On stability of multiple access systems with minimal feedback

Research output: Contribution to journalArticlepeer-review

Abstract

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)
Translated title of the contributionО стабильности систем случайного множественного доступа с минимальной обратной связью
Original languageEnglish
Pages (from-to)1805–1821
Number of pages17
JournalSiberian Electronic Mathematical Reports
Volume16
DOIs
Publication statusPublished - 2019

Keywords

  • (in)stability
  • Binary feedback
  • Foster criterion
  • Multiple transmission
  • Positive recurrence
  • Random multiple access
  • binary feedback
  • positive recurrence
  • random multiple access
  • ERGODIC ALGORITHMS
  • multiple transmission

State classification of scientific and technological information

  • 27 MATHEMATICS

Fingerprint Dive into the research topics of 'On stability of multiple access systems with minimal feedback'. Together they form a unique fingerprint.

Cite this