Fundamental Diagram in the HCM
The Highway Capacity Manual, shortly HCM, is a published by the Transportation Research Board of the U.S. National Academies of Science until 1950 and it collects procedures for computing the capacity and the quality of service of various highway facilities.
As in the 1950’s freeways were not common, only with the second edition of 1965 the TRB approached the study of the traffic on a motorway facility under the guidance of the Highway Capacity and Quality of Service Committee from US Bureau of Public Roads, introducing speed - flow curves as expression of the Fundamental Diagram for freeways. Although having performed a number of regression analysis of ...view middle of the document...
In 1994 TRB updated 1985 edition in order to consider various studies on freeway traffic and Fundamental Diagram models. The Committee reviewed studies and updated curves with judgmental approach, without providing equations. The 1994 edition provided two set of curves, for 4-lanes and 6/8-lanes freeways, with a capacity respectively equal to 2200 and to 2300 pc/h/ln. FD was provided only for stable regime, with a constant speed range from 0 to 1300 pc/h/ln for 70 mi/h FFS, and from 0 to 1750 pc/h/ln for 50 mi/h FFS, where FFS was introduced as the speed with flow close to 0.
In 1997 TRB provided a new update of 1985 edition. Statistical analysis were conducted on a significant data base of speed – flow data, and new curves were defined by judgmental fit to data. A set of curves was developed with respect to FFS, estimated by a specified methodology, and covering a range for capacity from 2250 pc/h/ln for 55 mi/h FFS to 2400 pc/h/ln for 70 -75 mi/h FFS. For all the curves it was identified a constant value for density at capacity, which is equal to 45 pc/mi/ln (28 pc/km/ln). The equations consider two-segments curves: the first segment for flow values between 0 and a Break Point flow identified for the specific FFS, with constant speed equal to FFS; the second segment for flow values between the same BP and the capacity, and speed which vary according to the formula:
v= FFS-a∙(q-BP)^b (3)
A new edition of the manual was published in 2000, but in this edition the curves were not changed in comparison with 1997 update. In the last HCM edition, 2010, the curves were expressed in the same form of (3) but they were recalibrated with updated values for BP, for a and b parameters, and for FFS estimation methodology.
Closely linked to the definition of the speed - flow curves in the different editions of the HCM is the definition of Levels of Service, which describes a range of operating condition on a freeway facility. Level of Service is indexed by the letters from A to F where A stands for free-flow conditions and F stands for jam conditions. LOS A represents free flow conditions: individual users are virtually unaffected by the presence of others in the traffic stream. LOS B is in the range of stable flow, but the presence of other users in the traffic stream begins to be noticeable. Also LOS C is in the range of stable flow, but it marks the beginning of the range of flow in which the operations of individual users becomes significantly affected by interactions with others vehicle in the traffic stream. LOS D represents high-density but still stable flow; small increases in traffic flow can cause operational problems. LOS E represents operating conditions close to the capacity level; operations are usually unstable and small increases in flow or minor perturbations within the traffic stream will cause breakdowns. LOS F is used to define forced or breakdown flow.
Fig. 2. HCM speed – flow curve for freeways (a) 1997/2000; (b) 2010