# A Random Access G-Network: Stability, Stable Throughput, and Queueing Analysis

## TL;DR

This paper introduces a novel random access G-network model that incorporates signals affecting stability, throughput, and delay, providing exact stability regions and queueing delay analysis for a two-user system.

## Contribution

It develops a new G-network model for random access systems with signals, deriving exact stability regions and queueing delay expressions, including bounds, for the first time.

## Key findings

- Exact stability region obtained for the system.
- Queueing delay expressions derived through Riemann boundary value problem.
- Explicit bounds for queueing delay provided.

## Abstract

The effect of signals on stability, throughput region, and delay in a two-user slotted ALOHA based random-access system with collisions is considered. This work gives rise to the development of random access G-networks, which can model virus attacks or other malfunctions and introduce load balancing in highly interacting networks. The users are equipped with infinite capacity buffers accepting external bursty arrivals. We consider both negative and triggering signals. Negative signals delete a packet from a user queue, while triggering signals cause the instantaneous transfer of packets among user queues. We obtain the exact stability region, and show that the stable throughput region is a subset of it. Moreover, we perform a compact mathematical analysis to obtain exact expressions for the queueing delay by solving a Riemann boundary value problem. A computationally efficient way to obtain explicit bounds for the queueing delay is also presented. The theoretical findings are numerically evaluated and insights regarding the system performance are derived.