Data networks
Erasures and noise in splitting multiple access algorithms
IEEE Transactions on Information Theory
Information theory and communication networks: an unconsummated union
IEEE Transactions on Information Theory
High-Throughput Random Access Using Successive Interference Cancellation in a Tree Algorithm
IEEE Transactions on Information Theory
Branching processes, the max-plus algebra and network calculus
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Computer Networks: The International Journal of Computer and Telecommunications Networking
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A simple numerical procedure is presented to determine the maximum stable throughput (MST) of various tree algorithms with free access by defining an associated multitype branching process such that the criticality of the branching process corresponds to the stability of the tree algorithm. More precisely, a bisection algorithm is proposed that only requires the computation of the dominant eigenvalue of the expectation matrix of the branching process, the size of which is typically below 20, at each step. Using this novel approach, many existing results on free-access tree algorithms are reproduced without much effort (e.g., channels with/without noise, variable length packets, interference cancellation, etc.). Furthermore, in an almost plug-and-play manner, the MST of the free access equivalent of many existing results on tree algorithms with blocked access is established (e.g., channels with capture, control signals, multireception capabilities, etc.). The method can be applied to the class of independent and identically distributed (i.i.d.) arrival processes, which includes the Poisson process as a special case. Apart from determining the MST, the probability that a size i collision is resolved in a finite amount of time when the arrival rate exceeds the MST can also be computed. Some limitations of the proposed methodology are discussed as well.