Dealing with traffic congestion is one of the most pressing challenges for cities. Transport authorities have implemented several strategies to reduce traffic jams with varying degrees of success. The use of reversible lanes is a common approach to improve traffic congestion during rush hours. A reversible lane can change its direction during a time interval to the more congested direction. This strategy can improve traffic congestion in specific scenarios. Most reversible lanes in urban roads are fixed in time and number; however, traffic patterns in cities are highly variable and unpredictable due to this phenomenon's complex nature. Therefore, reversible lanes may not improve traffic flow under certain circumstances; moreover, they could worsen it because of traffic fluctuations. In this paper, we use cellular automata to model adaptive reversible lanes(aka dynamic reversible lanes). Adaptive reversible lanes can change their direction using real-time information to respond to traffic demand fluctuations. Using real traffic data, our model shows that adaptive reversible lanes can improve traffic flow up to 40% compared to conventional reversible lanes. Our results show that there are significant fluctuations in traffic flow even during rush hours, and thus cities would benefit from implementing adaptive reversible lanes.