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Statistical modelling of traffic flow rate
Grabec, Igor ; Kalcher, Kurt, 1955 ; Švegl, Franc
Road traffic is a consequence of population activity to which many individuals participate. In spite of this, the traffic flow does not exhibit completely random character since the population ...activity is synchronized to a high extent. The synchronization is stimulated externally by environment due to variable illumination by solar light and weather conditions, and internally by population itself due to agreements about working days and holidays. The external stimulation can be physically described by the time and variables representing weather conditions, while the internal SIRWEC 2008 Abstract proceedings 47 one has to be modelled by some specific dynamic law. Consequently, we consider the road traffic flow as a non-autonomous dynamic phenomenon and describe its properties statistically by a non-parametric model. The basic information for the creation of the model is extracted from records of traffic flow rate and related environmental variables. In this presentation we represent the time variable by a periodically changing hour, and a day-code variable that takes into account the character of a day specified by the calendar, while the weather variables are not considered explicitly. Based on the time series of these variables and the recorded traffic flow rate an optimal predictor of thetraffic flow generator is created by using conditional average estimator. The condition is comprised of the hour, day-code and a certain number of past flow rate data. As an example the traffic flow rate at a representative point on a Slovenian high-way is modelled. The model is then utilized to forecast the future traffic flow rate. Seasonal variation is accounted by including into the modelling just a proper section of the past flow rate record. Applicability of this statistical method is indicated by the correlation coefficient r of the forecasted and really observed traffic flow time series. Forecasting in the year 2007 yields the mean value <r>~0.95 which indicates a rather accurate modelling. The performance of forecasting generally depends onthe combination of variables representing the condition. This dependence is demonstrated in the presentation by changing the number of past flow rate datain the condition. An optimal combination of variables comprising the condition is estimated by the analysis of correlation coefficient value. The resulting optimal combination provides new information for the theoretical treatment of traffic flow dynamics.
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