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.     

Welfare maximization for bus transit systems with timed transfers and financial constraints

Conventional and flexible bus services may be combined to better serve regions with a wide range of characteristics. If demand densities and resulting service frequencies are low, the coordination of bus arrivals at transfer stations may significantly reduce passenger transfer times. A method is proposed for integrating, coordinating, and optimizing bus services while considering many‐to‐many travel patterns, demand elasticity, financial constraints, and appropriate service type for various regions. The objective is to maximize welfare, that is, the sum of producer and consumer surplus. The problem is solved with a hybrid optimization method, in which a genetic algorithm with bounded integer variables is selected for solving one of the subproblems. The service types, fares, headways, and service zone sizes are jointly optimized. Sensitivity analyses explore how the choice among conventional and flexible busses depends on the demand, subsidy, and demand elasticity parameters. The results also show that welfare can increase due to coordination, and these increases are found to be higher in cases with high demand or low subsidy. Copyright © 2015 John Wiley & Sons, Ltd.     

Multiple period optimization of bus transit systems

Analytic models are developed for optimizing bus services with time dependence and elasticity in their demand characteristics. Some supply parameters, i.e. vehicle operating costs and speeds are also allowed to vary over time. The multiple period models presented here allow some of the optimized system characteristics (e.g. route structure) to be fized at values representing the best compromise over different time periods, while other characteristics (e.g. service headways) may be optimized within each period. In a numerical example the demand is assumed to fluctuate over a daily cycle (e.g. peak, offpeak and night), although the same models can also be used for other cyclical or noncyclical demand variations over any number of periods. Models are formulated and compared for four types of conditions, which include steady fixed demand, cyclical fixed demand, steady equilibrium demand and cyclical equilibrium demand. When fixed demand is assumed, the optimization objective is minimum total system cost, including operator cost and user cost, while operator profit and social welfare are the objective functions maximized for equilibrium demand. The major results consist of closed form solutions for the route spacings, headways, fares and costs for optimized feeder bus services under various demand conditions. A comparison of the optimization results for the four cases is also presented. When demand and bus operating characteristics are allowed to vary over time, the optimal functions are quite similar to those for steady demand and supply conditions. The optimality of a constant ratio between the headway and route spacing, which is found at all demand densities if demand is steady, is also maintained with a multi-period adjustment factor in cyclical demand cases, either exactly or with a relatively negligible approximation. These models may be used to analyze and optimize fairly complex feeder or radial bus systems whose demand and supply characteristics may vary arbitrarily over time.     

Maximizing net benefits for conventional and flexible bus services

Transit ridership is usually sensitive to fares, travel times, waiting times, and access times, among other factors. Therefore, the elasticities of demand with respect to such factors should be considered in modeling bus transit services and must be considered when maximizing net benefits (i.e. “system welfare” = consumer surplus + producer surplus) rather just minimizing costs. In this paper welfare is maximized with elastic demand relations for both conventional (fixed route) and flexible-route services in systems with multiple dissimilar regions and periods. As maximum welfare formulations are usually too complex for exact solutions, they have only been used in a few studies focused on conventional transit services. This limitation is overcome here for both conventional and flexible transit services by using a Real Coded Genetic Algorithm to solve such mixed integer nonlinear welfare maximization problems with constraints on capacities and subsidies. The optimized variables include service type, zone sizes, headways and fares. We also determine the maximum welfare threshold between optimized conventional and flexible services) and explore the effects of subsidies. The proposed planning models should be useful in selecting the service type and optimizing other service characteristics based on local geographic characteristics and financial constraints.     

Towards a general microeconomic model for the operation of public transport

After Vickrey's view, Mohring constructed a microeconomic model to determine the optimal frequency of buses serving a corridor with fixed demand. The main result was that frequency should be proportional to the square root of demand. The role of users' costs was shown to be crucial. This approach has evolved over the past decades, improving our understanding of public transport operations. This paper describes and analyses the evolution of microeconomic models for the analysis of public transport services with parametric demand, leading towards a more comprehensive one. An in-depth review of all the contributions in the academic literature is presented, emphasizing both the treatment of variables and the form of the results mostly in terms of frequency and fleet size. A series of partial new elements is also identified. An extension of Jansson's model for a single period is developed analytically, including the effect of vehicle size on operating costs and the influence of crowding on the value of time. Numerical simulations are used for comparison and analysis. A general model is then proposed where bus operations are optimized accounting for a number of simultaneous relations. Finally, the different models are discussed and compared.     

Vehicle scheduling under stochastic trip times: An approximate dynamic programming approach

Due to unexpected demand surge and supply disruptions, road traffic conditions could exhibit substantial uncertainty, which often makes bus travelers encounter start delays of service trips and substantially degrades the performance of an urban transit system. Meanwhile, rapid advances of information and communication technologies have presented tremendous opportunities for intelligently scheduling a bus fleet. With the full consideration of delay propagation effects, this paper is devoted to formulating the stochastic dynamic vehicle scheduling problem, which dynamically schedules an urban bus fleet to tackle the trip time stochasticity, reduce the delay and minimize the total costs of a transit system. To address the challenge of “curse of dimensionality”, we adopt an approximate dynamic programming approach (ADP) where the value function is approximated through a three-layer feed-forward neural network so that we are capable of stepping forward to make decisions and solving the Bellman’s equation through sequentially solving multiple mixed integer linear programs. Numerical examples based on the realistic operations dataset of bus lines in Beijing have demonstrated that the proposed neural-network-based ADP approach not only exhibits a good learning behavior but also significantly outperforms both myopic and static polices, especially when trip time stochasticity is high.     

Optimization of grid bus transit systems with elastic demand

Current analytic models for optimizing urban bus transit systems tend to sacrifice geographic realism and detail in order to obtain their solutions. The models presented here shows how an optimization approach can be successful without oversimplifying spatial characteristics and demand patterns of urban areas and how a grid bus transit system in a heterogeneous urban environment with elastic demand is optimized. The demand distribution over the service region is discrete, which can realistically represent geographic variation. Optimal network characteristics (route and station spacings), operating headways and fare are found, which maximize the total operator profit and social welfare. Irregular service regions, many‐to‐many demand patterns, and vehicle capacity constraints are considered in a sequential optimization process. The numerical results show that at the optima the operator profit and social welfare functions are rather flat with respect to route spacing and headway, thus facilitating the tailoring of design variables to the actual street network and particular operating schedule without a substantial decrease in profit. The sensitivities of the design variables to some important exogenous factors are also presented.     

Optimal bus service patterns and frequencies considering transfer demand elasticity with genetic algorithm

This paper attempts to optimize bus service patterns (i.e., all-stop, short-turn, and express) and frequencies which minimize total cost, considering transfer demand elasticity. A mathematical model is developed based on the objective total cost for a generalized bus route, which is optimized subject to a set of constraints ensuring sufficient capacity, an operable bus fleet, and service frequency conservation. To optimize the integrated service of a bus route with many stops, which is a combinatorial optimization problem, a genetic algorithm is developed and applied to search for the solution. A case study, based on a real-world bus route in New Jersey, is conducted to demonstrate the applicability and effectiveness of the developed model and the solution algorithm. Results show that the proposed methodology is fairly efficient, and the optimized bus service significantly reduces total cost.     

Optimal feeder bus routes on irregular street networks

The methodology presented here seeks to optimize bus routes feeding a major intermodal transit transfer station while considering intersection delays and realistic street networks. A model is developed for finding the optimal bus route location and its operating headway in a heterogeneous service area. The criterion for optimality is the minimum total cost, including supplier and user costs. Irregular and discrete demand distributions, which realistically represent geographic variations in demand, are considered in the proposed model. The optimal headway is derived analytically for an irregularly shaped service area without demand elasticity, with non‐uniformly distributed demand density, and with a many‐to‐one travel pattern. Computer programs are designed to analyze numerical examples, which show that the combinatory type routing problem can be globally optimized. The improved computational efficiency of the near‐optimal algorithm is demonstrated through numerical comparisons to an optimal solution obtained by the exhaustive search (ES) algorithm. The CPU time spent by each algorithm is also compared to demonstrate that the near‐optimal algorithm converges to an acceptable solution significantly faster than the ES algorithm.     

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.     

Joint optimization of a rail transit line and its feeder bus system

A model is developed for jointly optimizing the characteristics of a rail transit route and its associated feeder bus routes in an urban corridor. The corridor demand characteristics are specified with irregular discrete distributions which can realistically represent geographic variations. The total cost (supplier plus user cost) of the integrated bus and rail network is minimized with an efficient iterative method that successively substitutes variable values obtained through classical analytic optimization. The optimized variables include rail line length, rail station spacings, bus headways, bus stop spacings, and bus route spacing. Computer programs are designed for optimization and sensitivity analysis. The sensitivity of the transit service characteristics to various travel time and cost parameters is discussed. Numerical examples are presented for integrated transit systems in which the rail and bus schedules may be coordinated.     

Rail line length in a crosstown corridor with many-to-many demand

An analytical model that determines the optimal location and length of rail line along a crosstown transportation corridor with the objective of minimizing the total transportation cost is presented. A general, many-to-many passenger demand pattern is considered. The objective function, which includes the rail and bus riding costs, rail and bus operating costs, rail fleet costs and rail line costs, is minimized by using the classical optimization method with the aid of a computer program developed for the model. The model is applied to the Northwest-South transportation corridor in Calgary, Alberta, and the sensitivity of the optimal rail line location and length to the unit cost and demand parameters at their reasonable ranges is tested. It is found that although the total passenger demand, unit rail line cost, and unit bus operating cost have greater influence than the unit bus and rail riding costs, and unit rail fleet and operating costs, the optimal line length is generally insensitive to all these parameters. It is also found that the length of the existing LRT line in the corridor is comparable to the optimal line length obtained from the model, but the existing line should be extended further south in order to meet the heavier demand in that direction optimally.     

Bus policy — Conclusions from a case study

The main policy conclusions from a recent bus study in the new town of Telford in the U.K. are summarised and discussed. The choice of bus routes and their combination into networks is examined. Alternative fares systems are compared and the implications for the fare levels necessary to cover costs are discussed. It is argued that bus services can generally be financed from the fare-box but that, unless services are cut as passenger demand falls, unduly high fares will result and these will unnecessarily drive more passengers away from the buses. Several particular aspects of service marketing are then examined and the paper concludes by discussing the actual organisation of the bus services.     

Optimal design and benefits of a short turning strategy for a bus corridor

We develop a short turning model using demand information from station to station within a single bus line-single period setting, aimed at increasing the service frequency on the more loaded sections to deal with spatial concentration of demand considering both operators’ and users’ costs. We find analytical expressions for optimal values of the design variables, namely frequencies (inside and outside the short cycle), capacity of vehicles and the position of the short turn limit stations. These expressions are used to analyze the influence of different parameters in the final solution. The design variables and the corresponding cost components for operators and users (waiting and in-vehicle times) are compared against an optimized normal operation scheme (single frequency). Applications on actual transit corridors exhibiting different demand profiles are conducted, calculating the optimal values for the design variables and the resulting benefits for each case. Results show the typical demand configurations that are better served using a short turn strategy.     

Performance indicator analysis: A management tool for the improvement of bus transit operation in Bangkok

This paper intends to demonstrate that the performance indicator analysis technique can be successfully used as a diagnostic tool to identify operational inefficiency and ineffectiveness at the route level of transit operation. The technique has been applied on 14 bus routes of Bangkok Mass Transit Authority to reveal the inter-route differences in operational efficiency and effectiveness. Twenty performance indicators relating to costs of services, fuel consumption, staff ratio, crew productivity, fleet utilization, service output per bus, daily revenues, etc., were selected to represent the resource efficiency, resource effectiveness and service effectiveness of the bus system. Results of the analyses revealed that considerable variations existed across the routes against many of these 20 selected indicators. These included variations in terms of labor and capacity utilization, maintenance expenditure, etc., many of which can be improved through suitable managerial measures. Based on these findings, specific recommendations have been made for improvement in the deficient areas that are considered to be within the operator domain. These indicators also provide a basis for comparison over time, with other operators and standards. A ranking scale was also developed to determine the over all attractiveness of the routes.     

Modeling and optimizing urban bus transit considering headway variation for cost and service reliability analysis

Due to the stochastic nature of traffic conditions and demand fluctuations, it is a challenging task for operators to maintain reliable services, and passengers often suffer from longer travel times. A failure to consider this issue while planning bus services may lead to undesirable results, such as higher costs and a deterioration in level of service. Considering headway variation at route stops, this paper develops a mathematical model to optimize bus stops and dispatching headways that minimize total cost, consisting of both user and operator costs. A Genetic Algorithm is applied to search for a cost-effective solution in a real-world case study of a bus transit system, which improves service reliability in terms of a reduced coefficient of variation of headway.     

Multilevel modelling of Demand Responsive Transport (DRT) trips in Greater Manchester based on area-wide socio-economic data

Providing public transport in areas of low demand has long proved to be a challenge to policy makers and practitioners. With the developing economic, social and environmental trends, there is pressure for alternative solutions to the policy of subsidising conventional bus services. One potential solution is to adopt more flexible routes and/or timetables to better match the required demand. Therefore such ‘on demand’ or ‘Demand Responsive Transport’ (DRT) services (known as paratransit in the US) have been adopted in a number of locations. This paper seeks to explore the effects of area-wide factors on the demand of DRT by reporting the results of a statistical analysis of DRT service provision in the metropolitan region of Greater Manchester, the public transport authority of which offers one of the largest and most diverse range of DRT schemes in the UK. Specifically, this paper employs a multilevel modelling approach to investigate the impact of both DRT supply-oriented factors at the service area level and socio-economic factors at the lower super output area (LSOA) level on the average number of trips made by DRT per year. This hierarchical or ‘nested’ structure was adopted because typically the LSOAs within the same Service Area may share similar characteristics. It is found that the demand for DRT services was higher in areas with low car ownership, low population density, high proportion of white people, and high levels of social deprivation, measured in terms of income, employment, education, housing and services, health and disability, and living environment.     

Evaluating the impact of spatio-temporal demand forecast aggregation on the operational performance of shared autonomous mobility fleets

Fleet operators rely on forecasts of future user requests to reposition empty vehicles and efficiently operate their vehicle fleets. In the context of an on-demand shared-use autonomous vehicle (AV) mobility service (SAMS), this study analyzes the trade-off that arises when selecting a spatio-temporal demand forecast aggregation level to support the operation of a SAMS fleet. In general, when short-term forecasts of user requests are intended for a finer space–time discretization, they tend to become less reliable. However, holding reliability constant, more disaggregate forecasts provide more valuable information to fleet operators. To explore this trade-off, this study presents a flexible methodological framework to evaluate and quantify the impact of spatio-temporal demand forecast aggregation on the operational efficiency of a SAMS fleet. At the core of the methodological framework is an agent-based simulation that requires a demand forecasting method and a SAMS fleet operational strategy. This study employs an offline demand forecasting method, and an online joint AV-user assignment and empty AV repositioning strategy. Using this forecasting method and fleet operational strategy, as well as Manhattan, NY taxi data, this study simulates the operations of a SAMS fleet across various spatio-temporal aggregation levels. Results indicate that as demand forecasts (and subregions) become more spatially disaggregate, fleet performance improves, in terms of user wait time and empty fleet miles. This finding comes despite demand forecast quality decreasing as subregions become more spatially disaggregate. Additionally, results indicate the SAMS fleet significantly benefits from higher quality demand forecasts, especially at more disaggregate levels.

     

Investigating the impact of stochastic vehicle arrivals to optimal stop spacing and headway for a feeder bus route

Stop spacing and service frequency (i.e., the inverse of headway) are key elements in transit service planning. The trade‐offs between increasing accessibility and reducing travel time, which affect transit system performance, need to be carefully evaluated. The objective of this study is to optimize stop spacing and headway for a feeder bus route, considering the relationship between the variance of inter‐arrival time (VIAT), which yields the minimum total cost (including user and operator costs). A solution algorithm, called successive substitution, is adapted to efficiently search for the optimal solutions. In a numerical example, the developed model is applied to planning a feeder bus route in Newark, New Jersey. The results indicate that the optimal stop spacing should be longer that those suggested by previous studies where the impact of VIAT was ignored. Reducing VIAT via certain operational control strategies (i.e., holding/stop‐skipping, transit signal priority) may shorten stop spacing and improve accessibility. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimating commuter mode choice: A discrete choice analysis of the impact of road pricing and parking charges

Automobile use leads to external costs associated with emissions, congestion, noise and other impacts. One option for minimizing these costs is to introduce road pricing and parking charges to reduce demand for single occupant vehicle (SOV) use, while providing improvements to alternatives to encourage mode switching. However, the impact of these policies on urban mode choice is uncertain, and results reported from regions where charging has been introduced may not be transferable. In particular, revealed preference data associated with cost recovery tolls on single facilities may not provide a clear picture of driver response to tolls for demand management. To estimate commuter mode choice behaviour in response to such policies, 548 commuters from a Greater Vancouver suburb who presently drive alone to work completed an individually customized discrete choice experiment (DCE) in which they chose between driving alone, carpooling or taking a hypothetical express bus service when choices varied in terms of time and cost attributes. Attribute coefficients identified with the DCE were used in a predictive model to estimate commuter response to various policy oriented combinations of charges and incentives. Model results suggest that increases in drive alone costs will bring about greater reductions in SOV demand than increases in SOV travel time or improvements in the times and costs of alternatives beyond a base level of service. The methods described here provide an effective and efficient way for policy makers to develop an initial assessment of driver reactions to the introduction of pricing policies in their particular regions.