Macroscopic Traffic Variables Traffic flow theory (TFT) Zhengbing He, Ph.D., http://zhengbing.weebly.com School of traffic and transportation, Beijing Jiaotong University October 30, 2015 Zhengbing He, Ph.D., http://zhengbing.weebly.com Macroscopic Traffic Variables
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Macroscopic Traffic VariablesTraffic flow theory (TFT)
Zhengbing He, Ph.D.,http://zhengbing.weebly.com
School of traffic and transportation, Beijing Jiaotong University
Definition: vehicle number passing a cross-section per time unit.We call the maximum possible flow as capacity. (The capacity ofa highway lies between 1800 ∼ 2400 veh/h per lane.)
S2: q(x0, t,T ) = mT — from the definition.
S3: q(x , t,A) = mdxTdx ≈ Total distance covered by vehicles in A
Area A
we write as q(A) = d(A)|A|
S1: q(x , t0, L) =∑
n vidtdtL =
∑n viL
— from Total distance covered by vehicles in AArea A in S3
Example problem: in a two-lane road, vehicles travel at 60km/hon the left lane and at 120km/h on the right lane. Assume that1200 veh/h pass on both lanes. What are the density, the flow, the(space-mean) speed and the time-mean speed on this road?
The occupancy o of a vehicle is easy to obtain in S2; i.e., loopdetectors in practice. The relative occupancy b in S2 is givenby:
b(x0, t,T ) = 1T
∑m oi – Recall the definition of occupancy
If assume all vehicles have the same length l , we can get:b(x , t0, L) = lk(x , t0, L) – How to derive it
Note: this formula is not appropriate in practical situationsbecause inhomogeneity of the real traffic flow. If want to finddensity by using detectors, it is relatively better to usek = q
Edie’s definitions are important because it allows one to comparethe behavior of two traffic streams even if they have been observedin different ways, such as the comparison of A and B.
One should try to avoid the non-stationary area, such as C, becauseone value of the macroscopic variableonly corresponds to one traffic state.
The discrete nature of traffic requires time intervals of at least halfa minute if we want to achieve meaningful macroscopicinformation. When the time intervals exceed a duration of fiveminutes, certain dynamic characteristics are lost.