Changes in travel demand in a specific hour in weekdays and changes in the street network capacity due to the different reasons like bad driving and street maintenance etc. lead to traffic congestion in urban traortation networks, which is caused by random events and known as the recurrent traffic congestion. The objective of this article is twofold: 1) assessment of traortation network reliability subject to recurrent traffic congestion condition(s). To accomplish this, first, this reliability will be defined and next modeled subject to the conditions of ongoing awareness of network’s traffic congestion. 2) By applying street widening policy the above-mentioned models will be optimized. In this context, a network design model is provided with the objective of selecting network links set, for street widening, according to the budget constraint, to maximize the network reliability. This model is implemented on the Sioux Falls network. Street widening is a Np-hard problem, thus, using the Quantum-iired 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.