TY - JOUR

T1 - On stability of multiple access systems with minimal feedback

AU - Chebunin, Mikhail Georgievich

AU - Foss, Sergey Georgievich

N1 - Чебунин М.Г., Фосс С. Г. О стабильности систем случайного множественного доступа с минимальной обратной связью. - Сибирские электронные математические известия. - 2019. - Т. 16. - С. 1805–1821

PY - 2019

Y1 - 2019

N2 - We introduce and analyse a new model of a multiple access transmission system with a non-standard «minimal feedback» information. We assume that time is slotted and that arriving messages form a renewal process. At the beginning of any time slot n, each message present in the system makes a transmission attempt with a (common) probability pn that depends on the system information from the past. Given that Bn≥1 messages make the attempt, each of them is successfully transmitted and leaves the system with probability qBn, independently of everything else, and stays in the system otherwise. Here {qi} is a sequence of probabilities such that qi0>0 and qi=0 for i>i0, for some i0≥1. We assume that, at any time slot n, the only information available from the past is whether i0 messages were successfully transmitted or not. We call this the «minimal feedback» (information). In particular, if i0=1 and q1=1, then this is the known «success-nonsuccess» feedback. A transmission algorithm, or protocol, is a rule that determines the probabilities {pn}. We analyse conditions for existence of algorithms that stabilise the dynamics of the system. We also estimate the rates of convergence to stability. The proposed protocols implement the idea of ‘triple randomization’ that develops the idea of ‘double randomization’ introduced earlier by Foss, Hajek and Turlikov (2016)

AB - We introduce and analyse a new model of a multiple access transmission system with a non-standard «minimal feedback» information. We assume that time is slotted and that arriving messages form a renewal process. At the beginning of any time slot n, each message present in the system makes a transmission attempt with a (common) probability pn that depends on the system information from the past. Given that Bn≥1 messages make the attempt, each of them is successfully transmitted and leaves the system with probability qBn, independently of everything else, and stays in the system otherwise. Here {qi} is a sequence of probabilities such that qi0>0 and qi=0 for i>i0, for some i0≥1. We assume that, at any time slot n, the only information available from the past is whether i0 messages were successfully transmitted or not. We call this the «minimal feedback» (information). In particular, if i0=1 and q1=1, then this is the known «success-nonsuccess» feedback. A transmission algorithm, or protocol, is a rule that determines the probabilities {pn}. We analyse conditions for existence of algorithms that stabilise the dynamics of the system. We also estimate the rates of convergence to stability. The proposed protocols implement the idea of ‘triple randomization’ that develops the idea of ‘double randomization’ introduced earlier by Foss, Hajek and Turlikov (2016)

KW - (in)stability

KW - Binary feedback

KW - Foster criterion

KW - Multiple transmission

KW - Positive recurrence

KW - Random multiple access

KW - binary feedback

KW - positive recurrence

KW - random multiple access

KW - ERGODIC ALGORITHMS

KW - multiple transmission

UR - http://www.scopus.com/inward/record.url?scp=85078656166&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=42735170

U2 - 10.33048/semi.2019.16.128

DO - 10.33048/semi.2019.16.128

M3 - Article

AN - SCOPUS:85078656166

VL - 16

SP - 1805

EP - 1821

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -