The duration of incidents is a stochastic variable. This paper analyses the consequences of this stochastic nature of the duration in terms of average delay. It uses shockwave theory to describe emerging traffic states inspace and time. 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 described properly. Using the traffic states, the delay is analytically calculated for different basic network elements. The paper distinguishes between three scenarios: (1) an incident happens on a continuous road stretch; (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. The authors 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 delayof the incident with the expected duration. In the scenarios without spillback (the first two scenarios), the delay is proportional to the square of the blocking duration. The expected delay is expressed as a function of the variance of the blocking duration Also, the variance of the average delay per involved traveler is expressed as function of the variance of thedelay. In case spillback occurs, the delay grows faster than proportionalto the duration squared.
Abstract