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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 subject of extensive research, with 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 PRMA protocol for traffic with voice and data sources is investigated, and bifurcations of equilibrium points when control parameters change are determined. A bifurcation control scheme using state estimation is proposed to increase capacity of PRMA protocol, defined as number of simultaneous users within the system. By using Markov analysis, it is shown that 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 proposed bifurcation control scheme to PRMA protocol over a random packet error channel is also provided.