Conclusions

Conclusions and future scope

6.2 Conclusions

 LC increases for increase in average speed between two vehicles. The model for lateral clearance with 𝑣̅ can be represented by a deterministic part and stochastic part. The deterministic part consists of a linear relationship with positive slopes (m) and intercepts (c), whereas the stochastic part consists of Beta-distributed residuals (𝜑) which are homoscedastic with 𝑣̅. The residuals address the driver variability in LC behavior for similar speed levels. The general model can be represented as –

𝐿𝐶 = 𝑚𝑣̅ + 𝑐 + 𝜑

 The slope and intercept in above equation vary for different vehicle types. For a car-car pair, the average LC varies from 1.173 m at 0 km/h to 1.581 m at 60 km/h. The average LC maintained by different vehicle pairs is mentioned in Table 4.4. In general, cars and three- wheelers maintain more LC with heavy vehicles and LCV’s, whereas two-wheelers maintain the least LC among the vehicle types.

 Further, it is observed that vehicles maintain lesser LC between similar interacting vehicle types than dissimilar vehicle types. Due to this behavior, lateral clearance cannot be assumed as the sum of individual contribution of vehicles constituting the clearance.

 When a vehicle interacts with vehicles on both sides simultaneously, there is a compromise in maintaining lateral clearance at higher speeds for 3W-2W, car-2W and car-3W pairs. At 50 km/h average speed, the average LC decreases from 1.503 m to 1.347 m, 1.590 m to 1.481 m and 1.696 m to 1.455 m for car-3W, 3W-2W and car-2W pairs, respectively.

6.2.2 Analysis and modeling of longitudinal interactions

Longitudinal gaps are evaluated between a pair of leading and following vehicle (LV and FV) when the FV has stabilized behind LV and the relative speed between them is negligible (<5 km/h).

Their variations with amount of staggering (lateral centerline separation or CS of LV and FV) and average speeds (𝑣̅) are studied. The data are extracted from video data recorded for various traffic sections across different cities. They key observations from this study are-

 Longitudinal gaps (LG) increase with 𝑣̅ and decrease with CS. The variation can be represented by a deterministic part and stochastic part. The deterministic part consists of equation of a plane, having positive slope (a) with 𝑣̅, negative slope (b) with CS, and intercept (c). The stochastic part consists of Burr-distributed residuals (𝜑) which are heteroskedastic (fan-shaped nature) with 𝐿𝐺 and can be transformed appropriately to make them homoscedastic. The residuals address the driver variability for same speed or CS levels. The general model can be represented as –

𝐿𝐺 = 𝑎(𝑣̅) + 𝑏(𝐶𝑆) + 𝑐 + 𝜑

 The slopes and intercept in above equation vary for different vehicle types. For car-car pair, the average LG varies from 3.38 m at 0 km/h to 9.98 m at 60 km/h for CS=0 m, and from 2.13 m at 0 km/h to 8.73 m at 60 km/h for CS=1 m. The coefficients of above equation for different vehicle pairs are presented in Table 4.11. It is observed that LG increases with the

size of LV. For instance, at 30 km/h, and CS=0 m, LG for 2W-car, car-car, LCV-car and heavy vehicle-car pairs are 5.18 m, 6.67 m, 6.68 m and 6.88 m, respectively.

 If vehicle follows two vehicles simultaneously, then it compromises significantly on maintenance of longitudinal gap. This compromise is higher if a smaller vehicle is following a larger vehicle. The percentage change of LG with the introduction of a second leading vehicle is mentioned in Fig. 4.19, for different vehicle pairs, speeds and centerline separations. Further, the compromise is higher with increase of CS and decrease of 𝑣̅. As lateral clearance between two leading vehicles decreases, average longitudinal gap increases.

6.2.3 Overtaking decision-making criteria

Based on lateral veering of the approaching FV in collected video data of traffic streams, the categorical variable of overtaking decision of the following driver is determined. A logistic regression model is developed between the explanatory variables longitudinal gaps (LG), centerline separation (CS), relative speed (𝑣_{𝐿𝑉|𝐹𝑉}), average speeds (𝑣̅) and presence of hindrance to overtake (H); and the categorical variable decision to overtake. Predicted probability (p) of overtake occurring can be calculated by

𝑝 = 1 − [ 1 1 + 𝑒^−𝑧] where, z is log-odds to overtake and given by,

𝑧 = ln ( 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑡𝑜 𝑓𝑜𝑙𝑙𝑜𝑤

𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑡𝑜 𝑜𝑣𝑒𝑟𝑡𝑎𝑘𝑒) = 𝛽₀+ 𝛽₁𝑣̅ + 𝛽₂𝑣_{𝐿𝑉|𝐹𝑉}+ 𝛽₃𝐿𝐺 + 𝛽₄𝐶𝑆 + 𝛽₅𝐻.

This equation calculates the probability to overtake a particular vehicle for different combinations of LV and FV. From the development of this model, it is observed that-

 Probability to overtake increases with relative speed and centerline separation, and decreases with longitudinal gap and average speed between LV and FV. Further, this probability also decreases if there is a presence of hindering traffic or road edges to overtake.

 Probability to overtake a car by another car is more sensitive to change in centerline separation and average speed. Further, it is observed that smaller sized vehicles like two- wheelers have higher tendency to overtake.

 For a car-car pair, there is 8.9% decrease, 3.2% increase, 1.9% decrease, and 23% increase in probability to overtake on 5% increase of average speed, relative speed, longitudinal gap and centerline separation, respectively. Similar relationships are obtained for other pairs mentioned in Table 4.18.

6.2.4 Developed simulation model based on inter-vehicular gaps

A simulation model is developed based on lateral and longitudinal gap-maintaining behavior and overtaking decision modeling. Separate algorithms are devised for the reaction of drivers during following (maintaining a longitudinal gap), and during overtaking (allowable speed of vehicle

while maintaining lateral clearances during overtaking). Field input parameters include desired and lateral speeds, acceleration-deceleration values from previous studies, traffic composition and average flow levels. The developed model is well-calibrated with field conditions by using genetic algorithms. Its performance is also compared with a commercial software VISSIM, by validating both these models with field data. The validation is conducted for the following-

 Macroscopic properties (speed-flow relationship), and

 Microscopic properties (time headway distribution, speed distribution, average lateral shifts, lateral and longitudinal gap-maintaining behavior, etc).

It was observed that the developed model can replicate real traffic stream behavior at both macroscopic and microscopic levels. The developed model is also used for generating specific cases useful for a traffic engineer. They are mentioned below-

 The model was calibrated for an 11.5 m wide section in Bengaluru city. The capacity of this section is estimated by fitting of a generalized model for speed-density curves. The estimated capacity from developed model is observed as 6,400 veh/h.

 The capacity is observed to increase linearly with desired speed from 4,940 cars/h at 50 km/h to 8,140 cars/h at 120 km/h desired speeds, by generating a hypothetical car-only traffic stream in the simulation model.

 Further, the capacity increases with an increase of road width, but it does not get doubled by doubling the road width as observed in lane disciplined traffic. With the addition of more lanes, capacity per lane decreases.

 The simulation model is also used to segregate bus traffic from other vehicles in the stream, and model the two segregated streams. It is observed that the capacity improves from 6,400 to 7,500 veh/h by segregating bus traffic from other vehicles.