Accidents, bad weather, and temporary construction can disrupt road traffic. A driver's original route can be disrupted and delayed by several minutes or even hours. How can traffic be robust to such disruptions? In this paper, we propose a static robust user traffic assignment based on alternative paths along routes. The bi-objective model of the problem minimizes the generalized cost and the robustness of the paths used to assign the passengers. The results show that 10% of robustness is sufficient to compensate for its cost and absorb some of the delays caused by network disruptions.