# Speed – Density Relationship at Federal Route 50 from Batu Pahat to Ayer Hitam

Topic: ScienceEngineering
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Last updated: June 12, 2019

Ghani Department of Geotechnical and Transportation Engineering Universiti Tun Hussein Onn Malaysia [email protected] com ABSTRACT There is no published relationship between speed and density for Federal Route 50 Batu Pahat to Ayer Hitam. Report in Traffic Study Malaysia indicates the relationships of speed and traffic flows for uninterrupted flow facilities.

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Federal route is a road consists of junctions and carrying high through traffic volume.This study is conducted towards producing the relationships between speed and density for Federal Route 50. The relationships was developed using an existing traffic flow models. The specific aim of study is to determine which model is appropriate with respect to federal route traffic characteristics. The relationships of speed and density are the parameters that are very important for planning and modelling of transportation facilities.

In this study, travel speed and traffic flow were collected at several selected sites. The collected data were analyzed based on Greenshields, Greenberg, Underwood and Drake Model.The result of the analysis study has shown that Underwood Model is the most suitable model that can be used to define the relationships between speed and density based on Malaysia road condition. This study also indicates that several factors such as distance between junctions, speed limits and adjacent land use activities affect the value of mean travel speed on federal route. Key words: Speed; Flow; Density INTRODUCTION Speed is defined as rate of motion, as distance per unit time, generally in miles per hour (mph) or kilometres per hour (km/h).Rate of flow represents the number of vehicles passing a point during a time interval less than 1 hour, but expressed as an equivalent hourly rate. Density is defined as the number of vehicles occupying a given length of lane or roadway, averaged over time, usually expressed as vehicles per kilometer (veh/km) [1]. Federal Route 50 is a federal road in Johor, Malaysia.

It partially upgraded on 2002 with four-lane carriageway (from Batu Pahat to Kluang), else remain 2 lane alignments. At most section, the Federal Route 50 was built under the JKR R5 road standard, allowing maximum speed limit of up to 90 km/h [6].But, there are some speed limits like 50, 60 and 90 km/h at some point as synchronize with the road friction. The history of traffic studies have shown the situation is constantly changing according to location and time [3]. The study on urban roads such as traffic flow would have a significantly higher compared with rural roads. Location with high trip generation will always have the higher traffic flow. Traffic flow also varies over time.

Study time during peak hours would record the traffic flow higher compared to non-peak hours.Traffic flow is a rather complex involving the interaction between the driver of the vehicle, with other drivers and road environment [2]. For example, drivers in the traffic flow not only need to pay attention to driving, but he should also be alert to other drivers and road environment. This relationship is known as a combination of the driver-vehicle-road. Objective The main objectives of the study are as follow: (i) To obtain the relationship between speed and density for Federal Route 50 Batu Pahat – Ayer Hitam. (ii) To determine the suitability of the speed – density model for the Federal Route 50 Batu Pahat – Ayer Hitam.

iii) To determine the environmental factors that may affect the speed and density on Federal Route 50 Batu Pahat – Ayer Hitam. 1 MATERIALS AND METHODS Table 1: Models of Speed – Traffic Flow Model Specification Greenshields Greenshields make the assumption that the relationship between speed and density is straightshaped to facilitate settlement. Greenberg Greenberg concluded that the nonlinear model is more appropriate. Shows that the flow is zero when the density is zero and the current density peak, the flow can also be zero [5].Greenberg also assumes that the traffic density is proportional to the same height as the fluid that flows continuously. ???? (Free flow regime) ???? ?? = ???? ln ?? Speed Underwood Underwood was found that the free flow speed, vf is easy to be obtained is through observation only, while the optimum density, Do is a bit difficult to be observed and its value varies depending on the surrounding roads.

Drake Drake found that the rate curve, v and the density, D is S-shaped curve enter data that is required is the free flow speed, vf and optimum density, Do. It was found that the rate, v, will not reach zero even though the ensity has reached the peak density, Dj [4]. Speed Speed – Density Relationship of Model Modified by Edie (1961) ?? = ???? ?? ??? ?? ?? (Free flow regime) ?? = ???? ln ???? ?? (Congested regime) (Congested regime) Density Density Weakness The peak density is obtained through the Greenshields model is low.

The weakness of this model is the free stream velocity is infinite [4]. It shows no relationship between speed and flow when the flow is zero. Speed Equation, v Flow Equation, Q Density Equation, D Regression Type ???? ?? = ???? ? ?? ???? ???? 2 ?? = ?????? ? ?? ???? ???? ?? = ???? ? ?? ???? Linear and polynomial ???? ?? = ???? ln ?? ?? ???? ?? = ?? ln ???? ? ?? ???? ?? ???? Among the results obtained are independent of flow rate obtained by Underwood model is quite high. Among the weaknesses of this model is the speed, v, will not reach zero and the peak density, Dj, and is infinite.

?? = ???? ?? ??? ???? ?? = ???? ?? ?1 2 ?? 2 ???? 1 2 1 2 ?? = ?????? ln ln ???? ? ???? ?? ???? ?? = ???? ln ?? ???? ?? = ?????? 2 ln ?? ???? ?? = ???? 2 ln ?? Logarithmic and exponential Exponential and logarithmic Exponential and logarithmic 2 Methodology The speed and flow data collection were carried out and regression analysis was also conducted to find the best traffic flow model.Overall methodology is shown in Figure 3. Problem Statement -Determination of speed – density relationship at Federal Route 50 Determination method of observation Study area selection Data collection Study of speed – density relationship Greenshields Conclusion Selection of the most suitable model -The criteria used is the highest value of R2 Greenberg Underwood Drake Determination of compatible model by using Regression Analysis Figure 3: Flow Chart of Research Methodology Study Location The study was carried out at nine locations, as shown in Table 2.

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