A connected-vehicle-based dynamic control model for managing the bus bunching problem with capacity constraints

This paper describes a connected-vehicle-based system architecture which can provide more precise and comprehensive information on bus movements and passenger status. Then a dynamic control method is proposed using connected vehicle data. Traditionally, the bus bunching problem has been formulated into one of two types of optimization problem. The first uses total passenger time cost as the objective function and capacity, safe headway, and other factors as constraints. Due to the large number of scenarios considered, this type of framework is inefficient for real-time implementation. The other type uses headway adherence as the objective and applies a feedback control framework to minimize headway variations. Due to the simplicity in the formulation and solution algorithms, the headway-based models are more suitable for real-time transit operations. However, the headway-based feedback control framework proposed in the literature still assumes homogeneous conditions at all bus stations, and does not consider restricting passenger loads within the capacity constraints. In this paper, a dynamic control framework is proposed to improve not only headway adherence but also maintain the stability of passenger load within bus capacity in both homogenous and heterogeneous situations at bus stations. The study provides the stability conditions for optimal control with heterogeneous bus conditions and derives optimal control strategies to minimize passenger transit cost while maintaining vehicle loading within capacity constraints. The proposed model is validated with a numerical analysis and case study based on field data collected in Chengdu, China. The results show that the proposed model performs well on high-demand bus routes.     

Mitigation of disruptions in public transit by Bee Colony Optimization

Dispatchers in many public transit companies face the daily problem of assigning available buses to bus routes under conditions of bus shortages. In addition to this, weather conditions, crew absenteeism, traffic accidents, traffic congestion and other factors lead to disturbances of the planned schedule. We propose the Bee Colony Optimization (BCO) algorithm for mitigation of bus schedule disturbances. The developed model takes care of interests of the transit operator and passengers. The model reassigns available buses to bus routes and, if it is allowed, the model simultaneously changes the transportation network topology (it shortens some of the planned bus routes) and reassigns available buses to a new set of bus routes. The model is tested on the network of Rivera (Uruguay). Results obtained show that the proposed algorithm can significantly mitigate disruptions.     

Modeling the interaction between buses,passengers and cars on a bus route using a multi-agent system

This paper models part of a public transport network (PTN), specifically, a bus route, as a small-size multi-agent system (MAS). The proposed approach is applied to a case study considering a ‘real world’ bus line within the PTN in Auckland, New Zealand. The MAS-based analysis uses modeling and simulation to examine the characteristics of the observed system – autonomous agents interacting with one another – under different scenarios, considering bus capacity and frequency of service for existing and projected public transport (PT) demand. A simulation model of a bus route is developed, calibrated and validated. Several results are attained, such as when the PT passenger load is not close to bus capacity, this load has no effect on average passenger waiting time at bus stops. The model proposed can be useful to practitioners as a tool to model the interaction between buses and other agents.     

小件快运中的最短运输时间问题

小件快运经过多年的发展,已经成为公路客运一个新的经济增长点,越来越多的公路客运企业和汽车客运站加入到经营小件快运的行列,小件快运也逐渐由单个企业的独立运营发展到多个企业联合的网络化运营。对中转运输中多条运输线路进行分析,得到最短运输时间线路,从而提高运输效率。     

Plan-based flexible bus bridging operation strategy

Bus bridging has been widely used to connect stations affected by metro disruptions such that stranded passengers could resume their journeys. Previous studies generally assumed that a bus operates exclusively on one bridging route with given frequency, which limits the service flexibility and reduce the operational efficiency. We propose a strategy to instruct buses to operate on predefined bridging routes once they are dispatched from depots. Buses are allowed to flexibly serve different bridging routes. Each bus operates based on a bridging plan that lists the stations to serve in sequence instead of route frequencies. A two-stage model is developed to optimize the bridging plans and their assignments to buses with the objectives that balance the operational priorities between minimizing bus bridging time and reducing passenger delay. A Weight Shortest Processing Time first (WSPT) rule based heuristic algorithm is developed to solve the proposed model. The developed model is further incorporated in a rolling horizon framework to handle dynamic passenger arrivals during the disruption period. The effectiveness of the proposed strategy is demonstrated in comparison with alternative strategies in real-world case studies.     

Real-time control of buses for schedule coordination at a terminal

Recently, bus transit operators have begun to adopt technologies that enable bus locations to be tracked from a central location in real-time. Combined with other technologies, such as automated passenger counting and wireless communication, it is now feasible for these operators to execute a variety of real-time strategies for coordinating the movement of buses along their routes. This paper compares control strategies that depend on technologies for communication, tracking and passenger counting, to those that depend solely on local information (e.g., time that a bus arrived at a stop, and whether other connecting buses have also arrived). We also develop methods to forecast bus arrival times, which are most accurate for lines with long headways, as is usually the case in timed transfer systems. These methods are tested in simulations, which demonstrate that technology is most advantageous when the schedule slack is close to zero, when the headway is large, and when there are many connecting buses.     

Bus control strategies in corridors with signalized intersections

This paper proposes a new dynamic bus control strategy aimed at reducing the negative effects of time-headway variations on route performance, based on real-time bus tracking data at stops. In routes with high demand, any delay of a single vehicle ends up causing an unstable motion of buses and producing the bus bunching phenomena. This strategy controls the cruising speed of buses and considers the extension of the green phase of traffic lights at intersections, when a bus is significantly delayed. The performance of this strategy will be compared to the current static operation technique based on the provision of slack times at holding points. An operational model is presented in order to estimate the effects of each controlling strategy, taking into account the vehicle capacity constraint. Control strategies are assessed in terms of passenger total travel time, operating cost as well as on the coefficient of headway variation. The effects of controlling strategies are tested in an idealized bus route under different operational settings and in the bus route of highest demand in Barcelona by simulation. The results show that the proposed dynamic controlling strategy reduces total system cost (user and agency) by 15–40% as well as the coefficient of headway variation 53–78% regarding the uncontrolled case, providing a bus performance similar to the expected when time disturbance is not presented.     

Integrating bus services with mixed fleets

Conventional bus service (with fixed routes and schedules) has lower average cost than flexible bus service (with demand-responsive routes) at high demand densities. At low demand densities flexible bus service has lower average costs and provides convenient door-to-door service. Bus size and operation type are related since larger buses have lower average cost per passenger at higher demand densities. The operation type and other decisions are jointly optimized here for a bus transit system connecting a major terminal to local regions. Conventional and flexible bus sizes, conventional bus route spacings, areas of service zones for flexible buses, headways, and fleet sizes are jointly optimized in multi-dimensional nonlinear mixed integer optimization problems. To solve them, we propose a hybrid approach, which combines analytic optimization with a Genetic Algorithm. Numerical analysis confirms that the proposed method provides near-optimal solutions and shows how the proposed Mixed Fleet Variable Type Bus Operation (MFV) can reduce total cost compared to alternative operations such as Single Fleet Conventional Bus (SFC), Single Fleet Flexible Bus (SFF), Mixed Fleet Conventional Bus (MFC) and Mixed Fleet Flexible Bus (MFF). With consistent system-wide bus sizes, capital costs are reduced by sharing fleets over times and over regions. The sensitivity of results to several important parameters is also explored.     

Time of day intervals partition for bus schedule using GPS data

Time of day partition of bus operating hours is a prerequisite of bus schedule design. Reasonable partition plan is essential to improve the punctuality and level of service. In most mega cities, bus vehicles have been equipped with global positioning system (GPS) devices, which is convenient for transit agency to monitor bus operations. In this paper, a new algorithm is developed based on GPS data to partition bus operating hours into time of day intervals. Firstly, the impacts of passenger demand and network traffic state on bus operational performance are analyzed. Then bus dwell time at stops and inter-stop travel time, which can be attained based on GPS data, are selected as partition indexes. For buses clustered in the same time-of-day interval, threshold values of differences in dwell time at stops and inter-stop travel time are determined. The buses in the same time-of-day interval should have adjacent dispatching numbers, which is set as a constraint. Consequently, a partition algorithm with three steps is developed. Finally, a bus route in Suzhou China is taken as an example to validate the algorithm. Three partition schemes are given by setting different threshold values for the two partition indexes. The present scheme in practice is compared with the three proposed schemes. To balance the number of ToD intervals and partition precision, a Benefit Evaluation Index is proposed, for a better time-of-day interval plan.     

Optimizing bus-size and headway in transit networks

Optimization models for calculating the best size for passenger carrying vehicles in urban areas were popular during the 1980s. These studies were abandoned in the ‘90s concluding that it was more efficient to use smaller buses at higher frequencies. This article returns to this controversial question, starting from the point of view that any calculation of bus size can only be made after considering the demand for each of the routes on the system. Therefore, an optimization model for sizing the buses and setting frequencies on each route in the system is proposed in accordance with the premises detailed below. The proposed model is a bi-level optimization model with constraints on bus capacity. The model allows buses of different sizes to be assigned to public transport routes optimizing the headways on each route in accordance with observed levels of demand. At the upper level the model considers the optimization of the system’s social and operating costs, these are understood to be the sum of the user’s and operator’s costs. At the lower level there is an assignment model for public transport with constraints on vehicle capacity which balances the flows for bus sizes and headways at each iteration. By graphically representing the results of the model applied to a real case, a series of useful conclusions are reached for the management and planning of a fleet of public transport vehicles.     

Crowding in public transport systems: Effects on users,operation and implications for the estimation of demand

The effects of high passenger density at bus stops, at rail stations, inside buses and trains are diverse. This paper examines the multiple dimensions of passenger crowding related to public transport demand, supply and operations, including effects on operating speed, waiting time, travel time reliability, passengers’ wellbeing, valuation of waiting and in-vehicle time savings, route and bus choice, and optimal levels of frequency, vehicle size and fare. Secondly, crowding externalities are estimated for rail and bus services in Sydney, in order to show the impact of crowding on the estimated value of in-vehicle time savings and demand prediction. Using Multinomial Logit (MNL) and Error Components (EC) models, we show that alternative assumptions concerning the threshold load factor that triggers a crowding externality effect do have an influence on the value of travel time (VTTS) for low occupancy levels (all passengers sitting); however, for high occupancy levels, alternative crowding models estimate similar VTTS. Importantly, if demand for a public transport service is estimated without explicit consideration of crowding as a source of disutility for passengers, demand will be overestimated if the service is designed to have a number of standees beyond a threshold, as analytically shown using a MNL choice model. More research is needed to explore if these findings hold with more complex choice models and in other contexts.     

Optimization of bus allocation to depots by minimizing dead kilometers

In metropolitan cities, public transportation service plays a vital role in mobility of people, and it has to introduce new routes more frequently due to the fast development of the city in terms of population growth and city size. Whenever there is introduction of new route or increase in frequency of buses, the non‐revenue kilometers covered by the buses increases as depot and route starting/ending points are at different places. This non‐revenue kilometers or dead kilometers depends on the distance between depot and route starting point/ending point. The dead kilometers not only results in revenue loss but also results in an increase in the operating cost because of the extra kilometers covered by buses. Reduction of dead kilometers is necessary for the economic growth of the public transportation system. Therefore, in this study, the attention is focused on minimizing dead kilometers by optimizing allocation of buses to depots depending upon the shortest distance between depot and route starting/ending points. We consider also depot capacity and time period of operation during allocation of buses to ensure parking safety and proper maintenance of buses. Mathematical model is developed considering the aforementioned parameters, which is a mixed integer program, and applied to Bangalore Metropolitan Transport Corporation (BMTC) routes operating presently in order to obtain optimal bus allocation to depots. Database for dead kilometers of depots in BMTC for all the schedules are generated using the Form‐4 (trip sheet) of each schedule to analyze depot‐wise and division‐wise dead kilometers. This study also suggests alternative locations where depots can be located to reduce dead kilometers. Copyright © 2015 John Wiley & Sons, Ltd.     

Ridership estimation procedure for a transit corridor with new bus rapid transit service

Ridership estimation is a critical step in the planning of a new transit route or change in service. Very often, when a new transit route is introduced, the existing routes will be modified, vehicle capacities changed, or service headways adjusted. This has made ridership forecasts for the new, existing, and modified routes challenging. This paper proposes and demonstrates a procedure that forecasts the ridership of all transit routes along a corridor when a new bus rapid transit (BRT) service is introduced and existing regular bus services are adjusted. The procedure uses demographic data along the corridor, a recent origin–destination survey data, and new and existing transit service features as inputs. It consists of two stages of transit assignment. In the first stage, a transit assignment is performed with the existing transit demand on the proposed BRT and existing bus routes, so that adjustments to the existing bus services can be identified. This transit assignment is performed iteratively until there is no adjustment in transit services. In the second stage, the transit assignment is carried out with the new BRT and adjusted regular bus services, but incorporates a potential growth in ridership because of the new BRT service. The final outputs of the procedure are ridership for all routes and route segments, boarding and alighting volumes at all stops, and a stop‐by‐stop trip matrix. The proposed ridership estimation procedure is applicable to a new BRT route with and without competing regular bus routes and with BRT vehicles traveling in dedicated lanes or in mixed traffic. The application of the proposed procedure is demonstrated via a case study along the Alameda Corridor in El Paso, Texas. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal control of headway variation on transit routes

Headway control strategies have been proposed as methods for correcting transit service irregularities and thereby reducing passenger wait times at stops. This paper addresses a particular strategy which can be implemented on high frequency routes (headways under 10–12 minutes), in which buses are held at a control stop to a threshold headway. An algorithm is developed which yields the optimal control stop location and optimal threshold headway with respect to a system wait function. The specification of the wait function is based on the development of several empirical models, including a headway variation model and an average delay time model at control stops. A conclusion is reached that the headway variation does not increase linearly along a route, a common assumption made in many previous studies. Furthermore, the location of the optimal control stop and threshold value are sensitive to the passenger boarding profile, as expected. The algorithm itself appears to have practical application to conventional transit operations.     

Integrated optimization of transit priority operation at isolated intersections: A person-capacity-based approach

In this paper, a person-capacity-based optimization method for the integrated design of lane markings, exclusive bus lanes, and passive bus priority signal settings for isolated intersections is developed. Two traffic modes, passenger cars and buses, have been considered in a unified framework. Person capacity maximization has been used as an objective for the integrated optimization method. This problem has been formulated as a Binary Mixed Integer Linear Program (BMILP) that can be solved by a standard branch-and-bound routine. Variables including, allocation of lanes for different passenger car movements (e.g., left turn lanes or right turn lanes), exclusive bus lanes, and passive bus priority signal timings can be optimized simultaneously by the proposed model. A set of constraints have been set up to ensure feasibility and safety of the resulting optimal lane markings and signal settings. Numerical examples and simulation results have been provided to demonstrate the effectiveness of the proposed person-capacity-based optimization method. The results of extensive sensitivity analyses of the bus ratio, bus occupancy, and maximum degree of saturation of exclusive bus lanes have been presented to show the performance and applicable domain of the proposed model under different composition of inputs.     

Accounting for travel time variability in the optimal pricing of cars and buses

A number of studies have shown that in addition to travel time and cost as the common influences on mode, route and departure time choices, travel time variability plays an increasingly important role, especially in the presence of traffic congestion on roads and crowding on public transport. The dominant focus of modelling and implementation of optimal pricing that incorporates trip time variability has been in the context of road pricing for cars. The main objective of this paper is to introduce a non-trivial extension to the existing literature on optimal pricing in a multimodal setting, building in the role of travel time variability as a source of disutility for car and bus users. We estimate the effect of variability in travel time and bus headway on optimal prices (i.e., tolls for cars and fares for buses) and optimal bus capacity (i.e., frequencies and size) accounting for crowding on buses, under a social welfare maximisation framework. Travel time variability is included by adopting the well-known mean–variance model, using an empirical relationship between the mean and standard deviation of travel times. We illustrate our model with an application to a highly congested corridor with cars, buses and walking as travel alternatives in Sydney, Australia. There are three main findings that have immediate policy implications: (i) including travel time variability results in higher optimal car tolls and substantial increases in toll revenue, while optimal bus fares remain almost unchanged; (ii) when bus headways are variable, the inclusion of travel time variability as a source of disutility for users yields higher optimal bus frequencies; and (iii) including both travel time variability and crowding discomfort leads to higher optimal bus sizes.     

Bus Rapid Transit System in Istanbul: A Success Story or Flawed Planning Decision?

Abstract

There is a growing tendency in cities around the world to invest in Bus Rapid Transit (BRT) systems in an attempt to improve the capacity and quality of public transport services. The appeal of BRTs is based on their ability to combine the service level of rail transit systems with the flexibility of buses at relatively lower investment costs, and this was the motivation behind the opening of such a system in the Turkish city of Istanbul in 2007. This system has attracted mixed opinions as to its performance, as while passenger ridership figures are extremely high, proving the effectiveness of the system, there is an argument that the corridor should have been developed with rail technology, and that the BRT is failing to meet the demand. The paper presents a comprehensive analysis of this system, assessing its planning and performance through a comparative analysis of a number of BRTs in the world and Istanbul's metro and tram systems. The analysis confirms the success of the system in terms of passenger statistics, but also highlights a number of problems in certain planning decisions that should be addressed, thus taking the discussion beyond a simplified comparison of bus and rail technologies.     

Analyzing urban bus service reliability at the stop, route, and network levels

Improving the reliability of bus service has the potential to increase the attractiveness of public transit to current and prospective riders. An understanding of service reliability is necessary to develop strategies that help transit agencies provide better services. However, few studies have been conducted analyzing bus reliability in the metropolis of China. This paper presents an in-depth analysis of service reliability based on bus operational characteristics in Beijing. Three performance parameters, punctuality index based on routes (PIR), deviation index based on stops (DIS), and evenness index based on stops (EIS), are proposed for the evaluation of bus service reliability. Reliability involves routes, stops, punctuality, deviation, and evenness. The relationship among the three parameters is discussed using a numerical example. Subsequently, through a sampling survey of bus lines in Beijing, service reliability at the stop, route, and network levels are estimated. The effects of route length, headway, the distance from the stop to the origin terminal, and the use of exclusive bus lanes are also analyzed. The results indicate low service reliability for buses in Beijing and a high correlation between service reliability and route length, headway, distance from the stop to the origin terminal, and the provision of exclusive bus lanes.     

Designing large-scale bus network with seasonal variations of demand

Creating a bus network that covers passenger demand conveniently is an important ingredient of the transit operations planning process. Certainly determination of optimal bus network is highly sensitive to any change of demand, thus it is desirable not to consider average or estimated figures, but to take into account prudently the variations of the demand. Many cities worldwide experience seasonal demand variations which naturally have impact on the convenience and optimality of the transit service. That is, the bus network should provide convenient service across all seasons. This issue, addressed in this work, has not been thoroughly dealt with neither in practice nor in the literature. Analyzing seasonal transit demand variations increases further the computational complexity of the bus-network design problem which is known as a NP-hard problem. A solution procedure using genetic algorithm efficiently, with a defined objective-function to attain the optimization, is proposed to solve this cumbersome problem. The method developed is applied to two benchmarked networks and to a case study, to the city of Mashhad in Iran with over 3.2 million residents and 20 million visitors annually. The case study, characterized by a significant seasonal demand variation, demonstrates how to find the best single network of bus routes to suit the fluctuations of the annual passenger demand. The results of comparing the proposed algorithm to previously developed algorithms show that the new development outperforms the other methods between 1% and 9% in terms of the objective function values.     

Short-term post-earthquake bus transit planning in Managua

In December 1972 an earthquake hit Managua, Nicaragua, killing 5,000 inhabitants, while wounding 20,000 persons and destroying its core area of 13 square kilometers. The earthquake also seriously disrupted the bus transit system. Bus transit patronage fell as a result of the loss of population of 144,000 persons who moved temporarily out of the city, while costs rose appreciably as both round trip bus distances and the proportion of the trips on unpaved roads doubled with respect to pre-earthquake levels. By September 1973, ten of the thirteen bus companies were on the verge of bankruptcy and were demanding from the regulatory body stiff increases in fares.This paper presents analyses and recommendations for improving the short-term efficiency of bus routes in Managua by applying planning techniques suited to the data availability problems of developing countries.In view of the lack of cost data for the bus routes, a cost analysis was conducted; Jan de Weille's cost factors were adapted to Nicaragua to portray the near bankrupt condition of most routes. These cost factors were verified by means of selected interviews with the private transit entrepreneurs.Next, a simple patronage prediction model was developed which related patronage for a route to the population and employment served by the route. This simple patronage model was then applied to redesign the bus routes of Managua. A policy of bus route redesign coupled with the paving of city streets along the bus routes is shown to have sufficed in avoiding fare increases. Finally, the paper reviews the bus transit regulatory setting and develops some recommendations for its improvement.Adjunct Associate Professor of the Catholic University of America. This study was conducted while the author was stationed in Nicaragua as a consultant to Harvard Development Advisory Service.