Traffic Stream Models
This relationship indicates that speed approaches free-flow speed vt when density (and flow) approach zero (k-->0, and -->0). As density (and flow) increases, speeds are reduced until flow is a maximum (qmax), and speed and density approach their optimum values (v-->v0, and k-->k0). Further increases in density result in lower speeds (and lower flows) until density reaches its maximum value (kj) and correspondingly speed (and flow) approach zero (v-->0, and q-->0). Note that flows can be represented on the speed-density diagram as contour lines with the maximum flow contour (qmax) tangent to the speed-density line at optimum values of speed and density (v0 and k0).
By Combining equation 17 and 18 we obtain the flow-density relationship shows directly below the speed-density relationship in Figure 17 because of their common horizontal scales:
Equation 19
q=vfk-(vf/kj)k to the second power
Since dq/dk=0 when k-->k0 we obtain the optimum density k0 that will maximize flow is:
Equation 20
k0=kj/2
Previous Page / Next Page