Table of Contents

3.2.5 Negative Exponential Distribution

The negative exponential frequency distribution is illustrated in Figure 3.1. It is a continuous distribution and has the form:

\[f(\text{ x })=\lambda e^{-\lambda \text{ x }} \]3.11

where \(\lambda \) is a known parameter.

Figure 3.1: Negative exponential frequency distribution

The mean of the negative exponential distribution, or the expected value of x is:

\[E(\text{ x })=\frac{1}{\lambda } \]3.12

and the variance is:

\[\sigma ^{2} (\text{ x })=\frac{1}{\lambda ^{2} } \]3.13

The negative exponential is the simplest relationship used to describe the distribution of headways in randomly arriving traffic, as is discussed in Section 3.3. The displaced negative exponential distribution, a variation allowing for a minimum possible headway in a lane of traffic, is also discussed in Section 3.3, as are other types of headway distributions.