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This paper addresses the stability, bifurcation properties, and performance improvement of the packet reservation multiple access with hindering states (PRMA-HS) protocol, a medium access control scheme suitable for application in low earth orbit mobile satellite systems. The bistable behavior and bifurcation properties of the PRMA-HS protocol for a traffic with voice sources is investigated. A price based bifurcation control scheme is proposed to increase the capacity of the PRMA-HS protocol, defined as the number of simultaneous users sharing the same communication medium. Finally, a brief discussion concerning the extension of the proposed bifurcation control to PRMA-HS protocol over a random packet error channel is also provided.