The introduction of connected and autonomous vehicles (CAVs) provides a significant opportunity to address the persistently increasing problem of urban traffic congestion. By virtue of their connectivity and automation features, CAVs can reduce vehicle headways, thereby increasing road capacity and enhancing throughput. It has been hypothesized that CAV-infrastructure design policies can influence traveler behavior in ways that could reduce congestion. This research focuses on the potential of using CAV-dedicated lanes (CAVL) to alleviate traffic congestion in a bottleneck corridor that serves both human-driven vehicles (HDVs) and CAVs. We delve into investigating the impacts of CAVLs on the departure time and lane choices of morning commuters. The study first expresses traffic equilibrium conditions as a linear program with complementarity constraints. Then, a system-optimal commute congestion management design is formulated to minimize the overall system cost, which consists of queuing delays and early and late arrival costs. The results of the computational experiments suggest that: (i) the CAV technological advancements can significantly reduce traffic congestion under CAVL deployment with an almost similar effect as a tolling policy; and (ii) the lower value of time for CAV commuters leads them to depart closer to their desired arrival time without a tolling policy, which could significantly increase the bottleneck traffic congestion that commuters experience, particularly HDVs.