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Although transit stop location problem has been extensively studied, the two main categories of modeling methodologies, i.e., discrete models and continuum approximation (CA) ones, seem have little intersection. Both have strengths and weaknesses, respectively. This study intends to integrate them by taking the advantage of CA models' parsimonious property and discrete models' fine consideration of practical conditions. In doing so, we first employ the state-of-the-art CA models to yield the optimal design, which serves as the input to the next discrete model. Then, the stop location problem is formulated into a multivariable nonlinear minimization problem with a given number of stop location variables and location constraint. The interior-point algorithm is presented to find the optimal design that is ready for implementation. In numerical studies, the proposed model is applied to a variety of scenarios with respect to demand levels, spatial heterogeneity, and route length. The results demonstrate the consistent advantage of the proposed model in all scenarios as against its counterparts, i.e., two existing recipes that convert CA model-based solution into real design of stop locations. Lastly, a case study is presented using real data and practical constraints for the adjustment of a bus route in Chengdu (China). System cost saving of 15.79% is observed by before-and-after comparison. [ABSTRACT FROM AUTHOR]

Cities worldwide are deploying electric buses rapidly to enhance eco-friendly public transportation. Most existing electric transit systems rely solely on stationary charging at terminals and have to equip buses with large-sized batteries to maintain operation in networks. Consequently, the stationary-charging electric bus (SE-Bus) systems are subject to high battery costs, limited range per charge, long charging time (layover time), etc. These limitations may be addressed by integrating the new wireless power transfer technology, which provides contactless charging to the operating buses without extra delays. To guide wireless-charging electric bus (WE-Bus) designs in corridors, this paper proposes an optimization model to jointly optimize (i) the electric supply system and (ii) the transit service that are interdependent. Specifically, we construct parsimonious models for system metrics using five design variables/functions, i.e., battery size, the number of wireless power transfer (WPT) pads, stationary charging rate, service headways, and stop densities. Accordingly, we formulate the optimal design problem to minimize the generalized system cost as the sum of the transit agency's and patrons' costs. The problem is attacked by first decomposing into two sub-problems regarding (i) electric supply system design and (ii) transit service design and then solving them iteratively. The (i) sub-problem is converted to a linear programming problem by linearization, and the (ii) sub-problem is analyzed with optimal conditions. Numerical tests show the proposed solution approach produces accurate results. Extensive numerical experiments unveil several findings. First, the WE-Bus systems outperform the SE-Bus in various scenarios except when wireless charging facilities are too costly. Second, the optimized WE-Bus designs can reduce costs not only to the agency (with smaller-sized bus battery and reduced fleet cost) but also to patrons (who enjoy improved services with shorter headways). Additional parameter analyses also investigate the impacts of demand levels, wireless charging rates, depths of discharge, etc. Lastly, a case study in Chengdu (China) illustrates the application of the proposed model. • Models are built for wireless-charging electric bus (WE-Bus) designs. • The electric system and the transit service are jointly optimized. • WE-Bus systems show a wide range of application. • Optimized WE-Bus designs may save costs for the agency and transit patrons. [ABSTRACT FROM AUTHOR]

• Formulated CA models for designing shared bikes and transit in corridors. • The model admits spatially non-uniform demand and their choices of multiple routes. • Obtained analytic optimal conditions that yield new insights and promise an efficient solution algorithm. • The hybrid system outperforms single-mode transit system in a wide range. The prevalence of shared bikes in many cities is a double-edged sword to the local mass transit services. Some transit patrons may switch to cycling, causing declines in the transit ridership. Others may benefit from using bikes instead of walking to access transit. The complicated interactions between the two modes entail the necessity of designing them jointly. Unfortunately, the literature has focused on either the design of a single mode or joint designs idealized by assuming a uniform demand pattern. The latter class of works has limited practical values. This paper develops a continuum approximation (CA) model for optimizing the hybrid design of shared-bike and transit services in a corridor under spatially heterogeneous demand patterns. The model minimizes the generalized system cost considering various route options that patrons can choose from, including transit routes with walking or biking access and bike-only routes. The methodological challenges that arise due to patrons' route choices in the heterogeneous operating environment are overcome by incorporating a route assignment model into the CA modeling framework. We propose a bi-level algorithm to solve the model, where the upper level optimizes the hybrid design by exploiting some analytical properties of the CA model, and the lower level calculates the route assignment equilibrium. Numerical experiments show that the optimal hybrid design outperforms the conventional transit design for a wide range of operating conditions. The cost saving can be over 20%. Under certain conditions, the hybrid design can even reduce the total operating cost, making bike-sharing profitable for transit agencies. The practical applicability of our model is demonstrated via a case study of a real bus line in Chengdu, China. [ABSTRACT FROM AUTHOR]