Analytic and Numerical Solutions of an N Duplicate-Server System

We consider an N duplicate-server system, where each server consists of two reconfigurable duplicated units which are subject to breakdowns. This system is studied analytically using generating-functions, and also numerically using the matrix-geometric procedure. Using the generating-function approach we obtain a recursive expression of the queue-length probability distribution for N = 1. This expression is difficult to generalize to N ? 2. The numerical method is applicable for any value of N. For any N, we also obtain the condition for stability and the availability of the system.