Freely flowing traffic is modeled by randomly distributed sources on a line. Statistical parameters of the noise emitted from point sources of equal strength are derived in terms of the cumulants of the intensity normalized by its mean. The probability distribution of the normalized intensity is calculated from the cumulants by series expansions based on the type III distribution (related to the chi-square probability function) for the semi-infinite source line, and on the Poisson distribution for the short finite source line. It is shown by several examples that consideration of the type III distribution alone (or of the Poisson distribution alone, in the respective cases) is sufficient with respect to both the evaluation of percentile levels and the calculation of the mean and variance of the level distribution. The theoretical results are found to be consistent with field data.