СЛОТОВЫИ ALOHA С ИТЕРАЦИОННОМ ПРОЦЕДУРОЙ РАЗРЕШЕНИЯ КОЛЛИЗИЙ. СТАБИЛЬНОСТЬ И НЕСТАБИЛЬНОСТЬ

Abstract

Introduction: Cellular networks of the new generation consider Massive Machine Type Communication scenarios and a class of multiple random access algorithms Slotted ALOHA with coded random access. The algorithms of this class allow you to maintain a large number of devices, but they are unstable. Their non-stability leads to a longer time of delivering a message from a subscriber to the base station during the operation of large-scale systems of inter-machine communication. Purpose: Substantiation of non-stability of Slotted ALOHA algorithms with coded random access at any intensity of the input stream; proposal of a method for its stabilization; determination of the intensity at which the system will be stable. Results: A model of a random multiple access system is introduced for coded random access and a Poisson input flow. The functioning of the model is described with the use of a Markov chain with a countable number of states. It is proved that the Markov chain is non-returnable for any non-zero intensity of the input stream. Thus, the non-stability of a multiple access system for any coded random access algorithm is proved, and a modification of these algorithms is proposed. The operation of the model for the proposed modification is described using a two-dimensional Markov chain with a countable number of states. If the intensity of the input stream does not exceed a certain value limit, the two-dimensional Markov chain is ergodic. This suggests that the proposed modification of the algorithms ensures stable operation of the system. For any algorithm from the considered class, a method is proposed for determining the numerical value of the limiting intensity of the input stream at which the system is stable. Practical relevance: The proposed modification of the algorithms can be used to develop protocols oriented to a scenario with a large number of devices, a low message rate per device and a large total input intensity in the whole system.