## 2 Literature Review  
Since the inception of the traffic flow theory in the 1930s, a multitude of researchers have endeavored to develop mathematical models, which accurately represent the relationships between empirical traffic flow parameter values. During this period, many scientific papers, studies and projects were devoted to the development and validation of various deterministic [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28] and stochastic representations [29; 30; 31; 32] of basic traffic flow diagrams. The main goal of these efforts has been to represent the complex spatial and temporal characteristics of traffic flow more accurately. Over the past 90 years, researchers have proposed various forms of fundamental traffic flow diagrams in their attempt to improve the initial Greenshields linear \"speed-density\" model developed in 1934 [7; 8]. In 1959, [PERSON] proposed a logarithmic form of the speed-density relationship [9]. A year later, [PERSON] suggested that the speed-density relationship can be described by the negative exponential function [10], while in 1961, [PERSON] presented the first two-regime traffic flow model based on two logarithmic functions [11]. In 1966, [PERSON] developed the first traffic flow model specifically adapted for describing the relation between speed and density on urban roads [12]. In 1967, [PERSON] suggested that the speed-density relationship can be represented by Gaussian distribution [13]. At the same time, [PERSON] and [PERSON] [33] and independently [PERSON] [34] developed generalized \"speed-density\" models by expanding the initial Greenshields linear model with the introduction of additional adjustment factors. [PERSON], in 1990, proposed a combined linear-parabolic \"speed-density\" model [15]. In 1995, [PERSON] and [PERSON] independently presented new modified versions of the \"speed-density\" model [16; 35]. In 2003, [PERSON] and [PERSON] developed a three-dimensional fundamental traffic flow diagram, based on which, it is possible to describe the differences present in a \"flow-density\" relationship at different percentages of heavy vehicles in a traffic stream [19]. Over the last two decades, an increasing number of researchers have suggested that the \"speed-density\" relationship can be more accurately described by different forms of logistic and sigmoid functions [21; 23; 36]. In their pursuit of finding the optimal deterministic and stochastic functional forms for the \"speed-density\", \"flow-density\" and \"flow-speed\" models, the majority of researchers have predominantly focused on studying vehicle interactions within uninterrupted traffic flow conditions, which has been regarded as the basic traffic flow condition representative of establishing the fundamental relations between the main traffic flow parameters. On the other hand, only a limited number of researchers have studied specific functional relationships between the macroscopic and microscopic traffic flow parameters under interrupted traffic flow conditions [37; 38; 39; 40; 41; 42; 43; 44] and discussed the comparative differences between the values of traffic flow parameters measured in uninterrupted and interrupted traffic flow conditions [45; 46; 47; 48]. In a 1996 study, [PERSON] provided a comparative overview of the mathematical relations between speed, density and travel time, which can be used to describe the characteristics of traffic flow in uninterrupted and interrupted traffic stream conditions [45]. In 2005, [PERSON], [PERSON], [PERSON] and [PERSON] developed three distinct shock wave models, which can be used to convert vehicle speeds measured within uninterrupted traffic stream conditions on a road segment located prior to a signalized intersection into vehicle speeds present in the interrupted traffic stream conditions formed in the immediate vicinity of the signalized intersection [46]. In the same year, [PERSON] et al.