. Time-Dependent Expressions for Delay, Stop Rate and Queue Length at Traffic Signals. 1980.

AŽMAN, K. and J. KOCIJAN. Application of Gaussian processes for black-box modelling of biosystems. ISA Transactions. 2007, 46(4), pp. 443–457.

CHANG, G.-L. and C.-C. SU. Predicting Intersection Queue with Neural Network Models. Transportation Research Part C. 1995, 3(3), pp. 175–191.

CHANG, J., E. B. LIEBERMANN, and E. SHENK.PRASSAS. Queue Estimation Algorithm for Real-Time Control Policy using Detector Data. 2000. Available also from WWW: http://www.kldassociates.com/queuest.pdf.

DIAKAKI, C. Integrated Control of Traffic Flow in Corridor Networks. 1999.

FANG, F. C. and L. ELEFTERIADOU. Some Guidelines for Selecting Microsimulation Models for Interchange Traffic Operational Analysis. Journal of Transportation Engineering. 2005, 131(7), pp. 535–543.

FAUL, S. et al. Gaussian process modelling of EEG for the detection of neonatal seizure. IEEE Transactions on Biomedical Engineering. 2007, 54(12), pp. 2151–2162.

FRIEDRICH, B. et al. Data Fusion Techniques fo Adaptive Traffic Signal Control. In: Proceedings of 2003 IFAC Control in Transportaion Systems Conference. 2003.

GIRIANNA, M. and R. F. BENEKOHAL. Using genetic algorithms to design signal coordination for oversaturated networks. Journal of Intelligent Transportation Systems. 2004, 8(2), pp. 117–129.

GRAŠIČ, B., P. MLAKAR, and M. Z. BOŽNAR. Ozone prediction based on neural networks and Gaussian processes. Nuovo Cimento della Societa Italiana di Fisica, Sect. C. 2006, 29(6), pp. 651–662.

HENSHER, D. A. and K. J. BUTTON, eds. Handbook of Transport Modelling. 2000.

Highway Capacity Manual 2000. 2000.

HO, C.-H. and T.-L. HWANG. Modeling Real-Time Dynamic Queue Length for Urban Traffic Control Systems. In: Proceedings of the Intelligent Vehicles’94 Symposium. 1994, pp. 438–442.

HOMOLOVÁ, J. and I. NAGY. Traffic model of a microregion. In: HORÁČEK, P., M. ŠIMANDL, and P. ZÍTEK, eds. Preprints of the 16th World Congress of the International Federation of Automatic Control. Prague: IFAC, 2005, pp. 1–6.

KOCIJAN, J. and B. LIKAR. Gas-Liquid Separator Modelling and Simulation with Gaussian Process Models. In: Proceedings of the 6th EUROSIM Congress on Modelling and Simulation – EUROSIM 2007. 2007, pp. 7 pages.

LEDOUX, C. An Urban Traffic Flow Model Integrating Neural Networks. Transportation Research Part C. 1997, 5(5), pp. 287–300.

LEITH, D. J., M. HEIDL, and J. RINGWOOD. Gaussian process prior models for electrical load forecasting. In: Proceedings of 2004 International Conference on Probabilistic Methods Applied to Power Systems. 2004, pp. 112-117.

LEITHEAD, W. E., Y. ZHANG, and K. S. NEO. Wind turbine rotor acceleration: Identification using Gaussian regression. In: Proceedings of International conference on informatics in control automation and robotics (ICINCO). 2005, pp. 84–91.

LIKAR, B. and J. KOCIJAN. Predictive control of a gas-liquid separation plant based on a Gaussian process model. Computers and Chemical Engineering. 2007, 31(3), pp. 142–152.

MA, D. et al. A Method for Queue Length Estimation in an Urban Street Network Based on Roll Time Occupancy Data. Mathematical Problems in Engineering. 2012, 2012 pp. 12. Article ID 892575. doi: 10.1155/2012/892575.

MÜCK, J. Estimation Methods for the State of Traffic at Traffic Signals using

Detectors near the Stop-Line. Traffic Engineering and Control. 2002, 43(11),

pp. 429.

MYSTKOWSKI, C. and S. KHAN. Estimating Queue Lengths Using SIGNAL94, SYNCHRO3, TRANSYT-7F, PASSER II-90, and CORSIM. In: Proceedings of 78th Transportation Research Board Annual Meeting. 1998.

PAPAGEORGIOU, M. An integrated control approach for traffic corridors. Transportation Research Part C: Emerging Technologies. 1995, 3(1), pp. 19–30.

PAPAGEORGIOU, M. and G. VIGOS. Relating time-occupancy to space-occupancy and link vehicle-count. Transportation Research Part C. 2008, 16 pp. 1–17.

PŘIKRYL, J. and J. KOCIJAN. An Empirical Model of Occupancy-Queue Relation. In: Proceedings of 12th IFAC Symposium on Transportation Systems. 2009, pp. 000–000.

QUEK, C., M. PASQUIER, and B. B. S. LIM. POP-TRAFFIC: A Novel Fuzzy Neural Approach to Road Traffic Analysis and Prediction. IEEE Transactions on Intelligent Transportation Systems. 2006, 7(2), pp. 133–146.

RASMUSSEN, C. E. and C. K. WILLIAMS. Gaussian Processes for Machine Learning. Cambridge, MA: MIT Press, 2006.

SNELSON, E. Flexible and efficient Gaussian process models for machine

learning. 2007.

SNELSON, E., C. E. RASMUSSEN, and Z. GHAHRAMANI. Warped Gaussian processes. In: THRUN, S., L. K. SAUL, and B. SCHÖLKOPF, eds. Advances in Neural Information Processing Systems 16. 2004, pp. 337–344.

TRANSPORT SIMULATION SYSTEMS. AIMSUN: Advanced Interactive Microscopic Simulator for Urban and non-urban Networks. 2008. Available also from WWW: http://www.aimsun.com.

VIGOS, G., M. PAPAGEORGIOU, and Y. WANG. Real-time estimation of vehicle-count within signalized links. Transportation Research Part C. 2008, 16 pp. 18–35.

VILORIA, F., K. COURAGE, and D. AVERY. Comparison of Queue-Length Models at Signalized Intersections. Transportation Research Record. 2000, 1710 pp. 222–230.

VITI, F. and H. J. van ZUYLEN. Probabilistic models for queues at fixed control signals. Transportation Research Part B. 2009, 44(1), pp. 120–135. doi: 10.1016/j.trb.2009.05.001.

VITI, F. and H. J. van ZUYLEN. The dynamics and the uncertainty of queues at fixed and actuated controls: A probabilistic approach. Journal of Intelligent Transportation Systems: Technology, Planning, and Operations. 2009, 13(1), pp. 39–51. doi: 10.1080/15472450802644470.

VLAHOGIANNI, E. I., M. G. KARLAFTIS, and J. C. GOLIAS. Optimized and meta-optimized neural networks for short-term traffic flow prediction: A genetic approach. Transportation Research Part C. 2005, 13 pp. 211–234.

WANG, J. M., D. J. FLEET, and A. HERTZMANN. Gaussian Process Dynamical Models for Human Motion. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2008, 30(2), pp. 283–298.

YANG, D. et al. A robust vehicle queuing and dissipation detection method based on two cameras. In: Intelligent Transportation Systems (ITSC), 2011, 14th International IEEE Conference on. 2011, pp. 301–307.

ZHENG, J. et al. Measuring Signalized Intersection Performance in Real-

Time with Traffic Sensors. Journal of Intelligent Transportation Systems:

Technology, Planning, and Operations. 2013, 17(4), pp. 304–316. doi: 10.


ZUYLEN, H. J. van and F. VITI. Delay at controlled intersections: the old theory revised. In: Proceedigns of the 2006 IEEE Intelligent Treansportation Systems Conference. 2006, pp. 68–73.

ZUYLEN, H. J. van and F. VITI. Uncertainty and the Dynamics of Queues at Controlled Intersections. In: Proceedings of 2003 IFAC Control of Transporation Systems Conference. 2003.

DOI: http://dx.doi.org/10.14311/NNW.1901.%25x


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