Sum throughput on a random access erasure collision channel

The random access erasure collision channel captures, in an abstracted manner, several important features of a wireless environment shared by uncoordinated radios. The radios employ random access and, when contending, transmit over independent heterogeneous erasure channels with the common access point. The access point is capable of only receiving a single message at a time, and so any colliding messages are lost. The combined effects of the channel heterogeneity and the collision rule give rise to a natural question: how does the expected sum throughput vary with the subset of radios that are active? The subset of radios achieving the optimal throughput is found by a simple greedy packing procedure - add the radios, sorted by nonerasure probability, until a target offered load is exceeded.