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On the capacity of infinite population multiple access protocols

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1 Author(s)

We present bounds on the maximum channel utilization (with finite average delay) of synchronous multiple access communications protocols serving an infinite population of homogeneous stations. Messages arrive to the system as a series of independent Bernoulli trials in discrete time, with probability p of an arrival at each arrival point (the Poisson limit is explicitly included) and are then randomly distributed among the stations. Pippenger showed that the channel utilization cannot exceed \xi_{p} , where \xi_{l}=1 and \lim_{p \rightarrow 0} \xi_{p} \approx 0.744 . Using a "helpful genie" argument, we find the exact capacity for all p \geq 0.568 (where we find optimal protocols that obey first-come first-served); for smaller values of p, we present an improved upper bound that decreases monotonically to \approx 0.6731 in the Poisson limit as p \rightarrow 0 .

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IEEE Transactions on Information Theory  (Volume:28 ,  Issue: 3 )