Stochastic incident duration

Abstract

The duration of incidents is a stochastic variable with a variation spread. This chapter analyzes the consequences of this stochastic nature of the duration in terms of delay. It uses shockwave theory to describe traffic states. As opposed to a point queue model, the head and the tail of the queue are separately modeled and in this way the spatial extent of the queue is properly described. Using the traffic states, the delay is analytically calculated. The paper distinguishes between three scenarios: (1) an incident happens on a road stretch without any influence of a junction; (2) an incident happens upstream of a junction; a queue forms upstream of the incident and capacity of the downstream links is insufficient to handle the queue discharge rate; (3) an incident happens downstream of a junction and the tail of the queue crosses the junction. We derive a formula for the total delay. Because the delay is a non-linear function of the duration, the expected delay is not equal to the delay of the incident with the expected duration. In the scenarios without spillback (the first two scenarios), the delay is proportional to the square of the duration of the blocking. The expected delay is expressed as a function of the variance of the duration of the blocking. Also, the variance of the average delay per involved traveler is expressed as function of the variance of the delay.