Rate control for random access networks: The finite node case

We consider rate control for random access networks. In earlier work, we proposed a rate control mechanism which we analyzed using the well-known slotted Aloha model with an infinite set of nodes. In this paper, we extend this work to the finite node case and analyze two different packet-scheduling schemes: a backlog-dependent scheme where the retransmission probabilities depend on the total number of a backlogged packets at a given node, and a backlog-independent scheme. Using a Markov chain model, we derive conditions under which the rate control stabilizes the network. We also discuss how this mechanism can be used to provide differentiated quality-of-service both in terms of throughput and delay. We use numerical case studies to illustrate our results.