Ramp Metering

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Introduction ​

ALINEA ALINEA is a simple but effective ramp metering strategy that utilizes a local traffic-responsive feedback loop to maintain maximum throughput at the downstream merge area of an on-ramp. The ALINEA algorithm calculates the metering rate at each time step by computing the difference between the downstream desired occupancy and the aggregated downstream occupancy at each time step, multiplying that difference by a regulator parameter, and adding that result to the metering rate of the previous time step. The following equation implicitly calculates the metering rate:

$$ r(k) = r(k-1) + {K_{R}}\times({O_{DES}}-{O_{OUT}}(k)) $$xy

where

Detectors are placed on every freeway lane 500 m downstream of the acceleration lane. The detector data for each lane is aggregated together at each time step to calculate the occupancy value that is compared to the desired occupancy. The on-ramp contains two detectors: a presence detector directly behind the ramp meter signal controller and a passage detector immediately after the ramp meter signal controller. The presence detector ensures that the signal rests on red when no vehicles are detected and ensures that the ramp metering algorithm is being applied when a vehicle is detected. The passage detector ensures that the system does not break down in case vehicles stay queued up behind the signal controller. The figure below illustrates the ALINEA setup used in SwashSim.

The ALINEA flow chart below reads as follows:



where

Fuzzy Logic ​​ Another method though which ramp metering can be implemented into SwashSim is fuzzy logic. Fuzzy logic is more like human language than traditional logical algorithms such as ALINEA. Rather than forcing a yes or a no, fuzzy logic utilizes the linguistic variables such as very low, low, medium, high, and very high. To process the approximate information for the real world, the fuzzy logic controller is actually a set of linguistic control rules related by the concepts of fuzzy implication and the rule of inference. In SwashSim, detectors are placed upstream, downstream, and on the on-ramp. The inputs for the upstream detectors are occupancy, flow, and speed. The inputs for the downstream detectors are speed and v/c ratio. The input for the ramp detectors is occupancy. A graphic representation of the fuzzy logic setup in SwashSim is shown in the figure below.



The graphic below is an example of a typical fuzzy logic system. The following is a description of the major components of the fuzzy logic system:


 * Fuzzifier: The fuzzifier translates each input into a set of fuzzy variables via membership functions.
 * Rules: The rules are the set of regulations that are based on expert opinions.
 * Inference: The inference stage involves applying fuzzy operators and implication methods to the rule base, allowing the fuzzy inputs to be converted into one fuzzy output.
 * Defuzzifier: The defuzzifier produces a crisp output based upon the fuzzy output.



Fuzzy Sets The fuzzification process involves translating each input into a fuzzy set with understandable terms such as "low" and "high". This is done using membership functions, which are different for each input type. Upstream mainline inputs use the Gaussian function, downstream mainline and ramp inputs use the Sigmoid function, and the output uses the triangular function. The full list of inputs along with their specific fuzzy sets and membership functions is shown below.

Inputs

Upstream Mainline Occupancy Upstream mainline occupancy varies from 0 to 30% and is described as 3 Gaussian fuzzy sets: Low, medium, and high. The overlap is 50% and the parameters (center point and the sigma value) are found using the Matlab plot shown below. $$ Guassian(x;c,σ) = e^{-\frac{1}{2}(\frac{x-c}{σ})^{2}} $$

Upstream Mainline Flow Upstream mainline flow varies from 0 to 4,000 veh/h and is described as 3 Gaussian fuzzy sets: Low, medium, and high. The overlap is 50% and the parameters (center point and the sigma value) are found using the Matlab plot shown below. $$ Guassian(x;c,σ) = e^{-\frac{1}{2}(\frac{x-c}{σ})^{2}} $$

Upstream Mainline Speed Upstream mainline speed varies from 0 to 100 km/h and is described as 3 Gaussian fuzzy sets: Low, medium, and high. The overlap is 50% and the parameters (center point and the sigma value) are found using the Matlab plot shown below. $$ Guassian(x;c,σ) = e^{-\frac{1}{2}(\frac{x-c}{σ})^{2}} $$

Downstream Mainline Speed Downstream mainline speed varies from 0 to 100 km/h, activates at 50 km/h, and ends at 80 km/h. It is described as only 1 Sigmoid fuzzy set which is very low, and the parameters (center point and the sigma value) are found using the Matlab plot shown below. $$ Sig(x;a,c) = \frac{1}{1+e^{-a(x-c)}} $$

Downstream Mainline v/c Downstream mainline v/c ratio varies from 0 to 1 and is fully activated at 0.9. It is described as only 1 Sigmoid fuzzy set which is very high, and the parameters (center point and the sigma value) are found using the Matlab plot shown below. $$ Sig(x;a,c) = \frac{1}{1+e^{-a(x-c)}} $$

Ramp/Queue Occupancy Both the ramp and queue occupancies vary from 0 to 50%, and activate from 10% to 30%. They are described as only 1 Sigmoid fuzzy set which is very high, and the parameters (center point and the sigma value) are found using the Matlab plot shown below. $$ Sig(x;a,c) = \frac{1}{1+e^{-a(x-c)}} $$

Inference

Output

Ramp Metering The metering rate varies from 240 veh/h to 900 veh/h, and is described as 3 triangular fuzzy sets: Low, medium, and high. The overlap is 50%. $$ Triangle(x;a,b,c)=\left\{\begin{array}{l} 0,&\mbox{𝑥 ≤ 𝑎 }\\ \frac{x-a}{b-a},&\mbox{𝑎 ≤ 𝑥 ≤ b}\\ \frac{c-x}{c-b},&\mbox{𝑏 ≤ 𝑥 ≤ 𝑐}\\ 0,&\mbox{𝑥 ≥ 𝑐} \end{array}\right. $$ $$ Metering Rate = \frac{\sum^3_{i=1}{w_{i}}{c_{i}}{I_{i}}}{\sum^3_{i=1}{w_{i}}{c_{i}}} $$

where

$$w(Low) = RuleOutcome[3] \times 2 + RuleOutcome[4] \times 2 + RuleOutcome[8] \times 3 $$ $$w(Medium) = RuleOutcome[2] \times 1.5 + RuleOutcome[5] \times 1 $$ $$w(High) = RuleOutcome[1] \times 21.5 + RuleOutcome[6] \times 1 + RuleOutcome[7] \times 1 + RuleOutcome[9] \times 3 $$ $$c(Low) = \frac{0.5}{3} $$ $$c(Medium) = 0.5 $$ $$c(High) = 1- \frac{0.5}{3} $$ $$I(Low) = 0.5 $$ $$I(Medium) = 1 $$ $$I(High) = 0.5 $$



Test Networks ​

Limitations ​ References ​