Unexpected traffic delays in street networks impose irreparable cost to users. Recurrent traffic congestion is one of traffic delay’s sources. This phenomenon steams from demand variation and also street's capacity reduction, which is caused from accidentally events. this condition leads transportation network’s performance to an uncertain condition that needs probability indexes to evaluate it. The first purpose of this research is to evaluating urban transportation network performance in order to providing appropriate paths to users. Therefore, a mathematical model is presented to assess the network performance reliability subject to recurrent traffic congestions. One of the policies that may reduce traffic congestion, is street widening. The other purpose of this paper is providing a model to select a number of network's street for expanding by considering budget constrain, in way that increase network performance reliability, as much as, possible. Street widening is a Np-hard problem, thus, using the Quantum-inspired evolutionary meta-heuristic method is adopted instead of the accurate problem-solving methods, while accuracy is maintained and to a great extent, problem-solving time is reduced. Finally, a numerical example, which is applied on Sioux falls network, is presented.