Comparative Evaluation for Speed-Density Models for Highways in Developing Countries: A Case Study in Egypt
Journal of Applied Sciences Research
INTRODUCTION The fundamental diagram of a road segment depicts graphically the relationships among traffic flow characteristics, i.e., flow, speed, and density. The fundamental diagram plays an essential role in traffic flow theory and transportation engineering since sound mathematical models can offer a solid foundation for traffic flow analysis and efficient traffic control  . Among the three 'pair-wise' relationships (e.g., speed-density, flow-density, and speed-flow), the speeddensity
... the speeddensity relationship appears to be fundamental since it draws direct connection to everyday driving experience, i.e., how a driver's speed choice is influenced by the presence of other vehicles in their vicinity  . Moreover, the movement of vehicles on high-speed roads is governed by the behavior of drivers in leaving sufficient space (or gap) in front of the vehicle. Changing the spacing between vehicles means changing the traffic density on the road. Traditionally, two different approaches can be used for modeling the speed-density relation; namely, parametric modeling (statistical based), and non-parametric modeling (data mining based). In parametric modeling, the model has a basic statistical structure that follows specific statistical assumptions and relationships between the input and output variables. On the other hand, non-parametric modeling does not assume a fixed model structure. The model trains on the data to select the structure the best fits the variations within the data. Regarding the parametric modeling, the traffic flow speed-density relation models experienced more than 81 years of development since the first ever developed linear speed-density relation fitted by Greenshields  . Since then, various speed-density models have been developed with different parameters, structure, and calibrating data sources, all of which influence model interpretation. Some of the developed models preserve mathematical elegance by being presented by a single-equation and are known as single-regime models. Other models decompose the speed-density relationship into two pieces for better curve fitting and are known as two-regime models. In this case, mathematical elegance gradually gives its way to empirical accuracy. The literature is abundant with traffic models describing the speed-density relation of traffic characteristics in normal driving conditions where the lane discipline is strictly respected. The violation of lane discipline is very common in many developing countries. In these countries, drivers sometimes ignore the lane marking and move laterally across the road width to adjust their lateral position which creates a heterogeneous traffic environment. A review of the literature showed that limited studies were conducted to develop an understanding of the speed-density relation at developing countries, due to the heterogeneity in driving behaviors. Most reviewed studies that attempted to address this problem were conducted in India, where the presence of non-motorized vehicles yields a high degree of variation in physical and dynamical characteristics of vehicles on the road and especially the two-wheelers that have high maneuverability [4, 5, 6] . The situation in Egypt is less complicated than in India or similar countries' roads because the operation of non-motorized vehicles is not common on major roads. There have been many Egyptian studies attempting to model the speed-density relation for highways. For instance, El-Adawi  fitted a two-regime speeddensity model for traffic data collected from the 6th of October Road, a major road in Cairo (Egypt). Data was collected using a video camera covering the full Abstract Background: The highway speed-density relationship is fundamental since it draws a direct connection to how a driver's speed choice is influenced by the presence of nearby vehicles, however, in developing countries, the absence of lane discipline on most roads increases the frequent lateral movements and aggressive lane changes, yielding inefficient utilization of road width .Objective: This paper investigates the best model for presenting the speed-density relation for non-homogenous traffic due to the absence of lane discipline through evaluating a bunch of parametric (statistical based) and non-parametric (data-mining based) models for fitting the best speed-density relationship for traffic streams where lane discipline is absent. Results: Results indicated that exponential model produced the best fit followed by the extreme Gradient Boosting model with R 2 of 91%, and 88% respectively. Comparing the exponential model with other models developed in Egypt, under no lane discipline conditions, indicated that sites with higher free flow speed experience relatively higher speed and lower density at capacity compared with sites having lower free-flow speeds. Furthermore, the lane capacity obtained from the exponential model was about 1750 pcu/h. This lane capacity is about 80% of the lane capacity reported in the Highway Capacity Manual (HCM) for homogeneous traffic condition. Although other models developed in Egypt represented different free-flow speeds, they resulted in about the same lane capacity. Conclusions: Based on these findings, the speed-density relation for non-homogenous traffic, in developing countries, is best presented by the exponential model. Alsoa factor of 0.80 -0.85 should be used when applying the HCM procedure to estimate the saturation flow rate for non-homogenous traffic conditions, depending on the free flow speed on the road.