Relationship Between Mean Flow Rate and Probability of Breakdown at Freeway Bottlenecks

The relationship between mean flow and the probability of flow breakdown at freeway bottlenecks is investigated. The probability that flow breaks down within time t is viewed as an expected time-to-failure problem and is modeled as a negative exponential function of t and the mean time to breakdown. This allows the relationship between mean flow and the instantaneous probability of breakdown to be evaluated: since the instantaneous probability of breakdown is the reciprocal of the mean time to breakdown, the relationship may be discovered by plotting the reciprocal of the duration of periods of near-constant pre-breakdown flow against the mean flow. To evaluate this relationship, data were analyzed for thirty or more periods of pre-queue flow at each of thirteen bottlenecks. Results were generally negative: a significant correlation between the level and duration of pre-queue flow was found in only one case, suggesting that the relationship between mean flow and the probability of breakdown is weak or non-existent. Rather, at any given site, the probability of breakdown appears to be nearly equal over a considerable range of flow; however, these ranges vary considerably among sites. These findings suggest that flow breakdown may be the result of highly specific circumstances that vary by site but are only loosely related to average flow per lane.