## 1 Introduction
### Surrogate Safety Measures  
Surrogate safety measures derived from microscopic traffic simulations have recently been used to evaluate the safety of transportation systems (e.g., [6; 12; 13; 14; 15; 16; 17; 18], etc.). One of the major advantages of using simulation modeling is that it allows potential treatments to be tested before application [19]. Commonly used micro-simulation software include VISSIM [20], PARAMICS [21], AIMSUN [22], SUMO [23; 24], INTEGRATION [25], COR-SIM [26], MITSIMLab [27], etc. The SUMO model supports all the modeling functions needed to implement adequate surrogate safety measures. Therefore, in this study, both safety and mobility were used to adapt different speed limit strategies on Egyptian highways, and were evaluated using the SUMO microscopic traffic simulation model. SUMO has the ability to use different types of car-following (CF) models, such as the Krauss model (the default SUMO CF model) [28], the Intelligent Driver Model (IDM) [29], the Wiedemann74 model (2-parameter model), the Wiedemann99 model (10-parameter model), the Adaptive Cruise Control (ACC) model [30], etc. It is worth noting that the Wiedemann models are the default models used by the VISSIM software. The use of micro-simulations in road safety studies requires the use of surrogate safety indicators that are a function of the speed and distance of \"vehicle pairs\", such as time to collision (TTC) [31; 32], deceleration rate to avoid the collision (DRAC) [33], time to accident (TTA) [32], encroachment time (ET) [34], crash potential index (CPI) [18; 19], etc. SUMO allows extracting simulated conflicts as a direct result of the simulations. The raw trajectories of vehicle pairs can also be processed using the well-known surrogate safety assessment model (SSAM) [35]. In this study, TTC is used to reflect the potential of the accident and is calculated simply [36; 37]. TTC can be expressed as the time difference between two vehicles before they crash if they follow their respective trajectories at their current speeds [31]. Two-vehicle collision severity can be considered based on the lowest TTC value. [PERSON] (1990) [38] reported that potential collisions are a concern when the TTC value is less than 1.50 s for specific vehicles' interactions. [PERSON] (2005) [37] also suggested TTC \(\leq\) 1.50 s as a critical value for road safety in urban areas. In addition, AASHTO (2011 and 2018) [39; 40] recommended the TTC value of 2.5 s for brake reaction time, which is used in the development of highways' stopping sight distances. In addition to TTC, deceleration rate to avoid collision (DRAC) is used as another measure of safety performance. DRAC is defined as the rate at which a vehicle must decelerate to avoid collision with another vehicle [36; 37]. DRAC for rear-end (RE) conflicts can be expressed as [19]:  
\[DRAC(t)=\frac{\left(V_{n}(t)-V_{n-1}(t)\right)^{2}}{2(X_{n}(t)-X_{n-1}(t)-L_{n -1})} \tag{1}\]  
where:  
\(t\) = time interval;  
\(V\) = vehicle speed;  
\(n\) = following vehicle;  
\(n\) - 1 = leading vehicle;  
\(X\) = position of the vehicle;  
\(L\) = vehicle length. For potential angle crashes, estimates of DRAC are obtained as [19]:  
\[DRAC(t)=\frac{V_{n}{}^{2}(t)}{2D_{n}(t)} \tag{2}\]  
where \(D_{n}(t)\) is the distance between the projected collision point and vehicle \"\(n\)\" in the main traffic stream. AASHTO (2011, 2018) [39; 40] stated that most motorists decelerate at a rate greater than 4.5 m/s\({}^{2}\) when having to stop in front of unexpected object on the roadway. About 90% of all drivers decelerate at rates greater than 3.4 m/s\({}^{2}\), as this deceleration is within the driver's ability to stay within their lane and maintain control of the steering wheel while driving and braking on wet roads. Therefore, 3.4 m/s\({}^{2}\), which can be considered as a comfortable deceleration for most drivers, is recommended as the deceleration threshold to determine the stopping sight distance. [PERSON] [37] proposes a threshold value of 3.35 m/s\({}^{2}\) for critical situation. [PERSON] et al.