Optimal retransmission probability for S-ALOHA under the infinite population model

In this paper, a mathematical analysis method to simultaneously evaluate throughput and access delay considering an infinite population model is considered. Most of the previous related research has been done considering both finite population and saturation conditions where all the nodes in the system have always a packet ready to be transmitted and the transmission queue of each station is assumed to be always nonempty. This assumption is a good approximation for a Local Area Network working at full capacity; however, in a cellular system the assumptions of finite population and that every node in a cell has always a packet to transmit is not very realistic. Here, analytical results considering a S-ALOHA random access protocol with a Poisson arrival process - more suitable for the traffic model in a cellular system - for the users in the cells is presented. Using the Geometrical Backoff (GB) strategy, two approaches to find the optimum retransmission probabilities are developed; in the first one, the number of backlogged packets is required while a simpler and efficient alternative method requires only the knowledge of the new packet arrival rate.