A private or corporate network connects the offices of a single large organization, such as an airline or a bank, using leased private lines. To improve the reliability of network applications, fault-tolerance can be incorporated directly into the private network. In this paper, we use a state-space model to capture the effect of dynamic rerouting and repair and investigate the effect on reliability of different repair-and-rerouting strategies at the application or call level. To reduce the potentially large state space that results, we construct an approximate Markov model with a smaller state space by lumping together similar states. The lumped model includes coverage parameters that can be estimated without considering the original model in its entirety. This allows the state-space model to be solved accurately and efficiently. We compare results of the approximation technique with results obtained by a complete simulation of the original network. We expect similar approximation techniques to be effective on models with large state spaces which obtain processes with many time-scales.>

The ARIES reliability model, which models a class of repairable and nonrepairable fault-tolerant systems by a continuous-time Markov chain and uses the Lagrange-Sylvester interpolation formula to directly compute the exponential of the state transition rate matrix (STRM) that appears in the solution of the Markov chain, is discussed. The properties of the STRM for ARIES repairable systems are analyzed. Well-established results in matrix theory are used to find an efficient solution for reliability computation when the eigenvalues of the STRM are distinct. A class of systems that ARIES models for which the solution technique is inapplicable is identified. Several transformations which are known to be numerically stable are used in the solution method. The solution method also offers a facility for incrementally computing reliability when the number of spares in the fault-tolerant system is increased by one.>

It is observed that a large number of closed fault-tolerant systems modeled by a continuous-time Markov model referred to as the ARIES model have repeated eigenvalues. It is proven that the rate matrix representing the system is diagonalizable for every closed fault tolerant system modeled by ARIES. Consequently, the Lagrange-Sylvester interpolation formula is applicable to all closed fault-tolerant systems which ARIES models. Since the proof guarantees that the rate matrix is diagonalizable, general methods for solving arbitrary Markov chains can be tailored to solve the ARIES model for the closed systems directly.>