In order to increase the productivity and efficiency of transport services on the one hand, and customer satisfaction on the other, four main analytical methods for determining the number of vehicles needed during the relevant period are presented in [

1,

3,

12]. The first two methods in these papers ensure the average maximum daily occupancy of the vehicles during a given period. The other two methods elaborate on the capacities of the vehicles, which will never be exceeded with an additional constraint on the part of the route which is loaded more than the required availability. Numerical calculation of the average PWT at a station with a limited capacity of the intercity transport vehicles is described in [

13]. It is concluded that for a more accurate representation of PWT at the station, the reliability of supply services, passenger behavior and characteristics of the transportation system should be considered. The passenger transport problem is always observed from the viewpoint of costs and improvement of business transport companies. On the contrary, passenger satisfaction is rarely taken into account, especially when creating the timetable [

14]. Passenger satisfaction is directly related to the total travel time; the shorter the travel time the more satisfied the passenger is and vice-versa. Excluding the travel speed of the vehicle, the total travel time can be reduced by reducing PWT and the number of passenger transfers. Hence, in this paper, we use the term passenger satisfaction to refer primarily to PWT. A multicriteria approach to timetabling problems, with an emphasis on minimizing PWT at the station, is proposed in [

15,

16]. The authors in these papers analyze two criteria; namely, empty seat penalty (empty seat kilometers or empty seat hours) and approximate PWT at the station. The problem is solved using a multiobjective label-correcting algorithm that results in 43% saving of PWT with an acceptable load of the vehicle. In order to ensure fast and energy efficient urban rail transport, a nonlinear problem of minimizing the total travel time and energy consumption is presented in [

17]. The model reduces the cost (number of trains and energy consumption) and improves passenger satisfaction (reduced PWT and the number of transfers, thereby reducing the total travel time). Optimization of energy consumption and PWT can also be found in [

18]. The authors in this paper propose a bi-objective timetable optimization model to minimize PWT and energy consumption. The genetic algorithm (GA) is used for generating a solution with reduced total energy consumption and total passenger waiting time in comparison to the real timetable. The timetable synchronization problem (TSP) refers to the problem of waiting time during a transfer, which is usually solved using a branch and bound (B&B) method. In order to speed up the execution time, the optimization based heuristic method (OHM) is developed and compared with B&B in [

19]. It is concluded that OHM is much faster and optimizes the problem more efficiently. The scheduling problem is usually based on maximization of the number of synchronized vehicles arriving at the transfer station or minimization of the total waiting time at the station. For solving the latter problem, a genetic algorithm with local search is used in [

20]. The model is applied to a small bus network and the cost of the waiting time is reduced by 9.5%. An optimization model for synchronizing a timetable is proposed in [

21]; i.e., for minimizing the maximum PWT during the transfer and reducing the worst time of the transfer. Mathematical models with PWT as the objective function at the transfer station include a set of mixed integer programming (MIP) models [

22]. The model can be solved using a conventional MIP solver such as CPLEX solver (B&B) if there are fewer than 50 lines and by using genetic algorithms for a greater network. Additionally, a solution of the timetable synchronization problem is proposed in [

23]. The authors develop a multicriteria optimization model which takes the vehicle scheduling and passenger demand assignment into account. In order to solve the problem to obtain a set of Pareto-efficient solutions, a novel deficit function (DF)-based sequential search method is proposed. Minimization of the average transfer time in the periodic scheduling of trains (PRTS—periodic railway timetable scheduling problem) is solved using an improved differential evolution (DE) algorithm with dual population [

24]. A comparison of the presented model against the B&B method and greedy-based heuristic algorithm for using the PRTS simulation algorithm to solve the problem of schedules shows that the given model provides a better indicator for PRTS problem and numerical indicators of optimization functions. The problem of minimizing PWT at the station and the cost of vehicle occupancy is solved using the genetic algorithm in [

25]. The models developed for solving the problem of minimizing PWT at the station are defined with preserving the flow of passengers waiting at the station, as shown in [

26,

27]. The problem of PWT at the station occurs when there is a delay in the timetable. One possible solution is to include additional time delays according to the probability theory; i.e., the objective function includes an exponential distribution of delay,

$Exp\left(\right)$ with the expected delay, as shown in [

28,

29]. In [

30], the problem of minimizing train delays while maximizing the total satisfaction during a traffic jam (for example, a vehicular crash or similar) is solved using a heuristic algorithm. Timetable optimization is based on the optimal departure time of vehicles from the station for each line of vehicles in order to reduce PWT. A model which minimizes PWT and distinguishes a direct vehicle transfer from walking from one station to another is solved using a heuristic algorithm, the same as in [

31]. If the headway is reduced, the average PWT can be reduced as well. Minimization of the sum of headways results in minimization of the average PWT. The average PWT is equal to the ratio of the sum of headway squares and the sum of headways during which a traveler arrives. A numerical method for solving this issue is described in [

32].