An Infinite Phase-Size BMAP/M/1 Queue and its Application to Secure Group Communication

We derive the bounds of the mean queue length of an infinite phase size BMAP/M/1 queue which has an M/M/∞-type phase transition, and use them to evaluate the performance of secure group communication. Secure communication inside a groups on an open network is critical to enhance the internet capability. Extending the usual matrix analysis to the operator analysis, we derive a new estimation of the degradation of secure group communication model.