Optimization of bus stop locations for improving transit accessibility

A mathematical model is developed in this paper to improve the accessibility of a bus service. To formulate the optimization model, a segment of a bus route is given, on which a number of demand entry points are distributed realistically. The objective total cost function (i.e. the sum of supplier and user costs) is minimized by optimizing the number and locations of stops, subject to non‐additive users' value of time. A numerical example is designed to demonstrate the effectiveness of the method thus developed to optimize the bus stop location problem. The sensitivity of the total cost to various parameters (e.g. value of users' time, access speed, and demand density) and the effect of the parameters on the optimal stop locations are analyzed and discussed.     

Locating charging infrastructure for electric buses in Stockholm

Charging infrastructure requirements are being largely debated in the context of urban energy planning for transport electrification. As electric vehicles are gaining momentum, the issue of locating and securing the availability, efficiency and effectiveness of charging infrastructure becomes a complex question that needs to be addressed. This paper presents the structure and application of a model developed for optimizing the distribution of charging infrastructure for electric buses in the urban context, and tests the model for the bus network of Stockholm. The major public bus transport hubs connecting to the train and subway system show the highest concentration of locations chosen by the model for charging station installation. The costs estimated are within an expected range when comparing to the annual bus public transport costs in Stockholm. The model could be adapted for various urban contexts to promptly assist in the transition to fossil-free bus transport. The total costs for the operation of a partially electrified bus system in both optimization cases considered (cost and energy) differ only marginally from the costs for a 100% biodiesel system. This indicates that lower fuel costs for electric buses can balance the high investment costs incurred in building charging infrastructure, while achieving a reduction of up to 51% in emissions and up to 34% in energy use in the bus fleet.     

Numerical analysis of electric bus fast charging strategies for demand charge reduction

Electric transit buses have been recognized as an important alternative to diesel buses with many environmental benefits. Electric buses employing lithium titanate batteries can provide uninterrupted transit service thanks to their ability of fast charging. However, fast charging may result in high demand charges which will increase the fuel costs thereby limiting the electric bus market penetration. In this paper, we simulated daily charging patterns and demand charges of a fleet of electric buses in Tallahassee, Florida and identified an optimal charging strategy to minimize demand charges. It was found that by using a charging threshold of 60–64%, a $160,848 total saving in electricity cost can be achieved for a five electric bus fleet, comparing to a charging threshold of 0–28%. In addition, the impact of fleet sizes on the fuel cost was investigated. Fleets of 4 and 12 buses will achieve the lowest cost per mile driven when one fast charger is installed.     

An analytic investigation of optimal bus size

The use of smaller buses offers passengers a better service frequency for a given service capacity, but costs more to operate per seat provided. Within this trade-off there is an optimal bus size which maximises social benefit. A mathematical model is described which can be solved analytically to provide an explicit relationship between optimal bus size and factors such as operating cost, level of demand, and demand elasticities. The model includes: passenger demand varying with the generalised cost of travel according to a constant elasticity; the effect of changes in bus occupancy on average waiting times and on operating speed; the financial constraint that farebox revenue must equal operating cost less subsidy; an allowance for external benefits associated with generated demand, and for the effect of the flow of buses on traffic congestion; and an operating cost increasing linearly with bus size. The optimal size varies with the square root of demand, and with the unit cost to the power of 0.1 to 0.2. It also increases slowly with the proportion of cost covered by subsidy. For typical urban operating conditions in the United Kingdom the optimal size for a monopoly service lies between 55 and 65 seats assuming the observed relationship between cost and size; it is possible that changes in working practices could make smaller buses relatively cheaper to operate, so reducing the optimal size, but it seems unlikely to fall below 40 seats.     

Economic and ecological optimization of electric bus charging considering variable electricity prices and CO2eq intensities

In many cities, diesel buses are being replaced by electric buses with the aim of reducing local emissions and thus improving air quality. The protection of the environment and the health of the population is the highest priority of our society. For the transport companies that operate these buses, not only ecological issues but also economic issues are of great importance. Due to the high purchase costs of electric buses compared to conventional buses, operators are forced to use electric vehicles in a targeted manner in order to ensure amortization over the service life of the vehicles. A compromise between ecology and economy must be found in order to both protect the environment and ensure economical operation of the buses.In this study, we present a new methodology for optimizing the vehicles’ charging time as a function of the parameters CO_2eq emissions and electricity costs. Based on recorded driving profiles in daily bus operation, the energy demands of conventional and electric buses are calculated for the passenger transportation in the city of Aachen in 2017. Different charging scenarios are defined to analyze the influence of the temporal variability of CO_2eq intensity and electricity price on the environmental impact and economy of the bus. For every individual day of a year, charging periods with the lowest and highest costs and emissions are identified and recommendations for daily bus operation are made. To enable both the ecological and economical operation of the bus, the parameters of electricity price and CO₂ are weighted differently, and several charging periods are proposed, taking into account the priorities previously set. A sensitivity analysis is carried out to evaluate the influence of selected parameters and to derive recommendations for improving the ecological and economic balance of the battery-powered electric vehicle.In all scenarios, the optimization of the charging period results in energy cost savings of a maximum of 13.6% compared to charging at a fixed electricity price. The savings potential of CO_2eq emissions is similar, at 14.9%. From an economic point of view, charging between 2 a.m. and 4 a.m. results in the lowest energy costs on average. The CO_2eq intensity is also low in this period, but midday charging leads to the largest savings in CO_2eq emissions. From a life cycle perspective, the electric bus is not economically competitive with the conventional bus. However, from an ecological point of view, the electric bus saves on average 37.5% CO_2eq emissions over its service life compared to the diesel bus. The reduction potential is maximized if the electric vehicle exclusively consumes electricity from solar and wind power.     

Reduction of capacity and projected costs associated with seat belt installation on school buses

This study examines the potential effects the installation of seat belts on school buses would have on the fleet capacity in Alabama and the resulting cost implications. The study also documents the myriad research studies and professional opinions offered on the potential safety effects of equipping school buses with safety restraints/seat belts. Four seat configurations for the school buses were analyzed. The first configuration represents the most common current bus seating configuration without seat belts, 3 seats on each side of the aisle and 12 rows (3/3-12). The physical space required for seat belt hardware may result in a loss of a row of seats and may reduce the number of students seated per row. Thus, three more configurations were studied: loss of a row of seats (3/3-11), loss of one seat per row (3/2-12), and loss of both a row of seats and a seat per row (3/2-11). The capacity for each configuration for each bus using current pupil loads was determined. The costs associated with installation of seat belts, and purchase and operation of new buses were obtained. Should school bus seat belts become mandatory in Alabama, the results obtained in this study can be used by any school system to determine the optimum configuration for their pupils, which will identify the number of additional buses that must be purchased by the school system. This study found that many of the buses that would become overloaded due to seat belt installation and the resultant loss of seating will be carrying only a few excess pupils. Transportation supervisors may be able to handle such overloads by transferring these pupils to other buses or by adjusting their bus routes to minimize purchase of new buses. Additional suggestions for handling bus overloads were offered in the body of this report.     

Using non-real-time Automatic Vehicle Location data to improve bus services

Although real-time Automatic Vehicle Location (AVL) data is being utilised successfully in the UK, little notice has been given to the benefits of historical (non-real-time) AVL data. This paper illustrates how historical AVL data can be used to identify segments of a bus route which would benefit most from bus priority measures and to improve scheduling by highlighting locations at which the greatest deviation from schedule occurs. A new methodology which uses historical AVL data and on-bus passenger counts to calculate the passenger arrival rate at stops along a bus route has been used to estimate annual patronage and the speed of buses as they move between stops. Estimating the patronage at stops using AVL data is more cost-effective than conventional methods (such as surveys at stops which require much more manpower) but retains the benefits of accuracy and stop-specific estimates of annual patronage. The passenger arrival rate can then be used to calculate how long buses spend at stops. If the time buses spend at stops is removed from the total time it takes the bus to traverse a link, the remaining amount of time can be assumed to be the time the bus spends moving and hence the moving speed of the bus can be obtained. It was found that estimation of patronage and the speed of buses as they move between stops using AVL data produced results which were comparable with those obtained by other methods. However the main point to note is that this new method of estimating patronage has the potential to provide a larger and superior data set than is otherwise available, at very low cost.     

Bus garage location planning with dynamic vehicle assignments: A methodology

A simultaneous vehicle scheduling and bus garage location and sizing optimization is described. The methodology's importance lies in its treating garage locations and sizes and vehicle schedules as dynamic. In other bus garage planning methodologies, vehicle schedules are assumed fixed.     

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.     

Environmental life-cycle assessment of transit buses with alternative fuel technology

The paper presents a life-cycle assessment of costs and greenhouse gas emissions for transit buses deploying a hybrid input-output model to compare ultra-low sulfur diesel to hybrid diesel-electric, compressed natural gas, and hydrogen fuel-cell. We estimate the costs of emissions reductions from alternative fuel vehicles over the life cycle and examine the sensitivity of the results to changes in fuel prices, passenger demand, and to technological characteristics influencing performance and emissions. We find that the alternative fuel buses reduce operating costs and emissions, but increase life-cycle costs. The infrastructure requirement to deploy and operate alternative fuel buses is critical in the comparison of life-cycle emissions. Additionally, efficient bus choice is sensitive to passenger demand, but only moderately sensitive to technological characteristics, and that the relative efficiency of compressed natural gas buses is more sensitive to changes in fuel prices than that of the other bus types.     

Energy consumption and cost-benefit analysis of hybrid and electric city buses

This paper presents a cost-benefit analysis (CBA) of hybrid and electric city buses in fleet operation. The analysis is founded on an energy consumption analysis, which is carried out on the basis of extensive simulations in different bus routes. A conventional diesel city bus is used as a reference for the CBA. Five different full size hybrid and electric city bus configurations were considered in this study; two parallel and two series hybrid buses, and one electric city bus. Overall, the simulation results indicate that plug-in hybrid and electric city buses have the best potential to reduce energy consumption and emissions. The capital and energy storage system costs of city buses are the most critical factors for improving the cost-efficiency of these alternative city bus configurations. Furthermore, the operation schedule and route planning are important to take into account when selecting hybrid and electric city buses for fleet operation.     

Introducing change to transportation and energy systems: the case of alcohol fuels

This paper describes the application of optimization techniques to the problems of garage location and bus routing. The technique employed involves the decomposition of a garage location and bus routing model into two submodels. Solutions for the garage location and bus routing submodels are combined iteratively to find an optimal solution for the overall optimization model. Significant cost savings realizable for the Transit Authority of River City (Louisville, Kentucky) were calculated by implementing the results.     

Bus congestion, optimal infrastructure investment and the choice of a fare collection system in dedicated bus corridors

Microeconomic optimisation of scheduled public transport operations has traditionally focused on finding optimal values for the frequency of service, capacity of vehicles, number of lines and distance between stops. In addition, however, there exist other elements in the system that present a trade-off between the interests of users and operators that have not received attention in the literature, such as the optimal selection of a fare payment system and a designed running speed (i.e., the cruising speed that buses maintain in between two consecutive stops). Alternative fare payment methods (e.g., on-board and off-board, payment by cash, magnetic strip or smart card) have different boarding times and capital costs, with the more efficient systems such as a contactless smart card imposing higher amounts of capital investment. Based on empirical data from several Bus Rapid Transit systems around the world, we also find that there is a positive relationship between infrastructure cost per kilometre and commercial speed (including stops), achieved by the buses, which we further postulate as a linear relationship between infrastructure investment and running speed. Given this context, we develop a microeconomic model for the operation of a bus corridor that minimises total cost (users and operator) and has five decision variables: frequency, capacity of vehicles, station spacing, fare payment system and running speed, thus extending the traditional framework. Congestion, induced by bus frequency, plays an important role in the design of the system, as queues develop behind high demand bus stops when the frequency is high. We show that (i) an off-board fare payment system is the most cost effective in the majority of circumstances; (ii) bus congestion results in decreased frequency while fare and bus capacity increase, and (iii) the optimal running speed grows with the logarithm of demand.     

Bus dispatching at timed transfer transit stations using bus tracking technology

A timed transfer terminal synchronizes the arrival of incoming vehicles with the departure of outgoing vehicles so as to minimize transfer delays. Most bus timed transfer terminals follow fixed schedules, and do not utilize intelligent transportation systems for vehicle tracking and control. This paper reviews technologies that enable real-time control of timed transfer. We evaluate the benefits of tracking bus locations and executing dynamic schedule control through the simulation of a generic timed transfer terminal under a range of conditions. Based on empirical data collected by the Los Angeles County/Metropolitan Transit Agency, we found delay over segments of long-headway bus lines to be negatively correlated with lateness at the start of the segment, indicating that buses have a tendency to catch up when they fall behind schedule. The simulation analysis showed that the benefit of bus tracking is most significant when one of the buses experiences a major delay, especially when there is a small number of connecting buses.     

An optimization model for bus fleet replacement with budgetary and environmental constraints

ABSTRACT

As maintenance and operation costs increase with usage over time, equipment is replaced when the value of new equipment is more attractive. Some methods have been developed to solve this problem. In the public transport sector, such problems are frequently analyzed by fleet managers and determined by bus age restriction regulations. We propose an Integer Programming model that integrates both budgetary and environmental constraints (CO₂ emissions) which, as far as we know, have not previously been studied in conjunction. The study aims to determine the optimal replacement plan for a fleet of diesel buses of different size, age, maintenance costs and emissions rates, with new (less polluting) diesel buses over a time horizon of 50 years. The results indicate that it is possible to reduce emissions with a low annual budget using an optimal replacement policy.     

Integrated optimization of bus priority operations in connected vehicle environment

Most previous works associated with transit signal priority merely focus on the optimization of signal timings, ignoring both bus speed and dwell time at bus stops. This paper presents a novel approach to optimize the holding time at bus stops, signal timings, and bus speed to provide priority to buses at isolated intersections. The objective of the proposed model is to minimize the weighted average vehicle delays of the intersection, which includes both bus delay and impact on nearby intersection traffic, ensuring that buses clear these intersections without being stopped by a red light. A set of formulations are developed to explicitly capture the interaction between bus speed, bus holding time, and transit priority signal timings. Experimental analysis is used to show that the proposed model has minimal negative impacts on general traffic and outperforms the no priority, signal priority only, and signal priority with holding control strategies (no bus speed adjustment) in terms of reducing average bus delays and stops. A sensitivity analysis further demonstrates the potential of the proposed approach to be applied to bus priority control systems in real‐time under different traffic demands, bus stop locations, and maximum speed limits. Copyright © 2016 John Wiley & Sons, Ltd.     

Environmental benefits of natural gas for buses

This paper presents a life cycle assessment comparing diesel buses with buses fueled by natural gas. The data for the emission of pollutants are based on the MEET Project of the European Commission (EC), supplemented by data measured for diesel and gas buses in Paris. The benefits of the gas fueled bus are then quantified using the damage cost estimates of the ExternE Project of the EC. A diesel bus with emissions equal to Standard EURO2 of the EC is compared with the same bus equipped with a natural gas engine, for use in Paris and in Toulouse. The damage cost of a diesel bus is significant, in the range of 0.4–1.3

/km. Natural gas allows an appreciable reduction of the emissions, lowering the damage cost by a factor of about 2.5 (Toulouse) to 5.5 (Paris). An approximate rule is provided for transferring the results to other cities. A sensitivity analysis is carried out to evaluate the effect of the evolution of the emissions standard towards EURO3, 4 and 5, as well as the effect of uncertainties. Finally a comparison is presented between a EURO2 diesel bus with particle filter, and a gas fueled bus with the MPI engine of IVECO, a more advanced and cleaner technology. With this engine the damage costs of the gas fueled bus are about 3–5 times lower than those of the diesel with particle filter, even though the latter has already very low emissions.     

A dynamic evacuation model for pedestrian–vehicle mixed-flow networks

In urban emergency evacuation, a potentially large number of evacuees may depend either on transit or other modes, or need to walk a long distance, to access their passenger cars. In the process of approaching the designated pick-up points or parking areas for evacuation, the massive number of pedestrians may cause tremendous burden to vehicles in the roadway network. Responsible agencies often need to contend with congestion incurred by massive vehicles emanating from parking garages, evacuation buses generated from bus stops, and the conflicts between evacuees and vehicles at intersections. Hence, an effective plan for such evacuation needs to concurrently address both the multi-modal traffic route assignment and the optimization of network signal controls for mixed traffic flows. This paper presents an integrated model to produce the optimal distribution of vehicle and pedestrian flows, and the responsive network signal plan for massive mixed pedestrian–vehicle flows within the evacuation zone. The proposed model features its effectiveness in accounting for multiple types of evacuation vehicles, the interdependent relations between pedestrian and vehicle flows via some conversion locations, and the inevitable conflicts between intersection turning vehicle and pedestrian flows. An illustrating example concerning an evacuation around the M&T stadium area has been presented, and the results indicate the promising properties of our proposed model, especially on reflecting the complex interactions between vehicle and pedestrian flows and the favorable use of high-occupancy vehicles for evacuation operations.     

Life cycle ownership cost and environmental externality of alternative fuel options for transit buses

This paper assesses alternative fuel options for transit buses. We consider the following options for a 40-foot and a 60-foot transit bus: a conventional bus powered by either diesel or a biodiesel blend (B20 or B100), a diesel hybrid-electric bus, a sparking-ignition bus powered by Compressed Natural Gas (CNG) or Liquefied Natural Gas (LNG), and a battery electric bus (BEB) (rapid or slow charging). We estimate life cycle ownership costs (for buses and infrastructure) and environmental externalities caused by greenhouse gases (GHGs) and criteria air pollutants (CAPs) emitted from the life cycle of bus operations. We find that all alternative fuel options lead to higher life cycle ownership and external costs than conventional diesel. When external funding is available to pay for 80% of vehicle purchase expenditures (which is usually the case for U.S. transit agencies), BEBs yield large reductions (17–23%) in terms of ownership and external costs compared to diesel. Furthermore, BEBs’ advantages are robust to changes in operation and economic assumptions when external funding is available. BEBs are able to reduce CAP emissions significantly in Pittsburgh’s hotspot areas, where existing bus fleets contribute to 1% of particulate matter emissions from mobile sources. We recognize that there are still practical barriers for BEBs, e.g. range limits, land to build the charging infrastructure, and coordination with utilities. However, favorable trends such as better battery performance and economics, cleaner electricity grid, improved technology maturity, and accumulated operation experience may favor use of BEBs where feasible.     

Optimal bus fleet management strategy for emissions reduction

Transportation is a major cause for environmental degradation via exhaust emissions. For many transit-oriented metropolitan areas, bus trips often constitute a sizeable mode share. Managing the bus fleet, in particular updating buses to comply with the newer emissions standards, therefore, can have a substantial impact on transportation-induced air quality. This paper presents the approach of remaining life additional benefit–cost (RLABC) analysis for maximising the total net benefit by either early-retiring or retrofitting the current bus fleet within their lifespans. By referring to the net benefits for different bus types estimated by RLABC analysis, the most beneficial management scheme for the current bus fleet can be identified. Optimal bus fleet management (BFM) models based on the RLABC analysis for the operator and the government are developed. Then a government subsidy plan is produced to achieve win–win solutions, which will offer efficient and flexible management schemes. To illustrate the approach, the largest bus company in Hong Kong, which carries more than 23% of the total trips in Hong Kong, is taken as a case study example. Instead of adopting a fixed retirement plan, such as replacing buses at the age of 17 as is currently practised, the proposed method develops an optimal BFM scheme that progressively phases out buses or retrofits them. This study produces promising results to demonstrate the large benefit of this approach for optimal bus fleet management.