ABSTRACT We propose a mathematical model including queueing theory to reduce the negative consequences generated by large queues of vehicles as a result of traffic incidents. The mathematical model maximizes the number of incidents’ responses, and minimizes the non-recurrent congestion generated by them, considering a predetermined time to clear them, and an average or maximum response time. The model is applied to real-world incident data from Avenida Brasil, Rio de Janeiro, and the results showed that it is possible to concentrate the attendance in the critical areas of the expressway. The mathematical model proposed in this work can be used as a decision tool to help the government defining the acceptable average time for incident response, and the number of tow trucks necessary to achieve a pre-established service level.