Abstract
The random process of counts has been introduced in the previous Sect. 1.2.1.Counting process and time headway process in traffic play a central role in highway design and control.
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Notes
- 1.
To calculate s2 we have used the expression \( {\text{s}}^{2} = ({\text{m}}_{2} - {\bar{\text{x}}}^{2} \cdot {\text{N}})/({\text{N}} - 1) \) where \( {\text{m}}_{2} = \sum {{\text{x}}_{\text{i}}^{2} } \cdot {\text{f}}_{\text{i}} \) is the sample second moment.
- 2.
With flow = 7.469 veh/15 s \( \cong \) 1800 veh/h, through indications in Table 5.3, we obtain \( {\text{k}} = 3 \) in place of \( {\text{k}} = 2 \). This difference in determining the numerical value of the same parameter arises quite frequently when statistical procedures of different origin are used in treating the same dataset. Quite obviously, the final model estimation is made by implementing a parameter suitable to find the model which at its best provides a close approximation to the measured counting distribution.
References
Gerlough, D.L., Huber, M.J., Traffic Flow Theory, TRB Report 165, Washington D. C., 1975
Haight, F.A., The Generalized Poisson Distribution”, Ann.Inst.Statist.Math, vol. 11, 1959
Kottegoda, N.T., Rosso, R., Applied Statistics for Civil and Environmental Engineers, Wiley-Blackwell, Hoboken, N.J., 2008
Gore, A., Paranjpe, S., A Course in Mathematical and Statistical Ecology, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001
Mauro, R., Branco, F., Update on the Statistical Analysis of Traffic Countings on Two-Lane Rural Highways”, Modern Applied Science, Vol. 7, n. 6, 2013
Papoulis, A., Pillai, U.S., Probability, Random Variables and Stochastic Processes, McGraw Hill, New York, 2002
May, A.D., Traffic Flow Fundamentals, Prentice Hall, New Jersey, 1990
Wentzel, E., Ovcharov, L., Applied Problems in Probability Theory, Mir Publisher Moscow, 1986
Cao, M., Tai, A.H., Chan, L.Y., New statistical distributions for group counting in Bernoulli and Poisson processes, Test, n. 21, 29–53, 2012
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Mauro, R. (2015). Counting Process. In: Traffic and Random Processes. Springer, Cham. https://doi.org/10.1007/978-3-319-09324-6_5
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