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

• Published in: IEEE open journal of the Communications Society Vol. 4; pp. 1728 - 1744
• Main Authors: Danufane, Fadil Habibi, Di Renzo, Marco
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Cellular communication; Cellular networks; Delay; delay distribution; Delays; Design parameters; Engineering Sciences; Geometry; Interference; local delay; Network reliability; Optimization; Packets (communication); Poisson point processes; Probability distribution functions; Reliability; Signal and Image processing; stochastic geometry; Stochastic processes; Wireless networks; Geometry; Cellular networks; Wireless networks; Stochastic processes; Interference; local delay; delay distribution; Delays; Reliability; Cellular networks stochastic geometry Poisson point processes local delay delay distribution; stochastic geometry; Poisson point processes
• ISSN: 2644-125X; 2644-125X
• DOI: 10.1109/OJCOMS.2023.3294791

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 facilitate the computation of the obtained analytical formulations, 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 simulations, 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.