Estimation of stochastic traffic capacity using extreme value theory and censoring: a case study in Salem, New Hampshire

• Autorzy: Laflamme E. M. , Ossenbruggen P. J.

Identyfikatory

DOI

10.5604/01.3001.0012.8366

• Języki publikacji: EN

Abstrakty

EN

In this work, we introduce a method of estimating stochastic freeway capacity using elements of both extreme value theory and survival analysis. First, we define capacity data, or estimates of the capacity of the roadway, as the daily maximum flow values. Then, under a survival analysis premise, we introduce censoring into our definition. That is, on days when flows are sufficiently high and congestion occurs, corresponding flow maxima are considered true estimates of capacity; otherwise, for those days that do not observe high flows or congestion, flow maxima are deemed censored observations and capacities must be higher than the observations. By extreme value theory, the collection of flow maxima (block maxima) can be appropriately approximated with a generalized extreme value (GEV) distribution. Because of small sample sizes and the presence of censoring, a Bayesian framework is pursued for model fitting and parameter estimation. To lend credence to our proposed methodology, the procedure is applied to real-world traffic stream data collected by the New Hampshire Department of Transportation (NHDOT) at a busy location on Interstate I-93 near Salem, New Hampshire. Data were collected over a period of 11 months and raw data were aggregated into 15-minute intervals. To assess our procedure, and to provide proof of concept, several validation procedures are presented. First, using distinct training and validation subsets of our data, the procedure yields accurate predictions of highway capacity. Next, our procedure is applied to a training set to yield random capacities which are then used to predict breakdown in the validation set. The frequency of these predicted breakdowns is found to be statistically similar to observed breakdowns observed in our validation set. Lastly, after comparing our methodology to other methods of stochastic capacity estimation, we find our procedure to be highly successful.

Słowa kluczowe

EN

stochastic capacity; estimation of traffic; daily flow maxima; capacity distribution function; censoring; computational Bayesian method

PL

przepustowość ruchu; szacowanie ruchu; metoda bayesowska

• Wydawca: Warsaw University of Technology, Faculty of Transport
• Czasopismo: Archives of Transport
• Rocznik: 2018
• Tom: Vol. 48, iss. 4
• Strony: 61--75
• Opis fizyczny: Bibliogr. 41 poz., rys., wykr.

Twórcy

autor

Laflamme E. M.

• Plymouth State University, Department of Mathematics, Plymouth, NH, USA

autor

Ossenbruggen P. J.

• University of New Hampshire, Department of Mathematics and Statistics, Durham, NH, USA

Bibliografia

• [1] AGYEMANG-DUAH, K. & HALL, F.L., 1991. Some Issues Regarding the Numerical Value of Freeway Capacity, Highway Capacity, and Level of Service. International Symposium on Highway Capacity. Karlsruhe, Netherlands, 1991. Rotterdam: AA Balkema, pp. 1-15.
• [2] BANKS, J.H., 2009. Flow Breakdown at Freeway Bottlenecks: Evidence from Automated Flow Analysis. Transportation Research Record: Journal of the Transportation Research Board. 2099(2009), pp. 14-21.
• [3] BHARADWAJ, N., MATHEW, S., PANI, A., ARKATKAR, S., JOSHI, G., & RAVINDER, K., 2016. Effect of Traffic Composition and Emergency Lane on Capacity: A Case Study of Intercity Expressway in India. Transportation Letters. DOI:10.1080/19427867.2016.1265237.
• [4] BRILON, W. & GEISTEFELDT, J., 2009. Implications of the Random Capacity Concept for Freeways. 2nd International Symposium on Freeway and Tollway Operations. Honolulu, HI, 2009.
• [5] BRILON, W., GEISTEFELDT, J., & REGLER, M., 2005. Reliability of Freeway Traffic Flow: A Stochastic Concept of Capacity. Proceedings of the 16th International Symposium on Transportation and Traffic Theory. College Park, Maryland, 2005, pp. 125-144.
• [6] BRILON, W., GEISTEFELDT, J. & ZURLINDEN, H., 2007. Implementing the Concept of Reliability for Highway Capacity Analysis. Transportation Research Record: Journal of the Transportation Research Board. 2027(2007), pp. 1-8.
• [7] BRILON, W. & ZURLINDEN, H., 2003. Overload probabilities and traffic activity as design criteria for road traffic systems. Research in Road Construction and Road-Traffic Technique (series). 870(2003).
• [8] CARLIN, B. P., & LOUIS, T.A., 2008. Bayesian Methods for Data Analysis. 3rd edition. Boca Raton, FL: Chapman and Hall/CRC.
• [9] CASSIDY, M.J. & BERTINI, R.L., 1999. Some Traffic Features at Freeway Bottlenecks. Transportation Research, Part B: Methodological. 33(1), pp. 25-42.
• [10] COLES, S., 2001. An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.
• [11] DONG, S., MOSTAFIZI, A., WANG, H., & LI, J., 2017. A Stochastic Analysis of Highway Capacity: Empirical Evidence and Implications. Journal of Intelligent Transportation Systems. DOI: 10.1080/15472450.2017.1396898.
• [12] ELEFTERIADOU, L. & LERTWORAWANICH, P., 2002. A Methodology for Estimating Capacity at Ramp Weaves Based on Gap Acceptance and Linear Optimization. Transportation Research, Part B: Methodological. 37B(5), pp. 459-483.
• [13] ELEFTERIADOU, L., ROESS, R.P., & MCSHANE, W.R., 1995. Probabilistic Nature of Breakdown at Freeway Merge Junctions. Transportation Research Record: Journal of the Transportation Research Board. 1484(1995), pp. 80-89.
• [14] GELMAN, A., CARLIN, J.B., STERN, H.S. & RUBIN, D.B., 2003. Bayesian Data Analysis. 2nd edition. Boca Raton, FL: Chapman and Hall/CRC.
• [15] GEISTEFELDT, J., 2008. Empirical Relation between Stochastic Capacities and Capacities Obtained from the Speed-Flow Diagram. Proceedings of the Symposium of the Fundamental Diagram: 75 years. Woods Hole, MA, 2008.
• [16] GEISTEFELDT, J., 2010. Consistency of Stochastic Capacity Estimations. Transportation Research Record: Journal of the Transportation Research Board. 2173(2010), pp. 89-95.
• [17] GEISTEFELDT, J. & BRILON, W., 2009. A Comparative Assessment of Stochastic Capacity Estimation Methods. 18th International Symposium on Transportation and Traffic Theory. Hong Kong, 2009.
• [18] HALL, F.L. & AGYEMANG-DUAH, K., 1991. Freeway Capacity Drop and the Definition of Capacity. Transportation Research Record: Journal of the Transportation Research Board. 1320(1991), pp. 91-98.
• [19] HALL, F.L., HURDLE, V., & BANKS, J., 1992. Synthesis of Recent Work on the Nature of Speed-Flow and Flow-Occupancy (or Density) Relationships on Freeways. Transportation Research Record: Journal of the Transportation Research Board. 1365 (1992), pp. 12-17.
• [20] HALL, R.W., 1995. Longitudinal and Lateral Throughput on an Idealized Highway. Transportation Science. 29(2), pp. 118-127.
• [21] HYDE, T. & WRIGHT, C.C., 1986. Extreme Value Methods for Estimating Road Traffic Capacity. Transportation Research, Part B: Methodological. 20B(2), pp. 125-138.
• [22] KAPLAN, E.L. & MEIER, P., 1958. Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association. 53, pp. 457-481.
• [23] KIM, J., MAHMASSANI, H. & DONG, J., 2010. Likelihood and duration of flow breakdown: modeling the effect of weather. Transportation Research Record: Journal of the Transportation Research Board. 2188(2010), pp. 19-28.
• [24] KUHNE, R.D., MAHNKE, R., & HINKEL, J., 2006. Modeling the Effects of Corridor Control Systems on Road Capacity. 5th International Symposium on Highway Capacity and Quality of Service. Yokohama, Japan, 2006, pp. 289-298.
• [25] LAFLAMME, E.M., 2013. Extreme value theory: Applications to estimation of stochastic traffic capacity and statistical downscaling of precipitation extremes. PhD. Thesis, University of New Hampshire (Durham, NH, USA).
• [26] LAFLAMME, E.M. & OSSENBRUGGEN, P.J., 2017. Effect of time-of-day and day-of the-week on congestion duration and breakdown: A case study at a bottleneck in Salem, NH. Journal of Traffic and Transportation Engineering (English Edition). 4(1), pp. 31-40.
• [27] LI, Z. & LAURENCE, R., 2015. An Analysis of Four Methodologies for Estimating Highway Capacity from ITS Data. Journal of Modern Transportation. 23(2), pp. 107-118.
• [28] LORENZ, M. & ELEFTERIADOU, L., 2001. Defining Freeway Capacity as Function of Breakdown Probability. Transportation Research Record: Journal of the Transportation Research Board. 1776(2001), pp. 43-51.
• [29] LUNN, D.J., THOMAS, A., BEST, N., & SPIEGELHALTER, D., 2000. WinBUGS - a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing. 10(2000), pp. 325–337.
• [30] MINDERHOUD, M.M., BOTMA, H., & BOVY, P.H.L., 1997. Assessement of Roadway Capacity Estimation Methods. Transportation Research Record: Journal of the Transportation Research Board. 1572(1997), pp. 59-67.
• [31] OZGUVEN, E. E. & OZBAY, K., 2008. Nonparametric Bayesian Estimation of Freeway Capacity Distribution from Censored Observations. Transportation Research Record: Journal of the Transportation Research Board. 2061(2008), pp. 20-29.
• [32] PERSAUD, B., YAGAR, S., & BROWNLEE, R., 1998. Exploration of the Breakdown Phenomenon in Freeway Traffic. Transportation Research Record: Journal of the Transportation Research Board. 1634(1998), pp. 64-69.
• [33] PERSAUD, B., YAGAR, S., TSUI, D., & LOOK, H., 2001. Study of Breakdown-Related Capacity for a Freeway with Ramp Metering. Transportation Research Record: Journal of the Transportation Research Board. 1748(2001), pp. 110-115.
• [34] PLUMMER, M., BEST, N., COWLES, K., & VINES, K., 2006. CODA: Convergence Diagnosis and Output Analysis for MCMC. R News. 6(2006), pp. 7-11.
• [35] PONZLET, M., 1996. Dynamik der Leistungsfähigkeiten von Autobahnen (Dynamics of Freeway Capacity). PhD. Dissertation, Institute for Transportation and Traffic Engineering, Ruhr-University Bochum.
• [36] R CORE TEAM, 2015. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria. Available from: http://www.Rproject.org/.
• [37] TRANSPORTATION RESEARCH BOARD, 2010. Highway Capacity Manual (HCM). Washington, D.C.
• [38] U.S. DEPARTMENT OF TRANSPORTATION, FEDERAL HIGHWAY ADMINISTRATION, 2012. Localized Bottleneck Reduction Program. U.S. Dept. of Transportation, Federal Highway Administration. [Viewed 2012]. Available from: http://www.ops.fhwa.dot.gov/bn/lbr.htm.
• [39] YANG, X. & ZHANG, N., 2005. The Marginal Decrease of Lane Capacity with the Number of Lanes on Highway. Proceedings of the Eastern Asia Society for Transportation Studies. 5(2005), pp. 739–749.
• [40] ZOCHOWSKA, R., 2014. Selected Issues in Modelling of Traffic Flows in Congested Urban Networks. Archives of Transport. 29(1), pp. 77-89.
• [41] ZURLINDEN, H., 2003. Ganzjahresanalyse des Verkehrsflusses auf Strassen (Whole year analysis of traffic flow on highways). Schriftenreihe des Lehrstuhls fuer Verkehrswesen der Ruhr-Universitaet Bochum. 26.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).