Distribution of traffic speed in different traffic conditions: an empirical study in Budapest

    Mohammad Maghrour Zefreh Affiliation
    ; Adám Török Affiliation


Fundamental diagram, a graphical representation of the relationship among traffic flow, speed, and density, has been the foundation of traffic flow theory and transportation engineering for many years. Underlying a fundamental diagram is the relation between traffic speed and density, which serves as the basis to understand system dynamics. Empirical observations of the traffic speed versus traffic density show a wide-scattering of traffic speeds over a certain level of density, which would form a speed distribution over a certain level of density. The main aim of the current research is to study on the distribution of traffic speed in different traffic conditions in the urban roads since the distribution of traffic speed is necessary for many traffic engineering applications including generating traffic in micro-simulation systems. To do so, the traffic stream is videotaped at various locations in the city of Budapest (Hungary). The recorded videos were analysed by traffic engineering experts and different traffic conditions were extracted from these recorded videos based on the predefined scenarios. Then their relevant speeds in that time interval were estimated with the so-called “g-estimator method” using the outputs of the available loop detectors among the videotaped locations. Then different parametric candidate distributions have been fitted to the speeds by Maximum Likelihood Estimation (MLE) method. Having fitted different parametric distributions to speed data, they were compared by three goodness-of-fit tests along with two penalized criteria (Akaike Information Criterion – AIC and Bayesian Information Criterion – BIC) in order to overcome the over-fitting problems. The results showed that the speed of traffic flow follows exponential, normal, lognormal, gamma, beta and chisquare distribution in the condition that traffic flow followed over-saturated congestion, under saturated flow, free flow, congestion, accelerated flow and decelerated flow respectively.

Keyword : speed distribution, traffic condition, urban road traffic, traffic flow dynamics, speed–density relationship, interrupted traffic flow

How to Cite
Maghrour Zefreh, M., & Török, A. (2020). Distribution of traffic speed in different traffic conditions: an empirical study in Budapest. Transport, 35(1), 68-86.
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Mar 18, 2020
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Bassani, M.; Catani, L.; Cirillo, C.; Mutani, G. 2016. Night-time and daytime operating speed distribution in urban arterials, Transportation Research Part F: Traffic Psychology and Behaviour 42: 56–69.

Bella, F.; Calvi, A. 2013. Effects of simulated day and night driving on the speed differential in tangent–curve transition: a pilot study using driving simulator, Traffic Injury Prevention 14(4): 413–423.

Bella, F.; Calvi, A.; D’Amico, F. 2014. Analysis of driver speeds under night driving conditions using a driving simulator, Journal of Safety Research 49: 45–52.

Berry, D. S.; Belmont, D. M. 1951. Distribution of vehicle speeds and travel times, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 31 July – 12 August 1950, University of California, CA, US, 589–602.

Casella, G.; Berger, R. L. 2002. Statistical Inference. Cengage. 688 p.

Castro, M.; Sánchez, J. A.; Vaquero, C. M.; Iglesias, L.; Rodríguez-Solano, R. 2008. Automated GIS-based system for speed estimation and highway safety evaluation, Journal of Computing in Civil Engineering 22(5): 325–331.

Chandra, S.; Bharti, A. K. 2013. Speed distribution curves for pedestrians during walking and crossing, Procedia – Social and Behavioral Sciences 104: 660–667.

Cullen, A. C.; Frey, H. C. 1999. Probabilistic Techniques in Exposure Assessment: a Handbook for Dealing with Variability and Uncertainty in Models and Inputs. Springer. 336 p.

D’Agostino, R. B. 2017. Goodness-of-Fit-Techniques. CRC Press. 576 p.

Delignette-Muller, M. L.; Dutang, C. 2015. Fitdistrplus: an R package for fitting distributions, Journal of Statistical Software 64(4): 1–34.

Dey, P. P.; Chandra, S.; Gangopadhaya, S. 2006. Speed distribution curves under mixed traffic conditions, Journal of Transportation Engineering 132(6): 475–481.

Du, Y.; Deng, F.; Liao, F.; Ji, Y. 2017. Understanding the distribution characteristics of bus speed based on geocoded data, Transportation Research Part C: Emerging Technologies 82: 337–357.

Fitzpatrick, K.; Carlson, P. J.; Wooldridge, M. D.; Brewer, M. A. 2000. Design Factors that Affect Driver Speed on Suburban Arterials. Report No FHWA/TX-00/1769-3. Texas Department of Transportation, Austin, TX, US. 164 p.

Gerlough, D. L.; Huber, M. J. 1975. Traffic Flow Theory: a Monograph. Transportation Research Board. 222 p.

Haight, F. A.; Mosher, W. W. 1962. A practical method for improving the accuracy of vehicular speed distribution measurements, Highway Research Board Bulletin 341: 92–116.

Hustim, M.; Fujimoto, K. 2012. Road traffic noise under heterogeneous traffic condition in Makassar city, Indonesia, Journal of Habitat Engineering and Design 4(1): 109–118.

Iannone, G.; Guarnaccia, C.; Quartieri, J. 2013. Speed distribution influence in road traffic noise prediction, Environmental Engineering and Management Journal 12(3): 493–501.

IMAGINE. 2006. Improved Methods for the Assessment of the Generic Impact of Noise in the Environment (IMAGINE). Funded under: FP6-Policies 2003–2006. Available from Internet:

Jiang, R.; Wu, Q.-S. 2007. The night driving behavior in a carfollowing model, Physica A: Statistical Mechanics and its Applications 375(1): 297–306.

Jun, J. 2010. Understanding the variability of speed distributions under mixed traffic conditions caused by holiday traffic, Transportation Research Part C: Emerging Technologies 18(4): 599–610.

Leong, H. J. 1968. The distribution and trend of free speeds on two lane two way rural highways in New South Wales, in 4th Australian Road Research Board (ARRB) Conference, 1968, Melbourne, Australia, 4(1): 791–814.

Liao, F. 2016. Modeling duration choice in space–time multi-state supernetworks for individual activity-travel scheduling, Transportation Research Part C: Emerging Technologies 69: 16–35.

Liao, F.; Arentze, T.; Timmermans, H. 2013. Incorporating space–time constraints and activity-travel time profiles in a multi-state supernetwork approach to individual activity-travel scheduling, Transportation Research Part B: Methodological 55: 41–58.

Lin, S.; He, M.; Tan, Y.; He, M. 2008. Comparison study on operating speeds of electric bicycles and bicycles: experience from field investigation in Kunming, China, Transportation Research Record: Journal of the Transportation Research Board 2048: 52–59.

Llorca, C.; Moreno, A. T.; Lenorzer, A.; Casas, J.; Garcia, A. 2015. Development of a new microscopic passing maneuver model for two-lane rural roads, Transportation Research Part C: Emerging Technologies 52: 157–172.

Lustri, C. 2010. Continuum Modelling of Traffic Flow. University of Sydney, Australia. 15 p. Available from Internet:

Maghrour Zefreh, M.; Baranyai, D.; Török, Á. 2016. Assessing the possibility of presenting a semi-stochastic speed–density function, MATEC Web Conference 81: 04002.

Maghrour Zefreh, M.; Török, Á. 2018a. Single loop detector data validation and imputation of missing data, Measurement 116: 193–198.

Maghrour Zefreh, M.; Török, Á. 2018b. Theoretical comparison of the effects of different traffic conditions on urban road traffic noise, Journal of Advanced Transportation 2018: 7949574.

Maghrour Zefreh, M.; Török, Á.; Mészáros, F. 2017. Average vehicles length in two-lane urban roads: a case study in Budapest, Periodica Polytechnica Transportation Engineering 45(4): 218–222.

Maurya, A. K.; Dey, S.; Das, S. 2015. Speed and time headway distribution under mixed traffic condition, Journal of the Eastern Asia Society for Transportation Studies 11: 1774–1792.

Maurya, A. K.; Das, S.; Dey, S.; Nama, S. 2016. Study on speed and time-headway distributions on two-lane bidirectional road in heterogeneous traffic condition, Transportation Research Procedia 17: 428–437.

McLean, J. R. 1979. Observed speed distributions and rural road traffic operations, in 9th Australian Road Research Board (ARRB) Conference, 21–25 August 1978, Brisbane, Australia, 9(5): 235–244.

Minh, C. C.; Sano, K.; Matsumoto, S. 2005. The speed, flow and headway analyses of motorcycle traffic, Journal of the Eastern Asia Society for Transportation Studies 6: 1496–1508.

Park, B.; Schneeberger, J. D. 2003. Microscopic simulation model calibration and validation: case study of vissim simulation model for a coordinated actuated signal system, Transportation Research Record: Journal of the Transportation Research Board 1856: 185–192.

Qu, X.; Zhang, J.; Wang, S. 2017. On the stochastic fundamental diagram for freeway traffic: model development, analytical properties, validation, and extensive applications, Transportation Research Part B: Methodological 104: 256–271.

Trozzi, C.; Vaccaro, R.; Crocetti, S. 1996. Speed frequency distribution in air pollutants’ emissions estimate from road traffic, Science of the Total Environment 189–190: 181–185.

Vadeby, A.; Forsman, Å. 2017. Changes in speed distribution: applying aggregated safety effect models to individual vehicle speeds, Accident Analysis & Prevention 103: 20–28.

Vadeby, A.; Forsman, Å. 2016. Speed distribution and traffic safety measures, in G. Yannis, S. Cohen (Eds.). Traffic Safety 4: 161–176.

Wang, D.; Zhou, D.; Jin, S.; Ma, D. 2015. Characteristics of mixed bicycle traffic flow on the conventional bicycle path, in TRB 94th Annual Meeting Compendium of Papers, 11–15 January 2015, Washington, DC, US, 1–14.

Wang, H.; Li, J.; Chen, Q.; Ni, D. 2009. Speed–density relationship: from deterministic to stochastic, in TRB 88th Annual Meeting Compendium of Papers DVD, 11–15 January 2009, Washington, DC, US, 1–20.

Wang, H.; Ni, D.; Chen, Q.-Y.; Li, J. 2013. Stochastic modeling of the equilibrium speed–density relationship, Journal of Advanced Transportation 47(1): 126–150.

Wang, Y.; Dong, W.; Zhang, L.; Chin, D.; Papageorgiou, M.; Rose, G.; Young, W. 2012. Speed modeling and travel time estimation based on truncated normal and lognormal distributions, Transportation Research Record: Journal of the Transportation Research Board 2315: 66–72.

Yu, R.; Abdel-Aty, M. 2014. An optimal variable speed limits system to ameliorate traffic safety risk, Transportation Research Part C: Emerging Technologies 46: 235–246.

Zou, Y. 2013. A Multivariate Analysis of Freeway Speed and Headway Data. PhD Dissertation. Texas A&M University, TX, US. 122 p. Available from Internet:

Zou, Y.; Zhang, Y. 2011. Use of skew-normal and skew-t distributions for mixture modeling of freeway speed data, Transportation Research Record: Journal of the Transportation Research Board 2260: 67–75.