Modelling Mixed Traffic Time Headway Distribution Induced by Bus Rapid Transit (BRT) in Cape Town, South Africa
Authors: Modupe Abayomi , Ben-Edigbe Johnnie 
Published: January 2024

Background:
The safety and capacity of roadways are immensely influenced by time headways, a major traffic flow characteristic. Time headways are frequently utilized in various aspects of traffic and transportation engineering studies, including capacity analyses, studies of safety, modelling of lane-changing and car-following behaviour, and level of service assessment.
Time headway, measured in seconds, refers to the distance between two subsequent passing cars moving over a single spot on the road. This paper reports the statistical modelling of the time headway distribution of a mixed traffic flow scenario caused by BRT via statistical headway distribution models. The paper posits that the introduction of BRT dedicated lane and its adopted design configuration induces anomalous traffic flows on its adjoining lanes with attendant time headway differentials, irrespective of the type of adopted design configuration for the corridor. The objectives of this study were to fit the BRT-induced time headway distribution to probability distribution models and determine the most appropriate distribution model that fits the data derived using the goodness of fit tests. Consequently, this contribution, therefore, fills the gap in research with respect to determining the precise model that fits the time headway distribution of mixed traffic flow scenarios induced by BRT.

Methods:
The time headway distribution data collected at four designated road segments on a multilane provincial route R27 caused by BRT dedicated lane in Cape Town, South Africa, were fitted to five probability distribution models viz, Lognormal, Inverse Gaussian, Log-logistic, Generalized Extreme Value (GEV), and Burr using MATLAB software. The fitted headway data were with respect to the traffic flows on the adjoining lanes to BRT or traffic flow ‘without BRT’. Precisely, the empirical data were collected over a three-month period using an Automatic Traffic Counter (ATC). Using ModelRisk software, the goodness of fit of the probability models was assessed by the Akaike Information Criterion (AIC), the Schwartz or Bayesian Information Criterion (SIC or BIC), the Hannan Quinn Information Criterion (HQIC), and the loglikelihood (LLH) model performance criteria respectively. The distribution model with the lowest AIC criterion and largest loglikelihood (LLH) values describe the model that best fits the headway data across the four sites.

Results:
Results showed that the models fitted the headway data well at each site by visual inspection of the attendant Probability Density Function (PDF) and the Probability plots (P-P). However, the Burr distribution provided the overall best fit based on the AIC and LLH values at 95% confidence and 0.05 significance levels across the four sites. At sites 02, 03, and 04, it ranked first with the lowest AIC values of 4025.99, 2595.56, 3815.36, and corresponding largest LLH values of -2008.98, -1293.76, and -1903.66, respectively, while the lognormal distribution performed best at site 01, with AIC value of 4445.14 and LLH value of -2220.57, closely followed by the Burr distribution with AIC and LLH values of 4453.05 and -2222.51, respectively. The P-values, which ranged between 0.65 and 0.80, showed the likelihood of the occurrence of the data sets under the null hypothesis. Hence the null hypothesis was accepted.

Conclusion:
The study concluded that the introduction of BRT dedicated lanes affects the adjoining lanes’ mixed traffic time headways’ distribution, and the headways are continuously distributed, hence fitting continuous probability distributions.