Markov Modeling of Availability and Unavailability Data

Abstract

Markov models are often used in performance and dependability analysis and allow a precise and numerically stable computation of many result measures including those which result from rare events. It is, however, known that simple exponential distributions, which are the base of Markov modeling, cannot adequately describe the duration of availability or unavailability intervals of components in a distributed system. Commonly used in modeling those durations are Weibull, log-normal or Pareto distributions that can also capture a possibly heavy tailed behavior but cannot be analyzed analytically or numerically. An alternative to applying the mentioned distributions in modeling availability or unavailability intervals are phase type distributions and Markovian arrival processes that still result in a Markov model. Based on experiments for a large number of publically available availability traces, we show that phase type distributions are a flexible alternative to other commonly known distributions and even more that Markov models can be easily extended to capture also correlation in the length of availability or unavailability intervals.