On the Relation Between the Finite and the Infinite Population Models for a Class of RAA's

We examine the relation between the finite and the infinite population models for a class of random access algorithms. The algorithms in the class are a combination of random access and reservation techniques, they are synchronous, and they are studied under the condition that each of the users can monitor the channel feedback continuously (full feedback sensing). For any finite number of independent and identical users in the system, and any i.i.d. arrival process per user, the algorithms are stable, provided that the total input rate is less than one. However, as the population size increases, the stability of an algorithm in the class is determined by its throughput in the presence of the infinite population model for all practical purposes.