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Traffic arrivals at signal intersection approaches is inherently stochastic. This variability is typically reflected by I-ratio and there is a general consensus that the presence or absence of nearby upstream signal affects Variance to Mean Ratio (I-ratio). However, the effect of time resolution on arrival variability and the interaction effect between upstream signal and time resolution is yet to be examined in detail. This can lead to model misspecification and invariably, erroneous outcomes. This work examines the effect of time resolution and intersection type and their interaction on I-ratio and the resultant probability distributions. Traffic arrivals were measured at high time resolution- 10 seconds interval and then aggregated to lower time resolutions (30-150 seconds) at six intersections. Spectral density analysis showed statistically significant periodicity, specifically at 30 seconds interval with p-values < 0.0001 at all connected intersections while observations at isolated intersections lacked periodicity. Two-way ANOVA using I-ratio as the dependent variable and intersection type and time-resolution as the independent variables was performed. Statistically significant effect with F-value 8.606 at p-value < 0.0001 and R2 value 0.32 were observed. Intersection type, time resolution and the interaction between them were statistically significant, with p-values 0.002, < 0.0001 and 0.000 respectively. The combined effect of these factors led to a wide I-ratio range of 0.37-9.2. Negative Binomial, Poisson, and Binomial distributions represented 76.4, 20.4 and 4.2% of all I-ratios observed. Therefore, in contrast to literature which recommends Poisson, Negative Binomial may be a better suited probability distribution for traffic arrivals.
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Adams, W. F. (1936). Road traffic considered as a random series. J. Inst. Civ. Engrs, 4, 121-130. https://dx.doi.org/10.1680/ijoti.1936.14802
Akcelik, R. (1988). The highway capacity manual delay formula for signalized intersections. ITE journal,58(3), 23-27
Armstrong, R. A., Eperjesi, F., and Gilmartin. B. (2002) The application of analysis of variance (ANOVA) to different experimental designs in optometry. Ophthal. Physiol. Opt. 22: 248-256
Barua, S., Das, A., & Roy, C.K (2015). Estimation of Traffic Arrival Pattern at Signalized Intersection Using ARIMA Model. International Journal of Computer Applications (0975-8887). https://dx.doi.org/10.13140/RG.2.1.5029.9363
Beckmann, M. J., McGuire, C. B., & Winsten, C. B. (1956). Studies in the Economics of Transportation. Yale University Press.
Cheng Cheng, Yuchuan Du, Lijun Sun & Yuxiong Ji (2015): Review on Theoretical Delay Estimation Model for Signalized Intersections, Transport Reviews. https://dx.doi.org/10.1080/01441647.2015.1091048
Farivar, S (2015). Modeling Capacity and Delay at Signalized Intersections with Channelized Right-turn Lanes Considering the Impact of Blockage. PhD Thesis. University of Nevada, Reno, Department of Civil and Environmental Engineering,
Francesco Viti & Henk J. Van Zuylen (2009) The Dynamics and the Uncertainty of Queues at Fixed and Actuated Controls: A Probabilistic Approach, Journal of Intelligent Transportation Systems, 13:1, 39-51 https://dx.doi.org/10.1080/15472450802644470
Gerlough D.L., and Barnes, F.C. Poisson and Other Distributions in Traffic. Eno Foundation for Transportation, Saugatuck, CT, 1971
Gerlough D.L., and Huber, M.J. Traffic Flow Theory. TRB, Special Rept. 165, 1975
Greenshields, B. D., Shapiro, D., & Ericksen, E. L. (1947). Traffic Performance at Urban Street Intersections. New Haven, CT: Tech. Rep. No. 1, Yale Bureau of Highway Traffic
Ha, D. H., Aron, M., & Cohen, S. (2012). Time Headway variable and probabilistic modeling. Transportation Research Part C, 25, 181-201. https://dx.doi.org/10.1016/j.trc.2012.06.002
Harahap, E., Darmawan, D., Fajar, Y., Ceha, R., Rachmiatie, A. (2019) Modeling and simulation of queue waiting time at traffic light intersection. Journal of Physics: 1188(2019) 012001 https://dx.doi.org/10.1088/1742-6596/1188/1/012001
HCM. (1985-2010). Highway capacity manual. Washington, DC: Transportation Research Board.
Heidemann, D. (1994) Queue Length and Delay Distributions at Traffic Signals. Transpn. Res.-B. Vol. 28B, No. 5, pp. 377-389
Kim, H (2014) Statistical notes for clinical researchers: Two-way analysis of variance (ANOVA)-exploring possible interaction between factors. Open lecture on statistics https://dx.doi.org/10.5395/rde.2014.39.2.143
Kinzer, J. P. (1933). Application of the Theory of Probability to Problems of Highway Traffic. Inst. Traff. Engrs.,5, 118-124
Law, A.M. (2013). A Tutorial On How To Select Simulation Input Probability Distributions. Proceedings of the 2013 Winter Simulation Conference
Leeuwaarden, van, J. S. H. (2006). Delay analysis for the fixed-cycle traffic-light queue. (Report Eurandom; Vol. 2006014). Eindhoven: Eurandom.
Mauro, R., & Branco, F. Update on the Statistical Analysis of Traffic Counting on Two-Lane Rural Highways. Modern Applied Science; Vol. 7, No. 6; 2013. https://dx.doi.org/10.5539/mas.v7n6p6
May, A. D. (1990). Traffic flow fundamentals. New Jersey, NY: Prentice Hall
Miller, A. J. (1963). Settings for fixed-cycle traffic signals. OR, 373-386.
Moineddin, R., Upshur, R.E.G., Crighton, E., and Mamdani, M. (2003). Autoregression as a means of assessing the strength of seasonality in a time series. Population Health Metrics 2003, 1:10 http://www.pophealthmetrics.com/content/1/1/10
Newell, G. F. (1960). Queues for a fixed-cycle traffic light. The Annals of Mathematical Statistics, 31(3), 589-597.
Newell, G. F. (1965). Approximation methods for queues with application to the fixed-cycle traffic light. SIAM Review, 7, 223-240.
Olszewski, P. (1990). Modeling of Queue Probability Distribution at Traffic Signals. In Proceedings of the 11th International Symposium on Transportation and Traffic Theory. M. Koshi. Amsterdam, Elsevier: 549-588
Olszewski, P., S. (1994) Modeling probability distribution of delay at signalized intersections. Journal of advanced transportation. Vol 28, No. 3, pp 253-274. https://dx.doi.org/10.1002/atr.5670280306
Ritchie, S.G. (1983) Application of Counting Distribution for High Variance Urban Traffic Counts. Transportation Research Record 905
Rouphail, N., Tarko, A., & Li, J. (1999). Traffic flow at signalized intersections. Transportation Research Board Special Report 165 (Traffic flow theory), Chapter 9. Washington, DC.
SAS Institute Inc. (2018). User's Guide The SPECTRA Procedure
Tian, J., & Fernandez, G.C. (1998). Seasonal Trend Analysis of Monthly Water Quality Data (June 1, 1998). University of Alberta School of Business Research Paper No. 2013-1203,The Western Users of SAS Software, 1999, Available at SSRN: https://ssrn.com/abstract=2284439
Webster, F. V. (1958). Traffic Signal Settings. Road Research Technical Paper, 39.
Xing, Y., Gao, Z., Qu, Z., Hu, H. (2016) Study on Vehicle Delay Based on the Vehicle Arriving Distribution at Entrance Lanes of Intersection. Procedia Engineering 137, 599-608. https://dx.doi.org/10.1016/j.proeng.2016.01.297