TABLE OF CONTENTS A service model provides a structure that links the service-level attributes with those of the components in the lower layer. Once the relevant data is collected and organized with respect to the structure of the service model, additional processing and data mining are required to extract useful information from various parts of the service model to satisfy assurance applications. In this section, we will provide a fundamental mathematical framework for the service model and establish useful building blocks suitable for the analytical study of assurance problems. We will see that by representing KPIs as random variables, we are able to apply many powerful tools borrowed from the disciplines of statistical analysis and signal processing to solve difficult problems.
We start with some fundamental definitions of random variables, random processes, and their statistical properties. Then, we show how to model KPIs and KQIs as random variables and random processes. This introduction to the statistical modeling of KPIs and KQIs is important since a wealth of knowledge in statistical processing and estimation theory can potentially be applied to various OSS functions, including the definition of SLAs, detection of SLA violations, identification of the root cause of performance problems, identification of network or server-capacity bottlenecks, and prediction of trends. As an example, an SLA may include a condition that the measured IP packet delay should be no more than 30 ms for 99% of the packets. Compared to an SLA of 25-ms delay for 95% of ...
