Speed dispersion is essential for transportation research but inaccessible to certain sensors that simply record density, mean speed, and/or flow. An alternative is to relate speed dispersion with these available parameters. This paper is compiled from nearly a quarter million observations on an urban freeway and a resulting data-set with two speed dispersion measures and the three fundamental parameters. Data are examined individually by lane and aggregately by direction. The first dispersion measure, coefficient of variation of speed, is found to be exponential with density, negative exponential with mean speed, and two-phase linear to flow. These empirical relationships are proven to be general for a variety of coefficient ranges under the above function forms. The second measure, standard deviation of speed, does not present any simple relationships to the fundamental parameters, and its maximum occurs at around a half to two-thirds of the free flow speed. Speed dispersion may be significantly different by lane.Keywords: speed dispersion; coefficient of variation of speed; standard deviation of speed; macroscopic traffic flow model
IntroductionSpeed dispersion plays a key role in various aspects: for instance, traffic safety studies have shown that 'speed dispersion kills'; value pricing studies commonly associate travel reliability with speed dispersion; and operating efficiency, air emissions, and energy/gas consumption are all affected by speed dispersion. Unlike the fundamental traffic flow parameters (mean speed, density, and flow), research on the characteristics of speed dispersion is relatively sparse and incomplete. Speed dispersion is inaccessible in two ways. First, many traffic sensors, including ultrasonic and unpaired inductive loops, magnetometers, magnetic induction coils, and infrared, do not record individual speeds, and are unable to capture speed dispersions. Second, for the sensors capable of measuring individual speeds, it is not speed dispersion but mean speed that is the standard output. Obtainment of speed dispersion relies on exogenous calculation, and tends to be neglected by system administrators who typically release the fundamental parameter-based traffic information to the general public and academia.