Generalized survivability analysis of systems with propagated failures

Abstract

The paper presents a generalized model for quantifying and evaluating the survivability of systems and the services provided by the systems. For this purpose, we consider a multi-server system with infinite buffer, Markovian Arrival Process (MAP) and phase type (PH) service time distribution. The system is subject to the so-called propagated breakdowns. Accordingly, breakdowns arrive in bunches (we call them attacks) according to the MAP. Attacks consist of a random number of failures of different types defined by the required repair time. The process of arrival of different types of server failures within an attack is governed by phase type Markov process. The repair of a server takes an exponentially distributed time with intensity depending on the type of the occurred failure. We analyze the survivability of the system in terms of average time required for its complete recovery after an attack completion conditional no new attack arrives. In this paper, we consider two forms of recovery following the end of failure arrivals based on (1) the length of queue or (2) the number of broken servers reaching a preassigned level. To provide analysis of survivability, we first describe dynamics of the system by the multi-dimensional continuous time Markov chain. Then, we analyze survivability by means of matrix extension of so called method of collective marks. Numerical illustrations are also presented.