Translated title of the contribution: On stability of multiple access systems with minimal feedback

Mikhail Georgievich Chebunin, Sergey Georgievich Foss

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 fqig 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 contributionOn stability of multiple access systems with minimal feedback
Original languageRussian
Pages (from-to)1805-1821
Number of pages17
JournalSiberian Electronic Mathematical Reports
Publication statusPublished - 2 Dec 2019


  • (in)stability
  • Binary feedback
  • Foster criterion
  • Multiple transmission
  • Positive recurrence
  • Random multiple access

ASJC Scopus subject areas

  • General Mathematics


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