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A Game-Theoretic Perspective for Efficient Modern Random Access

Andreas Peter Juhl Hansen, Jeppe Roden Münster, Rasmus Erik Villadsen, Simon Bock Segaard, Søren Pilegaard Rasmussen, Christophe Biscio, Israel Leyva-Mayorga

TL;DR

A game-theoretic approach is followed for optimizing the access policies of selfish users in modern random access mechanisms to achieve a Nash equilibrium (NE) that optimizes the throughput of the system while considering the cost of transmission.

Abstract

Modern random access mechanisms combine packet repetitions with multi-user detection mechanisms at the receiver to maximize the throughput and reliability in massive Internet of Things (IoT) scenarios. However, optimizing the access policy, which selects the number of repetitions, is a complicated problem, and failing to do so can lead to an inefficient use of resources and, potentially, to an increased congestion. In this paper, we follow a game-theoretic approach for optimizing the access policies of selfish users in modern random access mechanisms. Our goal is to find adequate values for the rewards given after a success to achieve a Nash equilibrium (NE) that optimizes the throughput of the system while considering the cost of transmission. Our results show that a mixed strategy, where repetitions are selected according to the irregular repetition slotted ALOHA (IRSA) protocol, attains a NE that maximizes the throughput in the special case with two users. In this scenario, our method increases the throughput by 30% when compared to framed ALOHA. Furthermore, we present three methods to attain a NE with near-optimal throughput for general modern random access scenarios, which exceed the throughput of framed ALOHA by up to 34%.

A Game-Theoretic Perspective for Efficient Modern Random Access

TL;DR

A game-theoretic approach is followed for optimizing the access policies of selfish users in modern random access mechanisms to achieve a Nash equilibrium (NE) that optimizes the throughput of the system while considering the cost of transmission.

Abstract

Modern random access mechanisms combine packet repetitions with multi-user detection mechanisms at the receiver to maximize the throughput and reliability in massive Internet of Things (IoT) scenarios. However, optimizing the access policy, which selects the number of repetitions, is a complicated problem, and failing to do so can lead to an inefficient use of resources and, potentially, to an increased congestion. In this paper, we follow a game-theoretic approach for optimizing the access policies of selfish users in modern random access mechanisms. Our goal is to find adequate values for the rewards given after a success to achieve a Nash equilibrium (NE) that optimizes the throughput of the system while considering the cost of transmission. Our results show that a mixed strategy, where repetitions are selected according to the irregular repetition slotted ALOHA (IRSA) protocol, attains a NE that maximizes the throughput in the special case with two users. In this scenario, our method increases the throughput by 30% when compared to framed ALOHA. Furthermore, we present three methods to attain a NE with near-optimal throughput for general modern random access scenarios, which exceed the throughput of framed ALOHA by up to 34%.

Paper Structure

This paper contains 12 sections, 1 theorem, 25 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. System model
  4. A game-theoretic approach to user rewards
  5. with two users and no erasures
  6. General case with $N$ users
  7. with differential evolution
  8. Short-frame
  9. Best reply
  10. Results
  11. Conclusions
  12. Appendix

Key Result

Theorem 1

A mixed strategy profile $\mathbf{s}^*\! \in\! S$ is a NE if, and only if, the following two conditions hold for any player $i$game_wireless. 1) The utility of all pure strategies in the support $\delta(s_i^*)$ will be equal. Namely, 2) The utility of any pure strategy in the support $\delta(s_i^*)$ is greater than or equal to that of any $b_i\notin\delta(s_i^*)$. Namely, The proof is found in th

Figures (2)

  • Figure 1: Exemplary modern random access system where $N=3$ active users transmit repetitions of the same packet according to and the BS employs SIC for multi-user detection.
  • Figure 2: Throughput using Best reply given $M=100$ and $G=0.9$ for different rewards $r$ and decoding probabilities (a) $p=1$ and (b) $p=0.9$. The throughput with framed ALOHA and the distribution obtained with differential evolution in the asymptotic case $\Lambda_\infty(x)$ are included as benchmarks.

Theorems & Definitions (2)

  • Theorem 1: Conditions for the Nash Equilibrium
  • proof