A Mathematical Framework for the Evaluation of System Expected Utility Not Satisfied Under Periodic Demand

Abstract

In this paper, we consider a general system whose reliability can be characterized with respect to a periodic timedependent utility function related to the system performance in time. When an anomaly occurs in the system operation, a loss of utility is incurred that depends on the instance of the anomaly's occurrence and its duration. Under exponential anomalies' inter-arrival times and general distributions of maintenance time duration, we analyze the long-term average utility loss and we show that the expected utility loss can be written in a simple form. This allows us to evaluate the expected utility loss of the system in a relatively simple way, which is quite useful for the dimensioning of the system at the design stage. To validate our results, we consider as a use case scenario a cellular network consisting of 660 base stations. Using data provided by the network operator, we validate the periodic nature of users' traffic and the exponential distribution of the anomalies inter-arrival times, thus allowing us to leverage our results and provide reliability scores to the aforementioned network.