Timetable and Headway Adherence Assessment using the Gini Coefficient and the Lorenz Curve

Adherence to the schedule is of prime importance in public transport. This paper presents a specific application of the Gini coefficient, well known indicator in economics, for the headway adherence assessment. The paper shows that Lorenz curve, which is usually used to define mathematically the Gini coefficient, is a good indicator of the users' waiting time when it is based on the bus schedule. When it is computed on the basis of the ratio of observed headway to the schedule, it is a powerful visual tool that can be used by operators to detect the existence of irregularities on a bus line at a glance. An equation gives, in an idealistic case, the impact of any single traffic disturbance on the Gini coefficient, making this coefficient comprehensive. A detailed analysis is developed, based on the bus proportions according to the headway adherence level. These proportions are obtained from new indices coming from the derivative of the Lorenz curve. The values of these indexes alert the operator of any adherence disturbance. The examination of the Lorenz curve takes more time, but is worthwhile, giving the types of the irregularities The application of these indicators is carried on real-time data from the New Delhi bus network.

The Effect of Nonlinear Charging Function and Line Change Constraints on Electric Bus Scheduling

The recharging plans are a key component of the electric bus schedule. Since the real-world charging function of electric vehicles follows a nonlinear relationship with the charging duration, it is challenging to accurately estimate the charging time. To provide a feasible bus schedule given the nonlinear charging function, this paper proposes a mixed integer programming model with a piecewise linear charging approximation and multi-depot and multi-vehicle type scheduling. The objective of the model is to minimise the total cost of the schedule, which includes the vehicle purchasing cost and operation cost. From a practical point of view, the number of line changes of each bus is also taken as one of the constraints in the optimisation. An improved heuristic algorithm is then proposed to find high-quality solutions of the problem with an efficient computation. Finally, a real-world dataset is used for the case study. The results of using different charging functions indicate a large deviation between the linear charging function and the piecewise linear approximation, which can effectively avoid the infeasible bus schedules. Moreover, the experiments show that the proposed line change constraints can be an effective control method for transit operators.

Bus Tracking App for Universities Transportation

Shuttle buses have become an important means of transportation for students especially for those who rely on it to go to class. However, students often face difficulty knowing the current location of the bus and its estimated arrival time. Some of them are even unaware of the bus schedule provided by higher management. Consequently, they have to wait too long for their respective buses to arrive. Hence, for the convenience of those who want to plan their journey with shuttle buses, two applications are proposed. One application will track the location of the bus and the other application will be used by the students. Both proposed applications will be used along with an Android phone since it is mostly used by students. The main objectives of developing this application are to inform users regarding the current bus location and estimated arrival time. This application also provides users real-time forum so they can start conversations with others with the same application. Besides, the driver's profile is alsoincluded for the user's future reference.

The Waiting-Time Paradox

Suppose that you are going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer—possibly much longer—than what you might guess from looking at a bus schedule. This phenomenon, which is called the waiting-time paradox, has a purely mathematical origin. In this article, we explore the waiting-time paradox, explain why it occurs, and discuss some of its implications (beyond the possibility of being late for school).

PASSENGER TRANSPORTATION IMPROVEMENT BY EXAMPLE OF “NORTHERN FARM-STEAD – NEW-LANDS COMMUNITY” OF TSELINSKY AREA, ROSTOV REGION

The work purpose consists in the analysis of the situation in passenger transportation of countryside and bus distribution on routes. The route investigation was carried out at different daytime by means of passenger number calculation and data recordings in the prepared tables during a day, a week, a month and also during the year, that is, using a calculating-table method. The analysis of bus operation on a route allowed drawing conclusions that this route may be favorable for investors and economically profitable. Besides, it is socially necessary for low-income population groups having no their transport vehicles. The investigation novelty consists in the adaptation of a calculating-table method to rural routes. Conclusions: modern automobile passenger transportation company is impossible without efficient passenger transportation management; one of the main components in passenger transportation management is passenger service improvement, which can be achieved only by empiric investigations of passenger flows on the routes; at the proper selection of vehicles the analyzed car route can be commercially profitable and long-term that is ensured by a quantitative analysis of vehicles and specification of bus schedule taking into account the need of population in travels.

Improving schedule adherence based on dynamic signal control and speed guidance in connected bus system

Purpose The purpose of this paper is to develop a dynamic control method to improve bus schedule adherence under connected bus system. Design/methodology/approach The authors developed a dynamic programming model that optimally schedules the bus operating speed at road sections and multiple signal timing plans at intersections to improve bus schedule adherence. First, the bus route was partitioned into three types of sections: stop, road and intersection. Then, transit agencies can control buses in real time based on all collected information; i.e. control bus operating speed on road sections and adjust the signal timing plans through signal controllers to improve the schedule adherence in connected bus environment. Finally, bus punctuality at the downstream stop and the saturation degree deviations of intersections were selected as the evaluation criteria in optimizing signal control plans and bus speeds jointly. Findings An illustrative case study by using a bus rapid transit line in Jinan city was performed to verify the proposed model. It revealed that based on the proposed strategy, the objective value could be reduced by 73.7%, which indicated that the punctuality was highly improved but not to incur excessive congestion for other vehicular traffic. Originality/value In this paper, the authors applied speed guidance and the adjustment of the signal control plans for multiple cycles in advance to improve the scheduled stability; furthermore, the proposed control strategy can reduce the effect on private traffics to the utmost extend.

The Waiting-Time Paradox

Suppose that you're going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer - possibly much longer - than what the bus schedule suggests intuitively. This phenomenon, which is called the waiting-time paradox, has a purely mathematical origin. Different buses arrive with different intervals, leading to this paradox. In this article, we explore the waiting-time paradox, explain why it happens, and discuss some of its implications (beyond the possibility of being late for school).