Analysis of the Delay Distribution in Cellular Networks by Using Stochastic Geometry

TL;DR

This paper develops analytical and numerical methods using stochastic geometry to analyze delay distributions in large-scale cellular networks, providing insights for optimizing delay-sensitive applications.

Contribution

It introduces new analytical frameworks and efficient numerical approximations for delay distributions, including asymptotic analysis of packet loss probability in cellular networks.

Findings

Analytical formulations closely match Monte Carlo simulations.

Delay performance depends on decoding threshold, transmit power, and base station density.

Proposed methods aid in network optimization under reliability constraints.

Abstract

In this paper, with the aid of the mathematical tool of stochastic geometry, we introduce analytical and computational frameworks for the distribution of three different definitions of delay, i.e., the time that it takes for a user to successfully receive a data packet, in large-scale cellular networks. We also provide an asymptotic analysis of one of the delay distributions, which can be regarded as the packet loss probability of a given network. To mitigate the inherent computational difficulties of the obtained analytical formulations in some cases, we propose efficient numerical approximations based on the numerical inversion method, the Riemann sum, and the Beta distribution. Finally, we demonstrate the accuracy of the obtained analytical formulations and the corresponding approximations against Monte Carlo simulation results, and unveil insights on the delay performance with respect to several design parameters, such as the decoding threshold, the transmit power, and the deployment density of the base stations. The proposed methods can facilitate the analysis and optimization of cellular networks subject to reliability constraints on the network packet delay that are not restricted to the local (average) delay, e.g., in the context of delay sensitive applications.