Performance analysis of a hybrid switching system where voice messages can be queued

摘要

In the classical model of a hybrid switching system with movable boundary it is assumed that blocked voice messages are lost and do not affect the further functioning of the system. We describe a more realistic model where blocked voice messages are queued and then are served once a channel becomes free. The main mathematical difficulty in the analysis of such models lies in the fact that the underlying stochastic process has as state space the whole quadrant ℤ+2. We reduce the problem to a set of equations defined over the lattice semi-strip {1,...,N} × ℤ+. This in turn allows us to use available general mathematical theo