Estimating traffic stream space-mean speed and reliability from dual and single loop detectors, Transportation Research Record

The relationship between time-mean and space-mean speed that was derived by Wardrop (1) and presented in several textbooks (e.g. Hobbs and Richardson (2); May (3); Garber and Hoel (4)) is suitable for estimating time-mean speeds from space-mean speeds. However, in most cases it is desired to estimate the space-mean speed from time-mean speed measurements. Consequently, the paper develops a new formulation, which utilizes the variance about the time-mean speed as opposed to the variance about the space-mean speed, for the estimation of space-mean speeds. The paper demonstrates that the space-mean speeds are estimated within a margin of error from 0 to 1 percent. Furthermore, the paper develops a relationship between the space and time-mean speed variances and between the space-mean speed and the spatial travel time variance. In addition, the paper demonstrates that both the Hall and Persaud (5) and the Dailey (6) formulations for estimating traffic stream speed from single loop detectors are valid. However, the differences in the derivations are attributed to the fact that the Hall and Persaud formulation computes the space-mean speed (harmonic mean) while the Dailey formulation computes the time-mean speed (arithmetic mean)