Tailored Wakeby-type distribution for random bus headway adherence ratio

This paper addresses an interesting and practical bus headway adherence issue for a given public bus route with a number of bus stops. It first defines the random headway adherence ratio (HAR) at a particular bus stop of a specific bus route as the ratio of difference between actual bus headway and scheduled headway with respect to the scheduled headway. This study proceeds to customize a four-step procedure to estimate a probability distribution that can describe the random HAR at each bus stop of the bus route by using the automatic vehicle location (AVL) data. Our real case studies with 44,025 HAR data show that the 19 existing probability distributions including Lognormal, Gamma, Beta and Wakeby are unable to well fit these HAR data. This study thus proposes a tailored Wakeby-type distribution with five parameters. After deriving two fundamental propositions for the tailored Wakeby-type distribution, a tangible L-moment based method to estimate those parameters involved the tailored Wakeby distribution is presented. The tailored Wakeby-type distributions can meet our expectation via our real case studies. Finally, applications of the tailored Wakeby-type distribution derived for the random HAR are conducted.