Events Defined by Duration and Severity, With an Application to Network Reliability

Abstract

Communications networks are highly reliable and almost never experience widespread failures. But from time to time performance degrades and the probability that a call is blocked or fails to reach its destination jumps from nearly 0 to an unacceptable level. High but variable blocking may then persist for a noticeable period of time. Extended periods of high blocking, or events, can be caused by congestion in response to natural disasters, fiber cuts, equipment failures, and software errors, for example. Because the consequences of an event depend on the level of blocking and its persistence, lists of events at specified blocking and duration thresholds, such as 50% for 30 minutes or 90% for 15 minutes, are often maintained. Reliability parameters at specified blocking and duration thresholds, such as the mean number of events per year and mean time spent in events, are estimated from the lists of reported events and used to compare network service providers, transmission facilities, or brands of equipment, for example. This article shows how data obtained with two-stage sampling can be used to estimate blocking probabilities as a function of time. The estimated blocking probabilities are then used to detect and characterize events and to estimate reliability parameters at specified blocking and duration thresholds. Our estimators are model-free, except for one step in a sampling bias correction, and practical even if there are hundreds of millions of observations. Pointwise confidence intervals for reliability parameters as a function of blocking and duration thresholds are built using a kind of “partial bootstrapping” that is suitable for very large sets of data. The performance of the algorithm for event detection and the estimators of reliability parameters are explored with simulated data. An application to comparison of two network service providers is given in this article, and possible adaptations for other monitoring problems are sketched.