In this paper, we consider a millimeter wave network deployed to cover an urban street. Each base station (BS) employs hybrid beamforming with a limited number of radio frequency (RF) chains. Its link to any user equipment (UE) is prone to being blocked by vehicles and pedestrians moving along the street. We propose a Round Robin (RR) access protocol with proactive cell switching in which each UE switches its connection to the least loaded line of sight BS at the end of its RR transmission frame or any time when its link is blocked. We compare the UE connectivity performance of the proposed protocol to the conventional cellular network association protocols and the RR protocols which switch only when the link is blocked. Our results reveal the impacts of different system parameters (i.e. the number of BSs, the number of RF chains, the length of RR transmission frame) on the performance of the protocol, and the importance of cell switching in dealing with load balancing as well as blockage