Relations among Density, Average velocity and Flux

From:http://www.kochi-tech.ac.jp/~cheon/traffic_e/traff_e021.html

So the argument seems to be headed for the diversion of the interest of drivers and the administrators. But fortunately, the two quantities characterizing both interests are closely related, or, in a sense, almost identical.

We have to make the concept of the fux slightly more precise. The literal interpretation of the above definition gives the varying number depending on the time and location of the measurement. So let us assume that flux at a given location is measured as an average over a sufficiently long period of time. Then the flux should be identical at every point of the road, since all the cars eventually pass through all locations of the road.

If a collection of cars of density rho advances with average velocity V_av, it will move the distance V_av in unit time, and the number of cars include within this distance is rho times V_av. This is precisely the number of cars passing through a point in unit time, which is the definition of the flux F. Therefore, we have

F = rho . Vav .

(1.1)

Once the density is fixed, there is no essential difference between judging something based on average velocity V_av or on flux F.

 

We can always numerically obtain F or V for a given rho. Graphical representation of rho-V (or rho-F) relation is achieved if we plot rho in horizontal and V (or F) in vertical axis to obtain a two dimensional graph. The rho vs. F plot is usually referred to as fundamental diagram of traffic flow.

Traffic current 就是Flux

We calculate the fundamental diagram (the traffic current against density).

from:http://prola.aps.org/pdf/PRE/v60/i1/p180_1

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