Approximate solution for the performability of Markovian queuing networks with a large number of servers.

In this paper, a simple and flexible approximate technique, capable of overcoming the state space explosion problem in computing the performability of large Markov models is presented. To show the capability of the proposed technique, MQL results are computed for parallel processing systems for large numbers of homogeneous processors and presented. In order to show the accuracy of the method, some of these results are validated using existing techniques whenever possible, and results obtained using different approaches are shown to be in good agreement. It is shown that, this approach can handle large state spaces. A case study is presented for 64, 128, 256, and 512-processor parallel processing systems with break-downs and repairs. This method can be further extended to compute the performability of large and complex networks.