# Efficient Intersection Management Based on an Adaptive Fuzzy-Logic Traffic Signal
## 1 Introduction  
Traffic congestion is one of the major problems of modern cities, causing time loss, pollution, and excessive fuel consumption [1, 2]. This problem is encouraged by the steady population growth of vehicles and the lack of efficiency in traffic management [3]. Traffic signals are intended to regulate traffic at road intersections, and their efficiency depends on the ability to balance the alternation of vehicle flows without worsening waiting times, queues, and density [4, 5]. However, due to inadequate signal timings, sometimes, traffic signals cause intersections to become traffic bottlenecks on the road network. Most traffic signals operate in either pre-timed or traffic-actuated modes [6, 7]. While pre-timed control is based on fixed signal timings, traffic-actuated control uses preset reductions and extensions to regulate the phases according to vehicle detection [8]. Unfortunately, due to the high uncertainty of the traffic arrivals, it is difficult to establish long-term optimum values for phases or extensions [9]. Moreover, due to their pre-set behavior, these schemes are unable to react to atypical events that disturb traffic [10]. As a consequence, such controllers are susceptible to cause long queues and excessive stops due to overestimated or underestimated timings. Since traffic is frequently fluctuating, proposals for adaptive traffic controllers have chosen to address the signal timing issue as an adaptation problem instead of an optimization problem [11]. Adaptive controllers solve the deficiencies of pre-timed and actuated controllers by continuously sensing different attributes of the traffic stream and adjusting the signal phases accordingly [12]. For this purpose, these approaches incorporate self-adjusting mechanisms to modify their internal logic configuration. Artificial intelligence methods have gained popularity to design adaptive controllers capable of addressing unpredictable traffic conditions. Numerous approaches have been proposed based on reinforcement learning (RL) [13; 14; 15], neural networks (NN) [16; 17; 18], deep reinforcement learning (DRL) [19; 20; 21; 22], and fuzzy logic (FL) [12; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34]. Due to their accuracy, computational requirements, as well as the supported amounts of states and actions, NN, DRL, and FL methods have demonstrated the best performances [35; 36; 37]. In practice, however, the main drawback of NN and DRL approaches is their complex designs and setup, whose understanding is difficult for operators. Conversely, fuzzy logic approaches are more intelligible, since they imitate human perception by using mappings between systems' inputs and outputs through verbal propositions and qualifying the scalar magnitudes with vague terms such as low, great, high, few, etc. [38]. In addition, such particular characteristics of fuzzy logic facilitate the inclusion of experts' knowledge in the controller design [35]. Typical FL-based controllers consider queue lengths, waiting time, traffic density, or flow rates as inputs and the green time for each phase as output. Nevertheless, in real traffic scenarios, flow rates can be easily measured with commercial vehicle counters, while the estimation of queue length, waiting time, or traffic density requires additional and sophisticated requirements [26; 39; 40; 41], which are not suitable for many cities. Furthermore, it is well known that arbitrary extensions of green phase duration may cause longer cycles, increasing the delay in the system. In this paper, an adaptive traffic signal FL controller for isolated intersections is proposed. The controller operates by using the arrival flow rate as the unique input to compute the proper cycle length. The computed cycle is proportionally split into the corresponding phases based on the effective green time estimation derived from [PERSON]'s method for signalization [42].