As observed from Figure 5-15, the conditional probability of lateral acceleration and longitudinal A/D decreases with the increase in conditioning (speed). The conditional non- exceedance probabilities for lateral and longitudinal acceleration of motorized 2W (longitudinal (A/D) β€ 1m/s2 and lateral acceleration β€ 0.5m/s2) with speeds exceeding thresholds of π ππππ β₯ 20 km/h and πππππ β₯ 40 km/h are observed to be 0.1 and 0.18 respectively. Similarly, for sedan cars, the conditional non-exceedance probabilities for lateral and longitudinal acceleration longitudinal (A/D) β€ 1 m/s2 and lateral acceleration β€ 0.5 m/s2) with speeds exceeding thresholds of π ππππ β₯ 20 km/h and πππππ β₯ 40 km/h are observed to be o.52 and o.825 respectively, which implies that the probability of maintaining same lateral and longitudinal A/D values increases at higher speeds. This indicates that at higher speed conditions a larger percentage of riders maintain lower lateral and longitudinal A/D values comparing to the lower speed conditions. Similar type of observation is observed for deceleration of all type of vehicles. Hence, from this observation it can be concluded that at higher speed conditions the probability of higher lateral and longitudinal manoeuvring decreases for all type of vehicles. It is also observed that the probability of obtaining higher lateral and longitudinal A/D is higher in case of motorized 2W and it decreases for 3W followed by H-back, sedan and SUV cars. This indicates a higher manoeuvring action of smaller vehicles comparing to cars. It is also observed that probability of lateral and longitudinal manoeuvre is less while the vehicle is decelerating compared to accelerating condition. This information can be useful to determine the propensity of risks associated with the riders.
The non-exceedance conditional probability of vehicle speeds is of particular importance in traffic operation and safety studies to essentially help in adopting suitable traffic management strategies. This is because for a particular exceedance or non-exceedance probability value π, the values lateral acceleration, longitudinal A/D and speed for the respective variables can be obtained from the 3-D Gaussian distribution for this probability π. Based on the results of this study and the graphical analysis of the conditional probabilities, it can be concluded that a sufficiently accurate method to model the dependence structures of all three vehicle dynamic parameters is to use the trivariate Gaussian distribution.
driving, are the key factors for vehicle stability and the driving safety. The proposed methodology can be used to characterise the driving style i.e. cautious or aggressive behaviour of the driver. The tire-forces model (g-g diagram) is used to implement safety margin concept.
The driving behaviour (adoption of safe or unsafe driving) is analysed by considering dynamic parameters like operating speed, lateral and longitudinal accelerations of the vehicles on straight roads of plain terrain. The proposed g-g diagram can easily demonstrate the safe or unsafe behaviour of a driver. The normalised accelerations with gravity (ax/g and ay/g) are plotted, and compared with the friction circle obtained from the design coefficient of friction.
The friction points lie outside the safety envelop are considered as the risk-taking driving behaviour and is considered as unsafe. It is observed that in all cases the drivers of different vehicles adopts the safe driving in case of plain terrain roads (i.e. nearly 99% data lies within safe limit envelope βg-g diagramβ) except the motorised 2Ws (97%). It is observed that the motorised 2Ws are the most risk-taking drivers compared to cars.
The proposed diagram for resultant acceleration and design speed (safety domain curve), can easily demonstrate the safe or unsafe driving behaviour. The acceleration trend with the progressive (distance) interpret the exact locations of the trajectory where the driver experience sudden acceleration or deceleration (braking) additionally the points where lateral acceleration crosses the lateral threshold of the road design as stated by Eboli et al. (2016). It can be concluded from the present study that in all cases the drivers (different regions of the country) mostly drive within safe limit except 2Ws. Motorized 2Ws mostly cross the safety domain very frequently.
This study also investigated the applicability of the copula based approach to model the joint distribution of longitudinal descriptors [operating speed, longitudinal (A/D)] and lateral descriptor [lateral acceleration] of five different type of vehicles (motorized 2W, 3W, H-back, Sedan and SUV cars) for no-lane based traffic streams. An initial assessment on the strength of association of the traffic variables corroborated strong negative correlation between speed and lateral acceleration, speed and longitudinal A/D, and positive dependence between lateral and longitudinal A/D.
To accurately reproduce the dependence structures between the associated variables, a variety of copula functions including the Gaussian copula and various Archimedean copulas like the Gumbel-Hougaard copula, the Frank copula, the Clayton copula, and the Joe copula were
employed in this research. The results of the study confirmed that Frank copula and Gaussian copula are the best fitted model for describing the bivariate dependence of the considered variables, in most of the vehicles cases. Conversely, owing to the enhanced flexibility in accommodating all ranges of dependence (β1,1) over multivariate Archimedean copulas, the multivariate Gaussian copula provided a convenient way to model the joint behaviour of all three vehicle dynamic parameters.
In light of the research conducted in this study, the recommendation is to use trivariate Gaussian copula for the amelioration of the realistic representation of ridersβ behaviour in lane-based as well as in no-lane based traffic streams, by suitably accommodating the dependent relationships between the longitudinal and lateral descriptors of different type of vehicles. The work undertaken in this study provides a framework for generating the traffic variables simultaneously by accommodating the dependent relationship and can have extensive applications in safety evaluation, planning, design of roadway systems and in traffic operation studies. Also the study of dynamic parameters of vehicles using friction circle concept can contribute to the road safety improvement. The defined safety domain is an important tool for finding the points on the trajectory, where the driving behaviour is safe/unsafe to inform him about his driving behaviour and produce the threshold of attention to take preventive measures.