# Intelligent Total Transportation Management System for Future Smart Cities
## 2 Materials and Methods
### General Optimization Method
The operational characteristics \(\mathbf{o}_{v_{i}}\) contains all the available real data: the real condition of the given \(i\)-th vehicle as load factor, age, used size of tires, and pressure in tires. The real motion of the \(i\)-th vehicle is characterized by a vector, \(\mathbf{x}_{v_{i}}\). The environment as air temperature, rain, or fog, is defined by the vector \(\mathbf{z}_{v_{i}}\) according to the \(i\)-th given vehicle. Finally, the noise vector contains the random noise as traffic jam, accident, or road reconstruction related to the given \(i\)-th vehicle and its pathway. Equation (2) seems solvable; nevertheless, it deals with a large number of vehicles reaching even some millions in large megacities. A more detailed evaluation of Equation (2) shows that it is nearly impossible to solve Problem (1). * At first, the objective function is nonlinear. It is enough to underline that the fuel consumption depends on the vehicle's drag, which is a function of the vehicle velocity square. Furthermore, the fuel consumption depends, e.g., on the number of stops or accelerations, or the duration of rush hours. Fuel consumption of the same types of cars might differ by 50%-80% depending on the drivers (\"young dynamic\"- or \"old lady\"-type drivers). * Next, vehicles' motion might be started and finished in any local places or at the borders of the investigated city areas. The given \(i\)-th vehicle may take part in traffic several times (moving-parking-moving). * Additionally, the situation may change dynamically because of an accident, tropical rain, or simple traffic conjunction. * Finally, demand and demand in given transportation means are changing quickly. Transportation networks planned and built based on demand forecast used available data on a given time of social and economic requirements. Therefore, the networks were planned for mass transportation and motorized vehicles. Nowadays, the system is weak in parking and bicycle or scooter lanes. On the other hand, it is good news that the young generation does not prefer to have a car; young people like to use car-sharing systems, and advanced, e-transportation solutions. Because of the difficulties in possibly solving the optimization Problem (1), several classes of methods are developed to solve the traffic optimization problem by its simplification and size reduction. At first, instead of the nonlinear objective Equation (2), a simplified linear function might be applied:  
\[E_{t}=f(x)=\frac{1}{\tau}\sum_{i=1}^{N}w_{v_{i}}e_{v_{i_{f}}} \tag{3}\]  
where \(e_{v_{i_{f}}}\) is minimum energy used by \(i\)-th vehicle during its move from start to the final position. Figure 3 shows the possible calculation of \(e_{v_{i_{f}}}\). It covers a part of the city road system. Ellipses give junctions, and lines show roads between the junctions. The \(i\)-th vehicle starts its motion at junction \(s\) (red state, \(jl-4\) in Figure 3), and finishes at state \(f\) (\(j+2\),\(l\)). The energy used for passing the junction (\(j\),\(l\)) and moving to next junction (\(p\), \(r\)), for example to (\(p=j+1\) and \(r=l-2\)), is defined as \(e_{v_{i_{j},j\
eq p}}=e_{v_{i_{j},j\
eq l+1}-2}\). The red lines show the path from junction \(s\) to junction \(f\) with minimum energy used. The minimum energy path does not necessarily equal to minimum time, minimum cost, or minimized environmental impact. (For example, electric or electric-hybrid vehicles may even generate energy during the decelerations. Therefore, \(e_{v_{i_{j},j\
eq p}}\), can even be negative.) In Equation (3), the weighting coefficients, \(w_{v_{i}}\), take into account the real operational conditions as load factors (as how many passengers are in the car). It is clear that the minimum energy used elements, \(e_{v_{i_{j},j\
eq p}}\), complete a special minimum energy used matrix, \(E_{min,~{}v_{i}}\), for each \(i\)-th vehicle. In a very generalized form, instead of a road system network, a grid can be defined for covering the urban area.