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This article is cited in 3 scientific papers (total in 3 papers)
Probability theory and mathematical statistics
On ergodic algorithms in systems of multiple access with partial feedback
M. G. Chebunin Novosibirsk State University, str. Pirogova, 2, 630090, Novosibirsk, Russia
Abstract:
We consider a model of a multiple access system with a non-standard partial feedback. Time is slotted.
Quantities of messages in different time slots are independent and identically distributed random variables.
At the beginning of each time slot each message presented in the system is sent to the channel with a certain probability, depending on available system history.
If $i\ge1$ messages are being passed simultaneously, each of them is being passed successfully with probability $q_i$,
and with probability $1-q_i$ transmission is distorted, the message remains in the system and tries to be sent later.
We consider the case when $q_i> 0$ only if $i \le i_0$ for a given $i_0 \ge1$.
By the end of the slot we receive information about the quantity of messages that were transmitted successfully
(it is the «feedback») — only this information is available.
The transmission algorithm (protocol) is a rule of setting transmission probabilities at different times based on the information, available to each moment.
In particular, if $q_1 = 1$ and $q_i = 0$ for all $i>1$ then this feedback is called «success-nonsuccess».
In this paper we study the existence of stable algorithms and the rate of convergence. Algorithms determined in this paper are
based on additional randomization idea proposed in [3].
Keywords:
random multiple access; binary feedback; positive recurrence; (in)stability; Foster criterion.
Received May 31, 2016, published September 29, 2016
Citation:
M. G. Chebunin, “On ergodic algorithms in systems of multiple access with partial feedback”, Sib. Èlektron. Mat. Izv., 13 (2016), 762–781
Linking options:
https://www.mathnet.ru/eng/semr712 https://www.mathnet.ru/eng/semr/v13/p762
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Abstract page: | 168 | Full-text PDF : | 40 | References: | 25 |
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