## 2 Literature Review  
The traffic control approaches, and traffic signals control have been classified into three types of strategies [2]:  
* Control of isolated intersection,
* Traffic light control with fixed time settings,
* Traffic-responsive coordinated and adaptive signal control. All these strategies implement the traffic lights durations as control influences. The cycles are not considered as tools for adaptive real-time control of the traffic behavior. For the evolution of the traffic signal control, one can refer to [4]. The simplest form of control is applied to isolated intersections under slow fluctuations of the traffic intensity [5]. Such control targets optimal settings in order to decrease the waiting time in front of the crossroad [6]. This isolated crossroad control with complication was applied as fixed time coordination control in a network of junctions. Traffic plans are evaluated off-line for each junction and the light durations are based on historical data about the traffic demands and statistical evaluations of the origin-destination matrices. The traffic responsible control strategy is implemented in various control systems, which are continuously cited in the references: OPAC (Optimal Policies for Adaptive Control) [5]; SCOOT (Split Cycle Offset Optimization Technique) [7]; SCATS (Sydney Coordinated Adaptive Traffic System) [5]; RHODES (Real time Hierarchical Optimized Distributed Effective System) [8]; PRODYN (the abbreviation comes from the terms Dynamical Programming) [9]; UTOPIA (Urban Traffic Optimization by Integrated Automation) [10]; TUC (Traffic-responsive Urban Control) [11]. The formal relations, which are used for the definition of the optimization problems, are based on the principles and models, which are taken from fluid dynamics, vehicle-following models, and couple lattice models [12]. Attempts to use different models and methods for modeling the traffic behavior, such as the bio-inspired models and hybrid artificial neural network optimization model, are under consideration, respectively, in [13] and [14]. A challenge for the traffic optimization is the lack of analytical relations between parameters such as delays and off-sets [15], as well as the actual throughput as a function of the green time of movement, cycle length, and time, which is obtained with the simulation environment VISSIM [16]. The advances in technology allow to forecast arrival and discharge rates of traffic flows in real time [17]. Our approach follows the analytic descriptions of the traffic behavior and the definition of the traffic optimization problem. An extended overview of the different forms of traffic optimization problems is given in [18]. The provided analysis classifies the content of the traffic control problems about their objectives and constraints. The main control variables and problem arguments are restricted up to the green lights' durations. Our specific place for problem characteristics is the simultaneous application of two objectives for the minimization of cycle length and maximization of traffic flows, which are not presented in this overview. Additionally, we extend the control space with both cycle lengths and green durations as arguments in an integrated hierarchically defined optimization problem. For the definition of our hierarchical optimization problem in this research, we apply relations based on the models of fluid dynamics. These models are applicable mainly to freeway traffic control with ramp metering [19] and applications of the store-and-forward approach [20,21]. For relevant applications of ramp metering, one can refer to [22]. The store-and-forward model is intensively exploited and complicated for usage in centralized and or decentralized control schemes [23]. Due to its simplicity, store-and-forward modeling is applied in traffic control algorithms [24,25]. Store-and-forward modeling is applied for obtaining different control gains in traffic optimization. In [26], green wave optimization was the main target of the control.