## 1 Introduction
In this study, special attention was paid to the increase in the fare for a limited-stop service. The distance of a bus corridor is also critical. The number of stops and average stop spacing commonly determine the distance of bus corridors. Mixed services operating within unreasonable conditions can lead to poor public transportation service quality. The number of vehicles in the mixed service does not increase in many routes. So, the waiting time for local service passengers increases, and the reduced in-vehicle time for limited-stop service passengers may be offset by increased waiting time. For the mixed service system, the total passenger travel time increases instead. The current literature on the evaluation of bus service efficiency has been mostly based on supervisory factors such as passenger perception. In most studies in the literature, the mixed service design problems were solved through heuristic methods that could not obtain global optimal solutions. Without access to a global optimal solution, the analysis of critical factors in the system cannot be carried out. Very few studies have focused on the impact of a bus corridor's distance on the performance of limited-stop and local services. In this paper, a limited-stop and local mixed-service model was proposed to minimize the total cost, combining the characteristics of fast speed of limited-stop and good accessibility of local. The increased fare for the limited-stop service was introduced into the  
Figure 1: Stopping patterns associated with a fixed-route service. model. The contributions of this study include: (1) The increased fare for the limited-stop service was proposed for the first time. Through case studies, we analyzed the effects of increased fare on the objective function and decision variables, and determined the range of increased fare. For the limited-stop operators, the increased fare improves the incentive to operate limited-stop services and avoids the decline in wages for drivers and revenues for individual operators of limited-stop services due to the decline in limited-stop passengers; according to the questionnaire survey, passengers could accept the increase in fare within a reasonable range to enjoy faster service. (2) The conditions for application of mixed limited-stop and local services were determined, combined with the parameters such as the number of bus stops and the average stop spacing. The achievements were conducive to improving the service quality of mixed services and avoiding the increase in \"door to door\" travel time for all passengers due to improperly designed mixed services. (3) From the algorithmic point of view, it was verified that the model of the limited-stop service and local mixed service was more suitable to be solved by Lingo software relative to the genetic algorithm. Solving the mixed service model by Lingo not only reduced the total cost, but also the global optimal solution obtained could be used to analyze the impact of fare and the conditions for application of the mixed service. The rest of the paper is organized as follows: Section 2 describes the proposed model, a mixed limited-stop and local bus service, along with the decision variables, objective function, and constraints. Section 3 analyzes the feasibility of the proposed model for the study case of Jinan, China. The Lingo software and the genetic algorithm were compared for the proposed model, with the results showing that the Lingo software program was better. Section 4 discusses the impacts of increasing the fare on the limited-stop service, the bus corridor's distance on the competitiveness of the mixed-service and local-only service, as well as the impacts under different hyper-parametrizations. Section 5 provides the conclusions and considerations of the paper.