## 1 Introduction  
Mass transit is the backbone of sustainable urban mobility, as it is the only mode of transport that can meet high passenger demand in cities. The cities of today often face high private car usage due to economic prosperity and unattractive alternatives. This generates unnecessary external costs due to increased space consumption, traffic congestion, noise pollution, air pollution and poor road safety. Quality of service in transit is determined by the success of its processes, as observed from the perspective of passengers, operators, and the local community. It is a complex matter because of different qualitative and quantitative approaches, and because there are different stages of using transit: walking (to access, egress or make transfers), waiting for vehicle arrivals, and riding in transit vehicles. Some of the indicators include generalized travel time or costs, transfer efficiency, vehicle occupancy, passenger comfort, arrival waiting time, network coverage, accessibility to people with disabilities, and operating speed. An important indicator representing quality of service is the service reliability, which is the extent of the real service approaching the theoretical one defined by the timetables [1], and it is traditionally demonstrated by the following [2]:  
* Punctuality--the rate of transit vehicles arriving at a certain point in the transit network in time; this is more important for higher intervals, and passengers rely on timetables to use public transport;
* Regularity--the rate of successful intervals between the vehicles; this is more important for smaller intervals, and passengers access the network randomly. Since travel time in the literature can have different meanings, to avoid confusion, in this study, we consider travel time as elapsed time vehicles spend in operation between any two observation points on a transit line, and by farthest, from source to destination terminal, excluding layovers. Therefore, we do not consider the passenger perspective, and travel time includes only the sum of stopping and running times between any two observation points on a transit line. Travel time is under the influence of many disturbance factors: traffic flow, signalized intersections, passenger exchange at stops, weather conditions, pedestrian crossings, maintenance, traffic accidents and driver behavior [3], so an ideal case of transit network in the street where travel time is a constant minimum is impossible, because two effects occur:  
* Travel time discrepancy: the average travel time is higher than the minimum travel time in the ideal conditions;
* Travel time variability: travel time deviates from the average value in both directions, creating early and late vehicles. Travel time variability has become much more accessible with the advent of automatic vehicle location (AVL) and automated passenger counting (APC) technologies since the 2000s [4]. Previous research has put more focus on travel time variability than discrepancy, since ideal conditions providing minimum travel time are more difficult to research; for example, ideal conditions are prone to driver and vehicle performance. Although travel time variability in this research does not encompass door-to-door passenger trips, it is important to mention the significance of variability for the passengers:  
* Since the average waiting time for vehicle arrival in urban transit is half of the interval [5], travel time variability causes fluctuations in the interval, and for some passengers, the actual waiting time at stops can be higher than the average;
* Since stopping time can gradually increase in highly occupied vehicles, travel time variability can contribute to higher stop times and a higher probability of vehicle bunching, additionally worsening the situation.