This paper theoretically analyzes the usage of directional slotted Aloha schemes for managing the peer-to-peer random access in fifth and sixth generation (5G/6G) systems. To this aim, the physical layer is modeled by accounting for interference and noise, while a Markov chain approach is developed to investigate the network behavior in the presence and in the absence of a separate feedback channel, which provides information concerning the success or not of each transmission attempt. Closed-form expressions for the coverage probability and for the transition matrices with and without feedback are derived to then evaluate the corresponding throughput. The analytical results, which are validated by independent Monte Carlo simulations, are used to estimate the impact of the antenna gain, of the burst length, and of the node density on the achievable performance, as well as to discuss the directional random access benefit/complexity tradeoff.
