Stochastic Analysis of the Duration of Occlusion of an Overhead Sign by a Leading Heavy Vehicle: Application to Sign Design

Abstract

With the increase in multilane expressways the use of overhead signs has also increased. A driver can miss an overhead sign because of occlusion of the sign by a leading heavy vehicle. Little or no research has been carried out to mathematically analyze conditions under which the driver of a light vehicle will not be able to read a sign because of a leading heavy vehicle. The lack of an analytical understanding of this phenomenon is reflected in the available design standards of the day. This paper analyzes the conditions that lead to occlusion of overhead signs because of a leading heavy vehicle. Next, the duration for which the occlusion occurs is determined. Subsequently, the results for duration of occlusion are used to evaluate whether enough time is left for the driver to read the sign. If enough time is not available then the driver is said to have “missed” the sign. Assuming that the speeds of the light and heavy vehicles and the distance headway between them vary randomly (around some expected values), the probability of missing a sign can be obtained using the analysis presented in this paper. Information on probability of missing a sign is used to determine alternative sign designs (in terms of sign characteristics and number of repetitions of the sign) that keep the probability of missing the information on a sign below a threshold.