A Framework for the Evaluation of Network Reliability Under Periodic Demand

TL;DR

This paper introduces a framework to evaluate network reliability based on a periodic utility function, analyzing long-term utility loss due to anomalies, with validation on cellular network data showing practical applicability.

Contribution

It extends existing models by incorporating periodic utility functions and general anomaly distributions, providing convergence analysis and real-world validation.

Findings

Expected utility loss converges to a simple form

Cellular network anomalies follow exponential inter-arrival times

Traffic exhibits quasi-periodic behavior

Abstract

In this paper, we study network reliability in relation to a periodic time-dependent utility function that reflects the system's functional performance. When an anomaly occurs, the system incurs a loss of utility that depends on the anomaly's timing and duration. We analyze the long-term average utility loss by considering exponential anomalies' inter-arrival times and general distributions of maintenance duration. We show that the expected utility loss converges in probability to a simple form. We then extend our convergence results to more general distributions of anomalies' inter-arrival times and to particular families of non-periodic utility functions. To validate our results, we use data gathered from a cellular network consisting of 660 base stations and serving over 20k users. We demonstrate the quasi-periodic nature of users' traffic and the exponential distribution of the anomalies' inter-arrival times, allowing us to apply our results and provide reliability scores for the network. We also discuss the convergence speed of the long-term average utility loss, the interplay between the different network's parameters, and the impact of non-stationarity on our convergence results.