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Connected autonomous vehicles (CAV) technologies are about to be in the market in the near future. This requires transportation facilities ready to operate in a mixed traffic environment where a portion of vehicles are CAVs and the remaining are manual vehicles. Since CAVs are able to run with less spacing and headway compared with manual vehicles or mixed traffic, allocating a number of freeway lanes exclusive to CAVs may improve the overall performance of freeways. In this paper, we propose an analytical managed lane model to evaluate the freeway flow in mixed traffic and to determine the optimal number of lanes to be allocated to CAVs. The proposed model is investigated in two different operation environments: single-lane and managed lane environments. We further define three different CAV technology scenarios: neutral, conservative, and aggressive. In the single-lane problem, the influence of CAV penetration rates on mixed traffic capacity is examined in each scenario. In the managed lanes problem, we propose a method to determine the optimal number of dedicated lanes for CAVs under different settings. A number of numerical examples with different geometries and demand levels are investigated for all three scenarios. A sensitivity analysis on the penetration rates is conducted. The results show that more aggressive CAV technologies need less specific allocated lanes because they can follow the vehicles with less time and space headways.