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This paper concerns stability analysis for the packet reservation multiple access (PRMA) protocol extendable for mobile satellite systems (MSSs). This protocol has been widely considered for providing speech and data communications in a terrestrial microcell system. Recently modified versions of the PRMA protocol have been the subject of extensive research, with the goal of application to low earth orbit mobile satellite systems (LEO-MSSs). These systems are expected to play a significant role in providing communication services to users around the world. The bistable behavior of the PRMA protocol for traffic with voice sources is investigated, and the bifurcations of the equilibrium points when control parameters change are determined. A price based bifurcation control scheme is proposed to increase the capacity of the PRMA protocol, defined as the number of simultaneous users within the system. By using Markov analysis, it is shown that the adaptively controlled system has a unique probability distribution function. Next, by using equilibrium point analysis (EPA) it is shown that the system possesses a unique equilibrium point. Finally, a brief discussion concerning the extension of the proposed bifurcation control scheme to the PRMA protocol over a random packet error channel is also provided.