Pitfall To Avoid When Estimating Incident-Induced Delay by Using Deterministic Queuing Models

The deterministic queuing model is the most widely used method to estimate the delay caused by freeway incidents. It has been applied in numerous studies to determine the impacts of incidents and to estimate the benefits of policies designed to reduce such impacts. Typically, the average duration per incident type is used to estimate the incident delay. This approach assumes that the “delay due to an average incident” is the same as the “average delay due to incidents.” In fact, because delay is a convex function of incident duration, the “delay due to an average incident” is always smaller than the “average delay due to incidents.” This paper shows that the underestimate of the total delay is a function of (a) the variance of the incident duration times, (b) the severity of the type of incident under consideration, and (c) the number of incidents of the type under consideration. A formula is presented that accurately determines the total delay. The formula depends on the mean and the variance of the incident duration times but does not require knowledge of the individual duration times. It is then shown how the averaging of duration times should be carried out in practice to avoid under- or overestimating the benefit of a reduction in incident duration. The concepts are illustrated using a stylized numerical example based on incident data from the Emergency Traffic Patrol in Chicago.