A class of tree algorithms with variable message length

In this paper we present and analyze a class of tree algorithms with variable message length. First we analyze the algorithm according to which a message, consisting of a number of packets, is transmitted continuously after the successful transmission of its first packet, referred to as the tree algorithm with variable message length. The analysis of the algorithm is presented for the two cases of small number of users and of large number of users. In both cases the analysis shows a considerable improvement for the maximum throughput, which gets larger as the average message length increases. Second, we present the reservation tree algorithm, R-Tree, which uses &test& packets instead of the message's first packet to resolve the collision among users. The R-Tree maximum throughput approaches one as the average message length increases, which for single packet messages can be a maximum throughput of 0.776 for infinite number of users.