## 5 Conclusions  
The smart cities paradigm involves the aim of developing more interconnected and sustainable urban environments. Within this aim, the enhancement of public transport systems is crucial for facilitating citizens to commute without using private cars. Since it is impossible to provide users with direct connections to every location of the city, an aspect that should be carefully planned when operating the public transport system is the synchronizations among different bus lines. In this line, this article introduced a novel Mixed-Integer Linear Programming (MILP) model for bus timetabling with a focus on enhancing the multi-leg trip while ensuring a minimum level of quality of service for passengers. As a second objective, the MILP model also aims at minimizing the cost of the system. The performance of the MILP model was assessed using a set of real-world instances from the public bus system of Montevideo, Uruguay. The set of instances included instances with different numbers of bus lines and different required levels of quality of service represented by the maximum tolerable waiting time for transferring passengers. The results showcased the competitiveness of the MILP model to provide a range of Pareto efficient solutions that explore the tradeoff between the number of successful transfers of passengers and system costs. Moreover, the results demonstrated the superiority of the MILP solutions over the existing timetables used in Montevideo, specially in terms of the number of successful transfers, but also in terms of the costs of the system. Particularly, the model excelled in terms of successful transfers, with an average percentage improvement of 65.77% for the best trade-off solution. It also demonstrated cost efficiency, with an average improvement of 27.24% for the best trade-off solution over the current timetable. Additionally, the results revealed that the capacity of the MILP model to synchronize bus schedules is amplified when passengers are willing to wait longer, leading to significant gains in the number of successful transfers obtained in solutions when the maximum tolerable waiting time is increased. Currently, our proposed approach has certain limitations that could be enhanced in various aspects to model a broader range of realistic public transport systems. This includes incorporating hybrid and electric buses and adopting a more advanced bus occupation model. Therefore, regarding future work, there are several promising directions related to addressing these limitations. One is the incorporation of electric or hybrid buses into the model to include more sustainable practices that are being implemented worldwide. This would involve introducing new control variables to assess the feasibility and benefits of using these types of buses on specific lines as well as developing new cost models for these types of buses. This would involve introducing new control variables (to evaluate the feasibility and benefits of using this type of bus on specific lines) and developing new cost models for this type of bus. Another line of research is improving the Quality of Service (QoS) model in relation to the occupancy of buses during direct trips. The approach  
Figure 8: Pareto fronts of representative instances. (**a**) Pareto front of instance 40.30.4, (**b**) Pareto front of instance 41.30.2, (**c**) Pareto front of instance 42.30.3, and (**d**) Pareto front of instance 42.90.3.  
followed in this article combines random boarding with deterministic passengers alighting. The first hypothesis is a standard assumption for arrival processes, but a stochastic alighting process is a more realistic approximation. The bus occupancy simulator can be extended to incorporate additional information, such as intelligent methods for inferring where passengers alight the bus [21]. Another relevant line for future work is evaluating the proposed algorithmic approach in a real setting, applying a microscopic traffic simulator and using real traffic information for public and private transportation.