Optimizing School Bus Stop Placement in Howard County, Maryland

A school bus problem is one of the most important logistical issues faced by governments and school administrations, which is widely depends on route optimization and scheduling. This study presents a mathematical model for the single-load school bus problem for urban areas, which considers bus stop selection, bus route generation, and school bus scheduling simultaneously. This model considers the possibility of demand outsourcing (e.g., students using parallel systems for transportation) and time windows in the school bus routing and scheduling (SBRS) problem. Each vehicle transports students from a bus stop to their school under the given constraints. Our goal is to maximize the transportation firm’s profits and increase the quality of service provided for students. To validate the presented model, the problem is solved by GAMS software, and the results are shown and analyzed. Finally, some sensitivity analyses are performed to show the efficiency of the presented model.

This paper proposes a School Bus Stop location and Routing Problem with Walking Accessibility and Mixed Load (SBSLRP-WA-ML), where the individual difference of walking accessibilities among students and the possibility of serving students attending different schools with the same bus simultaneously are considered. We first develop a mixed integer programming model for SBSLRP-WA-ML with the objective of minimizing the total commuting time, including walking time from the residence to school, in-vehicle travel time, and service time at stops. A two-stage solution method is then developed. In stage 1, an iterative clustering method based on k-means and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is used to locate bus stops aiming at minimizing the number of stops subject to various walking accessibilities. In stage 2, an improved ant colony optimization algorithm (IACO) integrating two local search operators is devised, which is used to generate bus routes with minimal total commuting time. A number of instances of different sizes are generated to verify the solution approach, and the influential factors with respect to total commuting time are analyzed. The model is also compared to the door-to-door school bus services. Comparison to similar methods and sensitivity analysis of parameters are also conducted to analyze the performance and robustness of the proposed approach.

In this dissertation, we solve a school bus routing problem of transporting students including special education (handicapped) students and assigning them in Oldham county education district. The main contribution of this research is that we consider special education students (Type-2) along with other students (Type-1) and design a comprehensive school bus schedule to transport both kinds of students at the same time. Also, a student assignment mathematical model is presented to optimize the number of bus stops in use as well as one important measure of service quality, the total student walking distance. Comparing to the classic clustering methods, heuristic methods, or other methods from previous literatures, a mathematical optimization model is developed to solve a student assignment problem and to obtain the global optimal solution. The modeling constraints include budget limit, travel time limit, equity, school time window, and etc. Especially, the main difference between our model and other models is that it takes Type-2 students into consideration along with critical constraints accordingly, and solves the resulting more complex problem. Moreover, the school bus routing model in this work is one of the most general optimization models representing the school bus routing problem. On the other hand, similar to all existing models, the developed model considers the total system cost as the objective function value to minimize, different bus capacities, and common vehicle routing constraints such as flow conservation on routes and subtour elimination. Furthermore, another main difference is that the bus scheduling and school time window is also considered and solved in the model. With two different types of students, both Type-1 and Type-2, the time restrictions are varying, resulting in more complexity and additional constraints. The results in this work present the difficulties of meeting the requirement of Type-2 student riding time limit and school time window simultaneously. Also, the constraints regarding service equity and quality are provided and they can be used by decision makers if necessary. Either densely populated urban areas or sparsely populated rural areas, the school bus routing problem is difficult to solve due to a large number of students or long travel distance. The school bus routing problem falls under vehicle routing problem (VRP) with additional requirements because each student represents one unit of capacity. In this dissertation, we present a modeling framework that solves a student assignment problem with bus stop selection, and subsequently a school bus routing problem with school

Special education students are usually routed on different buses than non-disabled general education students. To make the routes more efficient, this study proposes serving general students and special education students on the same bus at the same time (mixed ride) while allowing heterogeneous fleets and mixed loads. ESRI Location-Allocation tools and Google OR-Tools are used for bus stop selection, route generation, and bus stop optimization. Parallel cheapest insertion heuristic and metaheuristic, simulated annealing, are adopted to generate school bus routes. The effectiveness of the mixed ride approach is tested for three schools with 178 synthetic students’ locations data (including 12 with wheelchair) in New York City using a fleet of 14 buses spread over four types. The results show the mixed ride approach achieved 14.32% reduction in total travel distance and 10.46% reduction in total travel time. The mixed ride approach tends to return solutions with fewer vehicles and fewer bus stops, less average travel distance, and shorter average travel time.

Generally, Kandy city and traffic congestion go hand in hand. This situation becomes worse during school time. The geographical location of the city, the limited number of entrances and the large number of schools located within a small area are contributing to this condition. This study attempts to propose a new model to reduce school time traffic congestion using School Bus Routing Problem (SBRP) method. Network analysis in GIS facilitates the build of this system. SBRP seeks to plan an efficient schedule for school buses to pick up students from a bus stop and drop them to school by satisfying various constraints like; school time window, maximum walking distance and riding time, and the traffic. SBRP selects the nearest bus stops, generates suitable bus routes and visualizes traffic congestion on roads in Kandy city. Vehicle Routing Problem (VRP), closest facility, and location-allocation tools identify GIS-based solutions to SBRP. The proposed model selected suitable bus stops to drop students to a school and to generate the fastest bus route for the school buses. Visualizing a 12-hour daytime traffic in Kandy City, all schools are covered by the 56 fastest bus routes. The maximum riding time and distance limits to 59 minutes and 16 km respectively. Historical traffic data identifies 6.00 am to 8.00 am and 12.00 pm to 2.00 pm as the most traffic-congested time in the city. Finally, all problems of SBRP are solved and a systematic method is introduced to transport school students by optimizing the traveling time of students with existing traffic congestion.

In our country, school bus routes are determined by experiments of driver without considering the scientific optimum route and location. Traversing additional routes will always result an increase in vehicle movements and fuel consumption and enormous costs. Hence, this paper will study the school bus routing in Tehran considering special students and a model will be presented to minimize traveling distance and to prevent repetitive crossings through the bus stops and to determine the shortest routes by presenting a way to propel several students to a bus stop. The proposed model will solve via GAMS software. Because the model is NP-Hard, the Genetic algorithm is used to solve the large scale problem. The contribution of this paper is to consider gender separation in schools and buses. To solve this problem, an integer linear programming model is developed. The conclusion indicates a decrease in transportation time.

Limited number of berths can result in a subsequent bus stopping at the upstream of a bus stop when all berths are occupied. When this traffic phenomenon occurs, passengers waiting on the platform usually prefer walking to the stopped bus, which leads to additional walking time before boarding the bus. Therefore, passengers’ travel time consumed at a bus stop is divided into waiting time, additional walking time, and boarding time. This paper proposed a mathematical model for analyzing passengers’ travel time at conventional bus stop based on theory of stochastic service system. Field-measured and simulated data were designated to demonstrate the effectiveness of the proposed model. By analyzing the results, conclusion was conducted that short headway can reduce passengers’ waiting time at bus stop. Meanwhile, the theoretical analysis explained the inefficiency of bus stops with more than three berths from the perspective of passengers’ additional walking time. Additional walking time will increase in a large scale when the number of berths at a bus stop exceedsthe threshold of three.

The purpose of this Major Individual Project (MIP) was to identify public school bus stops in the city of Redlands with certain risks. Those risks being violent crimes, drug related crimes and the homes of convicted sex offenders. The MIP made use of the Kernel density function along with the Getis-Ord Hotspot function in ESRI’s ArcGIS 9.1 software. These functions were both used alone and combined. The Kernel Density function was used alone to derive a density surface that would be reclassified to produce a risk surface that would identify the risk of the school bus stops. The Hot Spot Analysis (Getis-Ord Gi*) with and without (z-score) Rendering were use in combination with the Kernel Density function. The pairing of these two functions, Kernel density and Hot Spot Analysis, was utilized to produce surfaces that would act as visual aids to better identify hot and cold spots. These surfaces were generated by using the Hot Spot Analysis functions to compute the Getis-Ord Gi* (with and without rendering) values. Those values were then used as the Population field for the Kernel density function that produced Hot Spot/Kernel density surface. These results were used to produce maps to aid police officers, and school officials and produce an IMS site to inform the parents of the community.

Effect of stoppage time on motion of a bus through a sequence of signals

Less dependency on public transport has caused a high reliance on private vehicles. This is due to several factors including a comfortable aspect, safety, and inconvenient infrastructure and facilities at the bus stop. This paper attempts to identify the significant determinants affecting the bus stop performance by evaluating 123 bus stops based on the developed indicators within maximum walking distance to transit stations along the proposed alignment of Light Rail Transit (LRT) stations. The indicators were adapted from Transport Assessment Indicators and suited with local guidelines which were subsequently developed into Transport Assessment Checklist. 13 indicators in the audit checklist were significantly reduced to five factors containing 12 significant indicators (factor loadings greater than 0.5) through Factor Analysis and Principal Components Analysis (PCA). These indicators were identified to give an effect on bus stop performance. The findings can help solve the low dependency on public transport by emphasizing the significant determinants at the bus stop for future improvement.

This study primarily aims to evaluate the affordability of Batik Solo Trans (BST) bus stops to school locations within Solo City and to develop a strategic placement plan for enhancing student accessibility throughout the city. The criteria for optimal placement adhere to the Minister of Public Works Regulations, which dictate that bus stops should be within a 400-meter radius or a 10-minute travel time for pedestrians. The research employs a comprehensive methodology, including a census of existing BST bus stops and high schools in Solo City. Using ArcGIS 10.2, we employ Buffer Proximity Analysis and Network Analysis to identify potential new bus stop sites, followed by quantitative and descriptive analysis of the results. The study’s findings reveal that BST bus stop accessibility to high schools in Solo City stands at an impressive 94%, with 350 out of 175 high schools having convenient access to 165 BST bus stop locations. In order to address accessibility gaps, the research suggests integrating 16 additional bus stops, especially at notable high school locations such as SMP Muhammadiyah PK Campus II, SMPN 18 Surakarta, and MAN 1 Surakarta. The proposed strategy aims to achieve full coverage with enhanced accessibility, visualized through cartographic representation.

SummaryThe 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.

Motorists’ knowledge of Florida’s school bus stop law (the Law) and various school bus signalizations was investigated and is summarized. The study focused on determining the level of motorists’ knowledge regarding their driving responsibilities as defined in the Law and the meaning of the various signalizations used on school buses. To gather the necessary information, a simple one-page survey was developed and distributed to a random sample of driver’s license examining offices in the state. Summary statistics indicate that significant confusion exists on the part of motorists regarding their responsibilities as defined in the Law as well as the meaning of the various school bus signalizations. In addition to the reporting of summary statistics, many logistic regression models were developed using the sample data to determine the odds ratios of increasing motorists’ knowledge of the Law and signalizations associated with explanatory variables including age, gender, ethnicity, receipt of a citation for violation of the Law, and recent exposure to safety information about the Law and signalizations via driver training courses, public service announcements (PSAs) on TV or radio, or some other form of electronic or printed media, for example. Findings from some of the models indicate that certain factors significantly increased and decreased the odds of motorists having knowledge of the Law and various signalizations. Recommendations include increasing the awareness of motorists through PSAs, adding questions to driver’s license examinations about stopping for school buses, and decreasing the period of time between required driver’s license renewals.

A column generation approach for a school bus routing problem with resource constraints

PurposeMost school bus related injury events in Sweden take place when the child is outside the bus. In order to enhance their safety, the societal costs of four different measures applied on “bus stops” on high speed roads were investigated.MethodsFrom a door-to-door perspective, a measure hierarchy, comprising the four existing measures, viz.: Rerouting using the current operating vehicle, New construction, Rerouting using a different operating vehicle, Speed reduction in the vicinity of the “bus stop” was applied.ResultsBy allocating 7.7 € per child per school day, almost nine out of ten children’s transportation safety may substantially be enhanced, simply by rerouting the current operating vehicle or using alternative operating vehicles.ConclusionsIn the investigated municipality it was feasible to enhance school transportation safety for children by implementing cheap and alternative measures.