Module 5 : Uninterrupted Flow
Lecture 25 : Ramp Metering
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Numerical example

Consider an off-ramp (Single-lane) pair, 225 meters apart, from a six lane freeway. The length of the first deceleration lane is 150m and that of the second deceleration lane is 90 m. What is the LOS during the peak hour for the first off-ramp given that the peak hour factor is 0.95, the heavy vehicle adjustment factor is 0.93, the driver adjustment factor is 1.0 and the proportion of through freeway flow remaining is 61.7%? The freeway volume is 4500 veh/hr and the first off-ramp volume is 300 veh/hr.
Figure 1: Numerical example
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Solution

  1. Convert volume to flow rate: Convert volume in veh/hr to flow rate in pc/hr as follows:
    $\displaystyle v_i$ $\displaystyle =$ $\displaystyle \frac{V_i}{(PHF\times~F_{hv}\times~F_p)}$  
    $\displaystyle V_{F}$ $\displaystyle =$ $\displaystyle 5093~\mathrm{pc/hr}~~(F_{hv}=0.930,F_{p}=1.0)$  
    $\displaystyle V_{R}$ $\displaystyle =$ $\displaystyle ~340~\mathrm{pc/hr}~~(F_{hv}=0.930,F_{p}=1.0)$  

  2. Compute $ V_{12}$ as below:
    $\displaystyle V_{12}$ $\displaystyle =$ $\displaystyle V_{R}+(V_{F}-V_{R})\times~PFD$  
      $\displaystyle =$ $\displaystyle 340+(5093-340)\times~(0.617)$  
      $\displaystyle =$ $\displaystyle 3273~\mathrm{pc/hr}$  

  3. Compute density at ramp influence area as below:
    $\displaystyle D_{R}$ $\displaystyle =$ $\displaystyle 2.642+0.0053~V_{12}-0.0183~L_{D}$  
    $\displaystyle D_{R}$ $\displaystyle =$ $\displaystyle 2.642+0.0053\times~3273-0.0183\times~150$  
    $\displaystyle D_{R}$ $\displaystyle =$ $\displaystyle 17.2~\mathrm{pc/km/ln}.$  

  4. Determine LOS: For $ D_{R}$=17.2 pc/km/ln the LOS is D.