# Renewal-Theoretic Packet Collision Modeling under Long-Tailed Heterogeneous Traffic

## TL;DR

This paper introduces a renewal-theoretic model for packet collision analysis in heterogeneous IoT networks, accounting for long-tailed traffic distributions and channel fading, enabling better performance evaluation of interference effects.

## Contribution

It develops a generic collision-time distribution model applicable to various traffic patterns, incorporating long-tailed idle times and channel fading, advancing interference analysis in IoT networks.

## Key findings

- Derived a collision-time distribution function for heterogeneous traffic.
- Proposed a PER model considering multipath fading and collision dynamics.
- Provided an efficient PER approximation for interference-limited scenarios.

## Abstract

Internet-of-things (IoT), with the vision of billions of connected devices, is bringing a massively heterogeneous character to wireless connectivity in unlicensed bands. The heterogeneity in medium access parameters, transmit power and activity levels among the coexisting networks leads to detrimental cross-technology interference. The stochastic traffic distributions, shaped under CSMA/CA rules, of an interfering network and channel fading makes it challenging to model and analyze the performance of an interfered network. In this paper, to study the temporal interaction between the traffic distributions of two coexisting networks, we develop a renewal-theoretic packet collision model and derive a generic collision-time distribution (CTD) function of an interfered system. The CTD function holds for any busy- and idle-time distributions of the coexisting traffic. As the earlier studies suggest a long-tailed idle-time statistics in real environments, the developed model only requires the Laplace transform of long-tailed distributions to find the CTD. Furthermore, we present a packet error rate (PER) model under the proposed CTD and multipath fading of the interfering signals. Using this model, a computationally efficient PER approximation for interference-limited case is developed to analyze the performance of an interfered link.