A Framework for the Evaluation of Network Reliability under Periodic Demand

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.