an assumed linear speed–density relationship. Empirical studies of current traffic stream patterns show a speed–flow relationship, that while similar to the theoretical parabolic relationship, is significantly different in one respect. The parabolic model for speed-flow yields a continuous change in speed with changes in flow rate, whereas the empirical relationship shows that traffic stream speed stays constant up to moderate flow rates, and then starts to decline in a curvilinear manner. The HCM [Transportation Research Board 2016] defines the relationship between average speed and flow rate as follows:
S = FFS pv BP≤ (6.1)
and( )( )2.02.0
45 p c
FFS v BP S FFS
c BP
− − = −
− < ≤pBP v c (6.2)
where
c = Capacity in pc/h/ln, vp = 15-min passenger car equivalent flow rate in pc/h/ln,
BP = Linear to curvilinear flow rate breakpoint value in pc/h/ln, and
45 = Density at capacity in pc/mi/ln, as shown in Table 6.2. Other terms are as defined previously.
Capacity is given by the following equation:
( )Min 2200 10 50 ,2400c FFS = + − 55 ≤ FFS ≤ 75 (6.3)