Research On Continuous Model And Its Discretization For Bus Line Service

The bus route service design can be divided into discrete model and continuous model according to the variables optimized by the model.The discrete model has many assumptions and is difficult to be solved to obtain the optimal solution,while the continuous model can efficiently and quickly obtain the global optimal solution.However,the continuous model has several drawbacks: First,the results of continuous model cannot be directly applied in practice.Besides,most of the existing studies are concentrated on single travel mode,which ignores the relationship between different travel modes.What's more,the transit line design works focus on the fuel vehicle bus.However,the electric bus is more and more popular and the charging problem needs to be considered.In response to the above problems,this paper takes the bus line as the research object,and uses the continuous model to analyze the design and optimization of the single-line bus service.For this problem,the research of works includes the following aspects:(1)Based on the comprehensive analysis of the continuum modeling to design a single bus line.According to the drawback that the results from continuum modeling cannot be applied to practice directly,this paper proposes a nonlinear optimization model with respect to the variables of bus stop locations.The bus stop density from continuum modeling can be converted into bus stop locations by using the proposed model.Different from the current midpoint and endpoint methods with weak theoretical basis,the proposed method is the first one by using model to obtain the best position of each stop based on the number of stops and the range of each stop location determined in the continuous model.Compared with the current methods,the final bus stop obtained by using the proposed discrete method can effectively save the system cost.(2)Based on the relationship between different travel services.Specifically,we take the mixed service of shared bicycles service and traditional bus service as an example and a model for the design of mixed transportation services in the corridor is proposed.In the proposed model,the locations of different services stops and bus frequency can be determined simultaneously.Different from the previous model wherein different vehicles are designed separately,the proposed model considers the correlation between different services,that is,complementarity and competition between different service.The proposed method can obtain the stop density and docking stations that varies with the spatial position.Finally,based on the obtained stop density,discrete methods can be used to obtain specific stops of different services for practical application.(3)Considering the facts that emission from fuel vehicles leads to air pollution and the used fuel is not renewable.Electric buses replacing or partially replacing traditional fuel vehicles is an inevitable trend.Therefore,we proposed a bi-level model to design the electric bus line.Unlike previous studies that only considered the design of corresponding charging facility equipment for fixed stop facility,this paper uses a continuous model to fully consider the interaction between bus service facility and charging facility.In the proposed model,the bus stop density,bus frequency,on-board batteries and charging facility equipment can be optimized simultaneously.(4)For continuous models of different bus service designs,corresponding solution algorithms are proposed.Specifically,for the traditional bus line discretization model,the conventional interior point method is used;for the hybrid bus service model,the first-order condition is used to obtain the analytical solution,and then the bi-level iterative solution algorithm is developed;and for the electric bus model,because only analytical solutions of station density and departure interval can be obtained for the upper level,the lower level problem is transformed into a linear programming problem,and then the corresponding bilevel iterative solving algorithm was designed to solve it.In addition,case studies are carried out by using hypothetical and actual real bus lines.In summary,this paper analyzes the different design requirements of bus services and builds continuous models for bus service design under different services,which provides theoretical support service design for the corridor.