“…It is well known that the travel time is hard to be precisely measured and predicted (Chakroborty, Kikuchi 2004;Vu, Khan 2010;Ng et al 2011). However, the travel times and their distributions are essential and fundamental for the research in different areas of public transport, including, for example, the bus route design (Kuo et al 2013), service planning (Furth, Muller 2007), reliability measurement (Van Lint et al 2008;Mazloumi et al 2010), timetable optimization (Yan et al 2012), bus dispatching (Dessouky et al 1999), and vehicle scheduling (Zhao et al 2006;Xu, Shen 2012). Moreover, the travel time is also the concern of passengers, which is one of key criteria for bus service quality (Abkowitz, Tozzi 1987;Uniman et al 2010;Van Oort et al 2012;Mori et al 2015).…”