Traffic flow modelling is studied in order to ease congestion on roads. However, congestion is also caused by irregular occurrences, such as traffic accidents, poor roads, vehicle disablement, spilled loads and hazardous materials. This study explored the area of poor roads which was considered to be as a result poor planning for road network repairs. Traffic flow was categorized to be either in low, intermediate, or high volume. Modelling for every flow required a different distribution namely the Exponential, Pearson type III and Normal distributions for low, intermediate and high traffic flow volume respectively. However, we modelled the trailers traffic flow using a model that covered all the 3 states, in this case,the Pearson type III distribution. Further,we investigated the shape of the probability distribution function assumed by the trailers. After data collection,extraction and analysis, Pearson type III distribution model was calibrated to fit. Lastly, Kolmogorov-Smirnov and Chi-square tests of goodness of fit was run on the observed data. Although, the data was also fitted into Normal, Erlang, Exponential, Beta and Gamma Distributions, Pearson type III distribution provided the best fit.
Traffic congestion in urban road and freeway networks leads to strong degradation of the network infrastructure and accordingly reduced output. Expansion of the available transportation continues to be one of the solution to the increasing traffic congestion, but with destruction of infrastructure.Traffic flow models are studied to be used in transport industry, in ensuring that traffic situations in our roads and highways are managed. Previous studies have modelled traffic flow by Pearson type III distribution and the Inhomogeneous Lighthill, Whitham and Richards Model (LWR) model .Research into application of Poisson to model traffic flow in the Kenyan Context is scanty. Therefore,the study models traffic flow of Thika-Nairobi highway using Poisson distribution model. The study fitted the Poisson model to a weekly traffic flow data obtained by measurement from a point method. The probability of the number of Matatu vehicles passing within the one minute period was varying and depending on the rush hours and normal hours.The parameters of the model were estimated using Analogical and Moments Method using the data from the sample. Based on Chi-square and index of dispersion values the Poisson model was identified as the adequate model for modelling traffic flow of Matatu .The observed data were used to estimate the expected data using the model.Vehicle arrivals can be evaluated by modelling arrival rate in a given interval of time and inter-arrival between the successive arrival of vehicles in a similar way.
The paper extends the work of Sarguta who derived recursive relations for univariate distributions by considering the ZIP continuous mixtures. The paper gives a recursive formular which can be used to evaluate the mixed distributions which can be used when the probability distribution functions cannot be evaluated explicitly. Integration by parts is often employed when deriving the recursive formulas. From section two up to section seven, we derived the recursive formulas for ZIP mixture distributions using Rectangular, Exponential, Gamma with two parameters, Poisson-Beta and Inverted-Beta as mixing distributions.
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