## 1 Introduction  
Due to rapid traffic urbanization, congestion is a frequent problem on road networks. Traffic transition is the adjustment of vehicles to the following conditions when changes are noticeable. As the number of vehicles grows, stop and go traffic increases, that is, frequent transition in traffic occurs. It is significant to characterize traffic transition to alleviate traffic congestion [1]. This can improve travel time, reduce pollution, utilize the traffic infrastructure efficiently, and increase the comfort level of drivers. The transitions are dependent on the allowable distance between vehicles to prevent traffic accidents. This allowable distance is known as safe distance headway. As the safe distance headway increases, traffic has the tendency to adjust, which causes transition. To prevent accidents, the safe distance headway should be maintained during transitions. Reduced safe distance headway causes accidents. This is an example of aggressive driver behavior. Ignoring the distance headway results in abrupt changes in speed. Consequently, smaller distance headway causes excessive acceleration and deceleration [2], which increases the vehicle emissions and ultimately results in large environmental pollution [3, 4]. It is also one of the major causes of accidents [5, 6]. Further, fuel consumption is also increased compared to with typical driver behavior [7]. Reduced distance headway causes tailgating, which results in rear-end collisions. Twenty-five percent of road accidents are due to tailgating [8; 9]. Further, driver sensitivity impacts the distance between the vehicles. With higher driver sensitivity, changes during transitions are quick, and vice versa for lower driver sensitivity. The sensitivity of new drivers is low, and they perceive conditions with delayed response [10] as compared to experienced drivers. This causes longer delays and smaller distance headway. Further, during night time, the driver sensitivity of an experienced driver is reduced by 35% [11]. Driving with reduced sensitivity results in accidents [12; 13]. The traversed time over a road segment determines the traffic changes and congestion [14]. This is an important parameter to be considered by urban planners to predict traffic conditions on a road network [15]. During congested periods, longer traversed time occurs with variable velocity. However, during smooth flow, the traversed time is smaller, traffic changes are negligible, and the tendency of road accidents is reduced. It is imperative to consider the safe distance headway, driver sensitivity, and traversed time during transitions to reduce accidents and effectively characterize a traffic system that can appropriately predict traffic evolution. The most widely used traffic systems are microscopic and macroscopic. Microscopic systems consider vehicle behavior in the near vicinity [16; 17]. For a larger number of vehicles, the mathematical details of drivers become complex, and is difficult to derive the theoretical laws as compared to macroscopic systems [18]. Macroscopic traffic systems consider the average traffic temporal and spatial evolution [19]. The macroscopic systems consider the density and velocity of a group of vehicles. This makes these types of systems independent from the number of vehicles, and it is easier to theoretically derive the system. The macroscopic systems are composed of a partial differential system with a number of traffic variables that consider the traffic physics and have realistic impact on the evolution. [PERSON] devised a microscopic traffic system in 1961 to characterize transitions during congestion [20]. The velocity of this system is impacted by distance headway. In other words, faster velocity is a result of larger distance headway and, conversely, slower velocity occurs for a smaller distance headway. However, this system ignores the driver perception of conditions. [PERSON] et al. proposed that the changes in velocity are due to the variation in traffic density [21].