When assessing the resilience of road transport networks, users’ response should be considered as they represent the main capability of the system to adapt to changes when any disruptive event occurs and to recover afterwards. Given the variability in users’ response, it seems deterministic approaches might not be adequate to represent the real system performance, thus, a stochastic perspective is required. This paper presents a new approach to assess the resilience of a traffic network when suffering from a disruptive event, considering the stochastic behaviour of the users, where their decisions will be biased by their perception of the traffic conditions rather than by the actual conditions. This approach provides more realistic patterns than the deterministic approach, mainly in terms of recovery times. The real traffic network Luxembourg-Metz has been used to illustrate the approach.