Optimizing IP Multicast through Delayed Multicast Tree Pruning

This paper studies the system parameters that affect the total cost of managing the multicast group on a router. A Petri net model is first proposed to describe the states and transitions of the multicast group management. Based on this model, a delayed vacation queue, extended from a simple M/M/l queue, is used to analyze the total cost of the multicast group management under various system conditions. The formal analysis reveals that the total cost of the multicast group management is minimized when a router delays a certain time to send its pruning messages to upper stream routers. Furthermore, a formula is derived to calculate the optimal delay time for sending the pruning messages under various system parameters to minimize the multicast group management cost. Finally, cost analysis examples demonstrate how other system parameters, such as multicast member arrival rate and message sending costs, affect the total cost of the multicast group management under various delay times for sending the pruning messages.