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We study new access schemes for a population of geographically distributed data users who communicate with each other and/or with a central station over a multiple-access broadcast ground radio packet-switching channel. We introduce and analyze alternating priorities (AP), round robin (RR), and random order (RO) as new conflict-free methods for multiplexing buffered users without control from a central station. These methods are effective when the number of users is not too large; as the number grows, a large overhead leads to a performance degradation. To reduce this degradation, we consider a natural extension of AP, called minislotted alternating priorities (MSAP) which reduces the overhead and is superior to fixed assignment, polling, and known random access schemes under heavy traffic conditions. At light input loads, only random access schemes outperform MSAP when we have a large population of users. In addition, and of major importance, is the fact that MSAP does not require control from a central station.