Reducing the Makespan in Hierarchical Reliable Multicast Tree
  In hierarchical reliable multicast environment, makespan is the time that is required to fully and successfully transmit a packet from the sender to all receivers. Low makespan is vital for achieving high throughput with a TCP-like window based sending scheme. In hierarchical reliable multicast methods, the number of repair servers and their locations influence the makespan. In this paper we propose a new method to decide the locations of repair servers that can reduce the makespan in hierarchical reliable multicast networks. Our method has a formulation based on mixed integer programming to analyze the makespan minimization problem. A notable aspect of the formulation is that heterogeneous links and packet losses are taken into account in the formulation. Three different heuristics are presented to find the locations of repair servers in reasonable time in the formulation. Through simulations, three heuristics are carefully analyzed and compared on networks with different sizes. We also evaluate our proposals on PGM (Pragmatic General Multicast) reliable multicast protocol using ns-2 simulation. The results show that the our best heuristic is close to the lower bound by a factor of 2.3 in terms of makespan and by a factor of 5.5 in terms of the number of repair servers. 
Sang-Seon Byun, Chuck Yoo