Modelling Occupancy-Queue Relation Using Gaussian Process

Jan Přikryl, Juš Kocijan


One of the key indicators of the quality of service for urban transportation control 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 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

Full Text:



AKÇELIK R. Time-Dependent Expressions for Delay, Stop Rate and Queue Length at Traffic Signals. Vermont South: Australian Road Research Board, 1980. Technical report AIR 367-1.

AŽMAN K., KOCIJAN J. Application of Gaussian processes for black-box modelling of biosystems. ISA Transactions. 2007, 46(4), pp. 443–457, doi: 10.1016/j.isatra.2007.04.001.

BISHOP C.M. Pattern recognition and machine learning. New York: Springer Science + Business Media, 2006. Information Science and Statistics series.

CHANG G.-L., SU C.-C. Predicting Intersection Queue with Neural Network Models. Transportation Research Part C: Emerging Technologies. 1995, 3(3), pp. 175–191, doi: 10.1016/0968-090X(95)00005-4.

CHANG J., LIEBERMANN E.B., SHENK PRASSAS E. Queue Estimation Algorithm for Real-Time Control Policy using Detector Data [online]. Huntington Station, NY: KLD Associates, 2000 [viewed 2015-01-19]. Technical report. Available from:

DIAKAKI C. Integrated Control of Traffic Flow in Corridor Networks. Chania, 1999. PhD thesis, Technical University of Crete.

FANG F.C., ELEFTERIADOU L. Some Guidelines for Selecting Microsimulation Models for Interchange Traffic Operational Analysis. Journal of Transportation Engineering. 2005, 131(7), pp. 535–543, doi: 10.1061/(ASCE)0733-947X(2005)131:7(535).

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, doi: 10.1109/TBME.2007.895745.

FRIEDRICH B., et al. Data Fusion Techniques for Adaptive Traffic Signal Control. In: S. TSUGAWA, M. AOKI, eds. Control in Transportation Systems 2003 (CTS ’03). A proceedings volume from the 10th IFAC Symposium, Tokyo, Japan. Amsterdam: Elsevier, 2003, pp. 86–91.

GIRIANNA M., BENEKOHAL R.F. Using genetic algorithms to design signal coordination for oversaturated networks. Journal of Intelligent Transportation Systems. 2004, 8(2), pp. 117–129, doi: 10.1080/15472450490435340.

GRAŠIČ B., MLAKAR P., BOŽNAR M.Z. Ozone prediction based on neural networks and Gaussian processes. Nuovo Cimento della Societa Italiana di Fisica, Sect. C. 2006, 29(6), pp. 651–662, doi: 10.1393/ncc/i2006-10011-5.

D.A. HENSHER, K.J. BUTTON, eds. Handbook of Transport Modelling. Oxford: Pergamon Press, 2000.

HO C.-H., HWANG T.-L. Modeling Real-Time Dynamic Queue Length for Urban Traffic Control Systems. In: Proceedings of the Intelligent Vehicles ’94 Symposium, Paris, France. Piscataway, NJ: IEEE, 1994, pp. 438–442, doi: 10.1109/IVS.1994.639558.

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

JOHANSEN T.A., SHORTEN R., MURRAY-SMITH R. On the Interpretation and Identification of Dynamic Takagi-Sugeno Fuzzy Models. IEEE Transactions on Fuzzy Systems. 2000, 8(3), pp. 297–313, doi: 10.1109/91.855918.

KLEIN L.A., MILLS M.K., GIBSON D.R. Traffic Detector Handbook: Third Edition – Volume I. McLean, VA: Federal Highway Administration, Turner-Fairbank Highway Research Center, 2006. Technical report FHWA-HRT-06-108.

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

KOCIJAN J., et al. Dynamic systems identification with Gaussian processes. Mathematical and Computer Modelling of Dynamic Systems. 2005, 11(4), pp. 411–424, doi: 10.1080/13873950500068567.

LAZARO-GREDILLA M. Bayesian warped Gaussian processes. In: F. PEREIRA, et al., eds. Advances in Neural Information Processing Systems 25: 26th Annual Conference on Neural Information Processing Systems 2012, Vancouver, Canada. Red Hook, NY: Curran Associates, Inc., 2013, pp. 1619–1627. Advances in Neural Information Processing Systems series. Available also from:

LEDOUX C. An Urban Traffic Flow Model Integrating Neural Networks. Transportation Research Part C: Emerging Technologies. 1997, 5(5), pp. 287–300, doi: 10.1016/S0968-090X(97)00015-6.

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

LEITHEAD W.E., ZHANG Y., NEO K.S. Wind turbine rotor acceleration: Identification using Gaussian regression. In: Proceedings of 2nd International conference on informatics in control automation and robotics (ICINCO 2005), Barcelona, Spain. Setúbal: INSTICC, 2005, pp. 84–91.

LIKAR B., KOCIJAN J. Predictive control of a gas-liquid separation plant based on a Gaussian process model. Computers and Chemical Engineering. 2007, 31(3), pp. 142–152, doi: 10.1016/j.compchemeng.2006.05.011.

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, Article ID 892575, 12 pp., 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.

R. MURRAY-SMITH, T.A. JOHANSEN, eds. Multiple model approaches to modelling and control. London: Taylor and Francis, 1997.

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

PAPAGEORGIOU M. An integrated control approach for traffic corridors. Transportation Research Part C: Emerging Technologies. 1995, 3(1), pp. 19–30, doi: 10.1016/0968-090X(94)00012-T.

PAPAGEORGIOU M., VIGOS G. Relating time-occupancy to space-occupancy and link vehicle-count. Transportation Research Part C: Emerging Technologies. 2008, 16(1), pp. 1–17, doi: 10.1016/j.trc.2007.06.001.

PŘIKRYL J., KOCIJAN J. An Empirical Model of Occupancy-Queue Relation. In: A. G. CHASSIAKOS, ed. Proceedings of 12th IFAC Symposium on Transportation Systems, Redondo Beach, CA, USA. Laxenburg, Austria: IFAC, 2009, pp. 456–461, doi: 10.3182/20090902-3-US-2007.00068.

QUEK C., PASQUIER M., LIM B.B.S. 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, doi: 10.1109/TITS.2006.874712.

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

SHI J.Q., CHOI T. Gaussian process regression analysis for functional data. Boca Raton, FL: Chapman and Hall/CRC, Taylor & Francis group, 2011.

SNELSON E. Flexible and efficient Gaussian process models for machine learning. London, 2007. PhD thesis, University College London.

SNELSON E., RASMUSSEN C.E., GHAHRAMANI Z. Warped Gaussian processes. In: S. THRUN, L. K. SAUL, B. SCHÖLKOPF, eds. Advances in Neural Information Processing Systems 16. Proceedings of NIPS 2003, Vancouver, Canada. Cambridge, MA: MIT Press, 2004, pp. 337–344. Available also from:

TRANSPORT SIMULATION SYSTEMS. AIMSUN v. 5.0.1. Advanced Interactive Microscopic Simulator for Urban and non-Urban Networks [software]. 2008-05-12.

TRANSPORTATION RESEARCH BOARD. Highway Capacity Manual 2000. Washington, DC: Transportation Research Board of the National Academies of Science, 2000.

Van ZUYLEN H. J., VITI F. Delay at controlled intersections: the old theory revised. In: Proceedigns of the 2006 IEEE Intelligent Transportation Systems Conference (IEEE ITSC 2006), Toronto, Canada. Piscataway, NJ: IEEE, 2006, pp. 68–73, doi: 10.1109/ITSC.2006.1706720.

Van ZUYLEN H. J., VITI F. Uncertainty and the Dynamics of Queues at Controlled Intersections. In: S. TSUGAWA, M. AOKI, eds. Control in Transportation Systems 2003 (CTS’03). A proceedings volume from the 10th IFAC Symposium, Tokyo, Japan. Amsterdam: Elsevier, 2003, pp. 43–48. Available also from:

VIGOS G., PAPAGEORGIOU M.,WANG Y. Real-time estimation of vehicle-count within signalized links. Transportation Research Part C: Emerging Technologies. 2008, 16(1), pp. 18–35, doi: 10.1016/j.trc.2007.06.002.

VILORIA F., COURAGE K., AVERY D. Comparison of Queue-Length Models at Signalized Intersections. Transportation Research Record. 2000, 1710, pp. 222–230, doi: 10.3141/1710-26.

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

VITI F., van ZUYLEN H.J. 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., KARLAFTIS M.G., GOLIAS J.C. Optimized and metaoptimized neural networks for short-term traffic flow prediction: A genetic approach. Transportation Research Part C. 2005, 13(3), pp. 211–234, doi: 10.1016/j.trc.2005.04.007.

WANG J.M., FLEET D.J., HERTZMANN A. Gaussian Process Dynamical Models for Human Motion. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2008, 30(2), pp. 283–298, doi: 10.1109/TPAMI.2007.1167.

YANG D., et al. A robust vehicle queuing and dissipation detection method based on two cameras. In: Proceedings of 14th International IEEE Conference on Intelligent Transportation Systems (IEEE ITSC 2011), Washington, DC. Piscataway, NJ: IEEE, 2011, pp. 301–307, doi: 10.1109/ITSC.2011.6082828.

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: 10.1080/15472450.2013.77110.



  • There are currently no refbacks.

Should you encounter an error (non-functional link, missing or misleading information, application crash), please let us know at
Please, do not use the above address for non-OJS-related queries (manuscript status, etc.).
For your convenience we maintain a list of frequently asked questions here. General queries to items not covered by this FAQ shall be directed to the journal editoral office at