Speed modeling and travel time estimation based on truncated normal and lognormal distributions

Travel time is a vital performance index in assessing transportation network performance. Vehicle speeds along any network route fluctuate, and route travel times are essentially random. This technical note first examines travel time modeling and estimation with the random modeling of speeds, and then a general approach is presented for travel time estimation based on speed distributions. Because normal and lognormal distributions are commonly employed for speed modeling in traffic engineering, travel time estimation is further discussed concerning distributions. Most probability distributions (including normal and lognormal) assume that a modeled random variable spreads over the whole or half-range of the real number axis, but in practice, any traffic quantity of interest makes sense only within a limited value range. The concept of truncated distributions is introduced, and specifically, the probability features of truncated normal and lognormal distributions are explored concerning the discussed travel time estimation issue.