Module 5 : Uninterrupted Flow
Lecture 25 : Ramp Metering
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Design of ramp metering

There are some considerations to be taken into account before designing and installing a ramp meter. Installation of a ramp meter to achieve the desired objectives requires sufficient room at the entrance ramp. The determination of minimum ramp length to provide safe, efficient, and desirable operation requires careful consideration of several elements described below:
  1. Sufficient room must be provided for a stopped vehicle at the meter to accelerate and attain safe merge speeds.
  2. Sufficient space must be provided to store the resulting cyclic queue of vehicles without blocking an upstream signalized intersection.
  3. Sufficient room must be provided for vehicles discharged from the upstream signal to safely stop behind the queue of vehicles being metered.
Provision for the distances mentioned is an integral part of ramp design. Figure 1 illustrates the requirements for the different types of distances explained above.

Minimum stopping distance to the back of queue

Sufficient stopping distance is required to be provided prior to entry to the ramp. Motorists leaving an upstream signalized interchange will likely encounter the rear end of a queue as they proceed toward the meter. Adequate maneuvering and stopping distances should be provided for both turning and frontage road traffic. This stopping distance calculated similar to the stopping sight distance which is a combination of the brake distance and lag distance travelled by a vehicle before stopping. The equation to calculate the minimum stopping distance is given below:

$\displaystyle X=vt+\frac{v^2}{2gf}$ (1)

where, X is the stopping distance in meters, v is the velocity of the vehicle in m/sec, t is the time in seconds, g is the gravity coefficient in $ \mathrm{m/sec^2}$, f is the friction coefficient. This is the minimum distance to be provided from the back of the queue for safe stopping of vehicles approaching the ramp.
Figure 1: Components of Ramp design criteria
\begin{figure} \centerline{\epsfig{file=qfDesignCriteria.eps,width=8 cm}} \end{figure}
Figure 1 shows Safe stopping distance, storage distance and acceleration distance which are respective three criteria for ramp design.

Storage distance

The storage distance is required to store the vehicles in queue to a ramp meter. The queue detector controls the maximum queue length in real-time. Thus, the distance between the meter and the queue detector defines the storage space. The following generalized spacing model can be used to determine the single-lane storage distance:

$\displaystyle L=aV-bV^2~~~\forall~V\leq1600~\mathrm{vph}$ (2)

In this equation, L (in meters) is the required single-lane storage distance on the ramp when the expected peak-hour ramp demand volume is V vph and a, b are constants. This figure shows the requirements for three metering strategies:
  1. Single-lane with single vehicle release per cycle.
  2. Single-lane with bulk metering (three vehicles per green).
  3. Dual-lane metering assuming single-line storage.
Figure 2: Variation of distance to meter with Ramp demand volume for different strategies of Ramp metering
\begin{figure} \centerline{\epsfig{file=qfDemandVolume.eps,width=8 cm}} \end{figure}
In the Figure 2 the curve is shown for the variation of storage distance i.e. distance to meter with ramp demand volume for different strategy used for Ramp metering.

Distance from meter to merge

The distance from meter to merge is provided so that vehicles can attain a suitable merging speed after being discharged from the ramp meter. AASHTO provides speed-distance profiles for various classes of vehicles as they accelerate from a stop to speed for various ramp grades. Figure 3, given below provides similar acceleration distances needed to attain various freeway merging speeds based on AASHTO design criteria.
Figure 3: Acceleration length v/s merge speed for different strategies of Ramp metering
\begin{figure} \centerline{\epsfig{file=qfDistanceSpeed.eps,width=8 cm}} \end{figure}
Table 1 provides the acceleration length for different merge speed and with ramps of different grade. The desired distances to merge increases with increasing freeway merge speed and the same ramp grade.

Table 1: Acceleration length of ramps
Merge speed Ramp Grade (%)
(kmph) -3 0 +3
60 90 112 150
70 127 158 208
80 180 228 313
90 248 323 466
100 331 442 665