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:

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

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.





Fuzzy Sets

Upstream Mainline Occupancy $$ Guassian(x;c,σ) = e^{-\frac{1}{2}(\frac{x-c}{σ})^{2}} $$

Upstream Mainline Flow $$ Guassian(x;c,σ) = e^{-\frac{1}{2}(\frac{x-c}{σ})^{2}} $$

Upstream Mainline Speed $$ Guassian(x;c,σ) = e^{-\frac{1}{2}(\frac{x-c}{σ})^{2}} $$

Downstream Mainline Speed $$ Sig(x;a,c) = \frac{1}{1+e^{-a(x-c)}} $$

Downstream Mainline v/c $$ Sig(x;a,c) = \frac{1}{1+e^{-a(x-c)}} $$

Ramp Demand/Queue Occupancy $$ Sig(x;a,c) = \frac{1}{1+e^{-a(x-c)}} $$

Ramp Metering $$ Triangle(x;a,b,c)=\left\{\begin{array}{l} 0,&\mbox{𝑥 ≤ 𝑎 }\\ \frac{x-a}{b-a},&\mbox{𝑎 ≤ 𝑥 ≤ b}\\ \frac{c-x}{c-b},&\mbox{𝑏 ≤ 𝑥 ≤ 𝑐}\\ 0,&\mbox{𝑥 ≥ 𝑐} \end{array}\right. $$ $$ Metering Rate = (900-240) \times ( \frac{\sum^3_{i=1}{w_{i}}{c_{i}}{I_{i}}}{\sum^3_{i=1}{w_{i}}{c_{i}}} + \frac{240}{900-240}) $$

where

Inference

w(Low) = RuleOutcome[3] x 2 + RuleOutcome[4] x 2 + RuleOutcome[8] x 3 w(Medium) = RuleOutcome[2] x 1.5 + RuleOutcome[5] x 1 w(High) = RuleOutcome[1] x 21.5+ RuleOutcome[6] x 1 + RuleOutcome[7] x 1 + RuleOutcome[9] x 3 c(Low) = 0.5/3 c(Medium) = 0.5 c(High) = 1- 0.5/3 I(Low) = 0.5 I(Medium) = 1 I(High) = 0.5

Scaled Metering Rate $$Scaled Metering Rate = \frac{Metering Rate - 240}{900-240}$$

References ​