Modelling of distribution of the "Matatu" traffic flow using Poisson distribution in a highway in Kenya

Abstract

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.

Poisson Distribution Function Modification to Model Short Time Intervals of Arrival Flow

“…Süreksiz dağılımlardan birisi de Poisson dağılımıdır. Fakat literatür çalışmalarında trafik akımının modellenmesi amacıyla poisson dağılımının kullanımı mevcuttur [9].Genel olarak geniş zaman aralıklarında poisson dağılımı trafik akımını modelleyebilmek amacıyla kullanılabilse de dinamik bir sinyalizasyon sistemi oluşturulması gerektiğinde daha kısa aralıklarda modellemeye ihtiyaç duyulmaktadır. Kavşağa yaklaşan akım içerisinde bulunan taşıtlar arası zaman cinsinden boşluk değerleri yoğun trafik durumunda kısa kalmaktadır.…”

A Novel Solution to Find the Dynamic Response of an Euler–Bernoulli Beam Fitted with Intraspan TMDs under Poisson Type Loading

“…A Poissonian white noise process is a type of delta-correlated process [40], that is "simple, robust and gives accurate results" [41] when used to model loading caused by free flowing traffic, i.e., traffic unencumbered by an unusually heavy volume that causes a continuous series of moving loads due to jams and tailbacks. Poissonian processes are most commonly defined as [11]:…”