Large homogeneous communication networks with Markovian access control II. Global behavior and residence time

A solution to the problem of dynamic analysis of large homogeneous communication networks with Markovian access control disciplines is given. For the case of multiple steady states and buffered users it is shown that: (i) the state space portrait of the system contains a one-dimensional stable manifold; (ii) the dynamics of the system can be reduced to a birth and death process defined on this manifold; and (iii) the residence time of each metastable steady state of the above birth and death process can be calculated on the basis of a new asymptotic procedure. Simulations show that this procedure results in acceptable precision.