###### Abstract  
In this work, the authors developed procedures to explain mean extra travel time (\(T\)) and extra travel time variability (\(V\)). This was carried out for situations (through simulations) where the fast vehicles' travel time, whose speed tendency (\(sp_{1}\)) is the permitted speed limit, is negatively affected (i.e., increasing travel time) by the presence of slow vehicles, whose speed tendency (\(sp_{2}\)) is half the speed limit. The speed limit was set in the range of 60 km/h to 90 km/h, with seven cases, and every case had eight simulations, each with different \(p_{1}\) (fast vehicles' percentage) and \(p_{2}=100\%-p_{1}\) (slow vehicles' percentage) values. \(p_{2}\) ranged from 10% to 80% at intervals of 10%, for a total of 56 simulations. From the simulations' data, we calculated the fast vehicles' extra travel time, which is the additional time to traverse an avenue segment owing to the presence of slow vehicles. The fast and slow vehicles recreate heterogenous traffic in terms of speed. We developed procedures for modeling \(T\) and \(V\) with \(p_{2}\), and \(V\) with \(T\). For modeling, \(\sim\)71.42% of the data from simulations was used. We find that the models' parameters values can be used for explaining the remaining data. In addition, we discovered that the pattern of \(p_{2}\) vs. \(V\), for \(p_{2}\) ranging from 50% to 80%, is different among \(sp_{1}\) cases and not linear. extra travel time; fast vehicles; heterogeneous speed; slow vehicles; variability +
Footnote †: journal: Applied  
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Footnote 0: _Applied_  
vehicles, the former are tempted to perform overtaking maneuvers, if possible. In [2], it was proven that the vehicles' travel speed (and thus also travel time) is affected, among others, by the traffic composition in terms of speeds. In [3], a relationship between speed variance and accidents was established, finding that an increase in average speed does not necessarily increase accident rates, but an increase in speed variance certainly increases them. In [4], the proposed algorithm triggers a need to overtake when the speed differential is 8 km/h. The work in [5] focuses on establishing (via simulations) the average travel time to complete a highway segment and the number of passenger cars' lane changes with different percentages of heavy trucks. The results show that both variables increase as the percentage of heavy trucks increases, with the influence of heavy trucks on traffic being notorious in heavy traffic. In [6], speed indicators on sites with uniform speed limits (65 mph for passenger vehicles and trucks/buses) and with differential speed limits (70 mph for passenger vehicles and 60 mph for trucks/buses) were investigated. The results from the models were a mean speed of 65.3 mph for the uniform case (one) and 66.9 mph for the differential case (two). Similarly, the 85 th percentile speed results were 70.7 mph for case one and 73.9 mph for case two. Finally, the standard deviation was 5.5 mph for case one and 6.8 mph for case two. Through simulations, the impact on traffic of differential speed controls was investigated in [7]. The speed control strategies were uniform posted speed limits (USLs), differential posted car-truck speed limits (DSLs), and differential mandated truck speed limits (MSLs). Considered positive for traffic safety, DSL and MSL reduce average travel speed, increase head-on time-to-collision, and reduce car-car overtaking. Considered negative, DSL and MSL increase percentage time spent following and total number of overtakes, decrease car-car overtaking, but increase car-truck overtaking. In [8], considering all types of vehicles, it was detected that the highest travel speed variability occur in freeways with DSL, followed by urban freeways with USL and a speed limit of 55 mph. For passenger cars, the speed was consistent when the speed limit was 70 mph, but at lower speed limits, more speed variation was detected. Different factors are related to free-flow speed; one of those is differential speed.