Planning school transport: design of routes with flexible school opening times

Abstract

This paper puts forward a methodology for designing a system for school transport which, apart from designing routes, specifies school opening times. Traditionally school opening times have always been identical in the same area meaning many buses have to be used at the same time. This paper suggests the staggering of school opening times in order to minimise the number of buses and thereby reduce the enormous costs involved in running them. The methodology is based on: a first phase which addresses the classic routing problem by using mixed integer lineal programming and a second phase which uses bi-level programming to find the vector for school opening times, which, when staying within the constraints of the problem, minimises the direct costs of the system. The upper level represents the evaluation of the system costs and the lower level finds the best combination of optimum routes for the same bus.     

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.     

Maximizing bus discharge flows from multi-berth stops by regulating exit maneuvers

Upon having loaded and unloaded their passengers, buses are often free to exit a multi-berth bus stop without delay. A bus need not wait to perform this exit maneuver, even if it requires circumventing one or more other buses that are still dwelling in the stop’s downstream berths. Yet, many jurisdictions impose restrictions on bus entry maneuvers into a stop to limit disruptions to cars and other buses. Buses are typically prohibited from entering a stop whenever this would require maneuvering around other buses still dwelling in upstream berths. An entering bus is instead required to wait in queue until the upstream berths are vacated.Analytical models are formulated to predict how bus discharge flows from busy, multi-berth stops are affected by allowing buses to freely exit, but not freely enter berths. These models apply when: a bus queue is always present at the stop’s entrance; buses depart the entry queue and enter the stop as per the restriction described above; and the stop is isolated from the effects of nearby traffic signals and other bus stops. We find that for these restricted-entry stops, bus-carrying capacities can often be improved by regulating the exit maneuvers as well. This turns out to be particularly true when the stop’s number of berths is large. Simulations show that these findings still hold when a stop is only moderately busy with entry queues that persist for much, but not all of the time. The simulations also indicate that removing any restrictions on bus exit maneuvers is almost always productive when stops are not busy, such that short entry queues form only on occasion, and only for short periods. We argue why certain simple policies for regulating exit maneuvers would likely enhance bus-stop discharge flows.     

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.     

Characteristics of multi-shop/ multi-termal delivery routes, with backghauls and unique items

This paper creates and evaluates spatial models for multiple stop delivery routes that are allowed to begin and end at separate terminals. Each terminal must deliver a set of unique items. These deliveries can be coordinated with deliveries from other terminals to form back-haul loops. The paper assumes that stops are uniformly distributed over a large region and that a strip-routing strategy is followed. Among the findings are that the optimal orientation of a delivery district is defined by the ellipse passing through the routing district and having the terminals as foci. The paper also determines optimal district shape, and determines which districts should be traveled in a single pass (entering and exiting at opposite ends), and which should be traversed in two passes (entering and exitin from the same end).     

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.     

Optimizing sustainable feeder bus operation considering realistic networks and heterogeneous demand

A mathematical model is developed to optimize social and fiscal sustainable operation of a feeder bus system considering realistic network and heterogeneous demand. The objective total profit is a nonlinear, mixed integer function, which is maximized by optimizing the number of stops, headway, and fare. The stops are located which maximize the ridership. The demand elasticity for the bus service is dependent on passengers' access distance, wait time, in‐vehicle time, and fare. An optimization algorithm is developed to search for the optimal solution that maximizes the profit. The modeling approach is applied to planning a bus transit system within Woodbridge, New Jersey. Copyright © 2011 John Wiley & Sons, Ltd.     

Bus routing strategies in a transit market: A case study of Hong Kong

Conventionally, the objective of transit routing is often set either to minimize the total operational cost, subject to a given level of service quality, or to maximize the service quality at a given acceptable cost. In a deregulated, commercial‐based environment however, such as bus and railway operations in cities of the UK and Hong Kong where several private firms compete in route‐based or area‐based market, routing becomes one of the means for higher returns rather than just for cost saving. In such a case, how do the transit providers set up their routes for profit‐maximization? Will the routing based on the provider's objective meet the user's objective? How do government regulations and policies affect the choice of transit provider's routing strategy? To answer these questions, we first examine the relationship between the objectives of users and transit providers, set up criteria for transit routing quality, and then investigate the possible routing configurations/patterns for a hypothetical case. These criteria include (1) the load factor of transit, (2) the level of route directness, (3) the level of route overlapping, and (4) the total number of routes and (5) the average of route length. These measures are finally applied to a real case in Hong Kong to examine the route changes of Kowloon Motor Bus from 1975 to 1995. The result of the empirical case reveais how key measures such as load factor are controlled by the bus operator and affected by government policies and how the bus routing pattern was adjusted to meet users' need. Facing the dilemma as evident in Hong Kong between the route directness and the efficiency of road use, we suggest that a rational multi‐modal routing structure be put in place if an institutional solution is introduced so that bus and other transit modes can form a sharing program or an alliance.     

Bus arrival time prediction at bus stop with multiple routes

Provision of accurate bus arrival information is vital to passengers for reducing their anxieties and waiting times at bus stop. This paper proposes models to predict bus arrival times at the same bus stop but with different routes. In the proposed models, bus running times of multiple routes are used for predicting the bus arrival time of each of these bus routes. Several methods, which include support vector machine (SVM), artificial neural network (ANN), k nearest neighbours algorithm (k-NN) and linear regression (LR), are adopted for the bus arrival time prediction. Observation surveys are conducted to collect bus running and arrival time data for validation of the proposed models. The results show that the proposed models are more accurate than the models based on the bus running times of single route. Moreover, it is found that the SVM model performs the best among the four proposed models for predicting the bus arrival times at bus stop with multiple routes.     

Transit stop inspection and maintenance scheduling: A GPU accelerated metaheuristics approach

Bus stops are integral elements of a transit system and as such, their efficient inspection and maintenance is required, for proper and attractive transit operations. Nevertheless, spatial dispersion and the extensive number of bus stops, even for mid-size transit systems, complicates scheduling of inspection and maintenance tasks. In this context, the problem of scheduling transit stop inspection and maintenance activities (TSIMP) by a two-stage optimization approach, is formulated and discussed. In particular, the first stage involves districting of the bus stop locations into areas of responsibility for different inspection and maintenance crews (IMCs), while in the second stage, determination of the sequence of bus stops to be visited by an IMC is modelled as a vehicle routing problem. Given the complexity of proposed optimization models, advanced versions of different metaheuristic algorithms (Harmony Search and Ant Colony Optimization) are exploited and assessed as possible options for solving these models. Furthermore, two variants of ACO are implemented herein; one implemented into a CPU parallel computing environment along with an accelerated one by means of general-purpose graphics processing unit (GPGPU) computing. The model and algorithms are applied to the Athens (Greece) bus system, whose extensive number of transit stops (over 7500) offers a real-world test bed for assessing the potential of the proposed modelling approach and solution algorithms. As it was shown for the test example examined, both algorithms managed to achieve optimized solutions for the problem at hand while there were fund robust with respect to their algorithmic parameters. Furthermore, the use of graphics processing units (GPU) managed to reduce of computational time required.     

School choice: understanding the trade-off between travel distance and school quality

Children are traveling longer distances to school, and the share traveling by car is increasing. This paper examines the effects of school attributes on school choice, which in turn gives rise to travel distance and mode choice. It is well known that school quality is capitalized into residential land values. Households willing and able to pay price premiums may choose to live closer to good-quality schools. In contrast, households with less ability to pay are likely to live in places with schools of lower quality. The California public school system has an open enrollment policy, which allows students to transfer out of their neighbourhood school when places are available. When this option is exercised, students may travel longer distances to school compared with students who attend their neighbourhood schools. We used travel diary data from the 2001 Post Census Regional Household Travel Survey to model school destination choices for K-12 students in the Los Angeles region, California. Parents may choose to send their children to neighbourhood schools, other schools within their home district, or out-of-district schools. We find that location, school quality, and other school features influence the probability of a school being chosen, and the extent to which these factors influence choice varies depending on the characteristics of the residential district and the attributes of the household.     

The influence of bus service satisfaction on university students' mode choice

The purpose of this study was to determine the relationship between bus service satisfaction and the transport mode of choice among university students in Qatar. The degree of bus service satisfaction was collected directly from questionnaire surveys, in which university students were asked questions in relation to their satisfaction with the bus service they used and their transport mode of choice. These questions were categorized into three factors according to confirmatory factor analysis: service at bus stops, service of busses, and service of drivers. Furthermore, the students were asked which mode of transport they used given the choice between public and private transport. This study presents a structural equation model to determine how much bus service satisfaction affects people's decisions about their transport mode. The results from the analysis showed that three key factors—namely, service at bus stops, service of busses, and service of bus drivers—were strongly correlated to the mode of choice. In particular, the bus stop was strongly associated with ease of use, shade, cleanliness, safety, and crowdedness level, while the bus itself influenced reliability, travel time, and frequency. Complying with traffic laws and the driver's attitude were also important contributors to the level of bus service satisfaction. Ultimately, this study will be beneficial for policy/decision‐makers. It will allow them to determine what needs to be accomplished to encourage people to use public transportation. Copyright © 2016 John Wiley & Sons, Ltd.     

The implications of school choice on travel behavior and environmental emissions

We examine the implications of school choice on walkability, school travel mode and overall environmental emissions. In developing this proof-of-concept model we show—and quantify—differences between city-wide schools and their neighborhood school counterpart. Our analysis demonstrates how children attending city-wide schools may have heightened travel distance, greenhouse gas emissions, and exposure to bus fumes. Using available data along with a series of informed assumptions we figure the city-wide school had six times fewer children walking, 4.5 times as many miles traveled, 4.5 times the system cost, and 3–4.5 times the amount of criteria air pollutants and greenhouse gas emissions. By providing bus service, the overall miles traveled (and resulting emissions) decreased 30–40% compared to the scenario without bus service, however system costs were higher for both the neighborhood and city-wide school (no pollution externality costs were factored in).     

Towards modal choice decision-making models: A case study of Lagos state transport corporation bus riders

Identification of the socioeconomic factors which affect the demand for buses, and the analysis of the use of the other transport modes by bus users are the two main objectives of this article. Work and school trips are highlighted as being very important trip purposes in Lagos metropolis by the multiple discriminant analysis model. It identifies mode of transport, distance, travel time, reliability, and the number of stops as significant mode choice variables. Multiple linear regression models for work and school trips identify mode of transport, transfort fare, travel time, annual income, and crew behaviour as significant variables in the choice of transport mode. These findings support the two alternative hypotheses of the study that the choice of bus is related to the individual perception of the quality of service of the different modes and that socioeconomic characteristics of the riders influence the patronage of buses. The attention of policy makers for the 22 transport corporations that operate inter-and intra-urban services in all the 21 states and the federal capital of Abuja in Nigeria is drawn to the importance of these variables for decisions.     

Development and validation of energy demand uncertainty model for electric city buses

The prediction of electric city bus energy demand is crucial in order to estimate operating costs and to size components such as the battery and charging systems. Unfortunately, there are unpredictable dynamic factors that can cause variation in the energy demand, particularly concerning driver choices and traffic levels. The impact of these factors on energy demand has been difficult to study since fast computing sufficiently accurate dynamic simulation models have been missing, properly quantified in terms of relevant inputs which contribute to energy demand. The objective is to develop and validate a novel electric city bus model for computing the energy demand, to study the nature and impact of various input factors. The developed equation-based model predicted real-world electric city bus energy consumption within 0.1% error. The most crucial unmeasurable input factors were the driven bus route, the number of stops, the elevation profile, the traffic level and the driving style. This understanding can be used to specify routes and stops for a given electric bus battery capacity. Worst-case scenarios are also necessary for electric bus sizing analysis. The best- and worst-case levels of the crucial factors were identified and with them synthetic best- and worst-case speed profiles were generated to demonstrate their effect to the energy demand. While the measured nominal consumption was 0.70 kWh/km, the computed range of variation was between 0.19 kWh/km and 1.34 kWh/km. For design sizing purposes, an electric city bus can have a broad range of possible energy consumption rates due to mission condition variations.     

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.     

Optimal transit routing with partial online information

This paper studies the routing strategy in a transit network with partial online information at stops. By partial online information, we mean that the arrival time of the incoming transit vehicles is available for a subset of the lines serving a stop. To cope with the partial information assumption, a new routing strategy is proposed and closed form formulae for computing expected waiting times and line boarding probabilities are derived. The proposed strategy unifies existing hyperpath-based transit route choice models that assume either no information or full information. Like many existing models, it ensures optimality when all information is available or the headway is exponentially distributed. The problem of determining the attractive set is discussed for each of the three information cases. In particular, a new heuristic algorithm is developed to generate the attractive set in the partial information case, which will always yield a solution no worse than that obtained without any information. The paper also reveals that, when information is available, an optimal hyperpath may contain cycles. Accordingly, the cause of such cycles is analyzed, and a sufficient condition that excludes cycles from optimal hyperpaths is proposed. Finally, numerical experiments are conducted to illustrate the impact of information availability on expected travel times and transit line load distributions. Among other findings, the results suggest that it is more useful to have information on faster lines than on slower lines.     

On the capacity of isolated, curbside bus stops

The maximal rates that buses can discharge from bus stops are examined. Models were developed to estimate these capacities for curbside stops that are isolated from the effects of traffic signals. The models account for key features of the stops, including their target service levels assigned to them by a transit agency. Among other things, the models predict that adding bus berths to a stop can sometimes return disproportionally high gains in capacity. This and other of our findings are at odds with information furnished in professional handbooks.     

Stochastic transit equilibrium

We present a transit equilibrium model in which boarding decisions are stochastic. The model incorporates congestion, reflected in higher waiting times at bus stops and increasing in-vehicle travel time. The stochastic behavior of passengers is introduced through a probability for passengers to choose boarding a specific bus of a certain service. The modeling approach generates a stochastic common-lines problem, in which every line has a chance to be chosen by each passenger. The formulation is a generalization of deterministic transit assignment models where passengers are assumed to travel according to shortest hyperpaths. We prove existence of equilibrium in the simplified case of parallel lines (stochastic common-lines problem) and provide a formulation for a more general network problem (stochastic transit equilibrium). The resulting waiting time and network load expressions are validated through simulation. An algorithm to solve the general stochastic transit equilibrium is proposed and applied to a sample network; the algorithm works well and generates consistent results when considering the stochastic nature of the decisions, which motivates the implementation of the methodology on a real-size network case as the next step of this research.     

Analysis of real-time control strategies in a corridor with multiple bus services

Control strategies have been widely used in the literature to counteract the effects of bus bunching in passenger‘s waiting times and its variability. These strategies have only been studied for the case of a single bus line in a corridor. However, in many real cases this assumption does not hold. Indeed, there are many transit corridors with multiple bus lines interacting, and this interaction affects the efficiency of the implemented control mechanism.This work develops an optimization model capable of executing a control scheme based on holding strategy for a corridor with multiple bus lines.We analyzed the benefits in the level of service of the public transport system when considering a central operator who wants to maximize the level of service for users of all the bus lines, versus scenarios where each bus line operates independently. A simulation was carried out considering two medium frequency bus lines that serve a set of stops and where these two bus lines coexist in a given subset of stops. In the simulation we compared the existence of a central operator, using the optimization model we developed, against the independent operation of each line.In the simulations the central operator showed a greater reduction in the overall waiting time of the passengers of 55% compared to a no control scenario. It also provided a balanced load of the buses along the corridor, and a lower variability of the bus headways in the subset of stops where the lines coexist, thus obtaining better reliability for all types of passengers present in the public transport system.