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We consider the uplink case of a cellular system where  bufferless mobiles transmit over a common channel to a base station, using the slotted aloha medium access protocol. We study the performance of this system under several power differentiation schemes. Indeed, we consider a random set of selectable transmission powers and further study the impact of priorities given either to new arrival packets or to the backlogged ones. Later, we address a general capture model where a mobile transmits successfully a packet if its instantaneous SINR (signal to interferences plus noise ratio) is lager than some fixed threshold. Under this capture model, we analyze both the cooperative team in which a common goal is jointly optimized as well as the noncooperative game problem where mobiles reach to optimize their own objectives. Furthermore, we derive the throughput and the expected delay and use them as the objectives to optimize and provide a stability analysis as alternative study. Exhaustive performance evaluations were carried out, we show that schemes with power differentiation improve significantly the individual as well as global performances, and could eliminate in some cases the bi-stable nature of slotted aloha

Modeling Slotted Aloha as a Stochastic Game with Random Discrete Power Selection Algorithms