### Relevant Studies  
Many studies have been carried out to facilitate signaling at intersections. Early work in traffic engineering began with the recommended methods for vehicle delay calculation. Some of the first proposed methods for delay calculations were developed by [PERSON] and [PERSON], and all subsequent research was a continuation of these two studies [6]. Since the study [6], performance improvement studies have begun to calculate signal durations. As a continuation of these methods, studies were carried out and described in the Highway Capacity Manual (HCM) in the literature, extending the delay analysis with research published in different years--1985, 1994, 1997, 2000, and 2010 [7; 8; 9; 10; 11]. In the further version of these studies, it is considered that performance improvement and optimization studies are mainly carried out using optimization methods, linear programming, fuzzy logic, decision-making models, and genetic algorithms. [PERSON] et al. aimed to optimize traffic lights using fuzzy logic to prevent traffic congestion at intersections [12]. [PERSON] et al. used the queuing theory for modeling and simulating waiting at traffic lights [13]. [PERSON] studied the queuing theory for traffic signal control and aimed to minimize total travel delay, using obtained performance values by queuing models [14]. [PERSON] et al. analyzed the tail lengths by modeling flow values with M/G/1 [15]. [PERSON] and [PERSON] developed and applied the fuzzy controller to reduce the total delay and average queue length in urban intersections [16]. [PERSON] et al. proposed a fuzzy-logic-based solution to manage traffic lights dynamically through taking into account the time of the day and the number of pedestrians about to cross the road [17]. [PERSON] developed the model to estimate the average delay of vehicles by using artificial neural networks in isolated intersections [18]. [PERSON] and [PERSON] studied the differential evolution bacteria foraging algorithm to improve the traffic capacity of intersections in urban areas [19]. [PERSON] described in another study the methods of queuing theory to optimize traffic signal phases on signal-controlled intersections [20]. [PERSON] et al. used the M/M/1 queuing model to get the performance of vehicular traffic on roads in city centers [21]. [PERSON] and [PERSON] made a comparison of queuing models M/M/1 and M/D/1 for vehicular traffic at districts in urban areas of cities [22]. In another queuing analysis of traffic flow, [PERSON] and [PERSON] modeled traffic queuing with the same models, M/M/1 and M/D/1, and they suggested their models by increasing the number of lanes or adjusting green light time for each direction in busy hours during the day. This study stands out as taking into account the non-ergodic condition, unlike the previous queuing analyses [23]. There are also some studies that aim to improve the traffic light controller to manage phases, using connected sensors. [PERSON] et al. designed a portable controller device that evaluates traffic density with IR sensors. They aimed to solve the problem of emergency vehicles in traffic jams [24]. [PERSON] et al. developed the ATAK system as a traffic management tool at signalized intersections and they used genetic and fuzzy-logic algorithms to manage and control the isolated or coordinated intersections [25]. This system uses the number of vehicles from the input sensors placed at 50 and 200 m intervals at the intersection entrances and the output sensors placed at 10 and 20 m intervals at the exits. ATAK is currently and actively used in many of the central intersections of the city of Istanbul. In another traffic control system developed by ISSD Inc, unlike the ATAK system, traffic signal control is performed by taking vehicle images from camera systems [26]. The calculation method used in the system starts with drawing the graphs of the time-dependent changes of the vehicles passing through the intersection arms.