The performance analysis of a random packet selection policy for multicast switching

A random packet selection policy for multicast switching is studied. An input packet generates a fixed number of primary copies plus a random number of secondary copies. Assuming a constant number of contending packets during a slot, the system is modeled as a discrete-time birth process. A difference equation describing the dynamics of this process is derived, the solution of which gives the distribution of the number of packets chosen. This result is extended to the steady-state distribution through an embedded Markov chain analysis. It is shown that the old packets have a larger number of copies than the fresh packets, and the copy distribution is derived. The packet and copy throughputs taking into account the old packets have been determined. The asymptotic distribution of the number of packets chosen is obtained for large switch sizes under saturation by applying results from renewal theory