The advantage of using a linear representation of the speed–density relationship is that it provides a basic insight into the relationships among traffic flow, speed, and density interactions without clouding these insights by the additional complexity that a nonlinear speed–density relationship introduces. However, it is important to note that field studies have shown that the speed–density relationship tends to be nonlinear at low densities and high densities (those that approach the jam density). In fact, the overall speed–density relationship is better represented by three relationships: (1) a nonlinear relationship at low densities that has speed slowly declining from the free-flow value, (2) a linear relationship over the large medium-density region (speed declining linearly with density), and (3) a nonlinear relationship near the jam density as the speed asymptotically approaches zero with increasing density. For the purposes of exposition, we present only traffic stream models that are based on the assumption of a linear speed–density relationship.
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