Fig. 1. HRM model. We consider a single-source multicast tree where the root is the unique source. The tree is divided into subgroups and feedback and transmissions/retransmissions are limited only between a proxy and the receivers of its subgroup.

Fig. 2. Mean delivery delay model reflecting heterogeneity and locations of proxies in which <p, d> on each link means <loss rate, delivery delay>.

Fig. 3. Conversion of general tree into its binary form with import of dummy nodes X₁ and X₂.

Fig. 4. Illustration of dynamic programming for D(u, k, v) in a tree.

Fig. 5. Pseudo code for configuring proxy set P_u. Proxy_Set() is called recursively.

Fig. 6. Mean delivery delay of all receivers with respect to the number of proxies.

Fig. 7. The number of different proxy nodes between the proxy sets with respect to the max fluctuation rate of per-link loss rate. Each proxy set is configured according to the first and the eighth measured loss rates.

Fig. 8. The number of different proxy nodes between the proxy sets with respect to the max fluctuation rate of per-link delay. Each proxy set is configured according to the first and the eighth measured delays.

Fig. 9. The number of different proxy nodes between the proxy sets when the per-link loss rates and delays are fluctuate simultaneously.

Fig. 10. Differences of all receivers’ average mean delay between the two proxy sets that are located using the first and eighth measured link statistics, respectively.

Fig. 11. Proxy set for receiver R_i.

Fig. 12. Illustration of case (1).

Fig. 13. Illustration of case (2).

Fig. 14. Illustration of case (3).

Fig. 15. Illustration of case (4).

Notations for expected delivery model

Notations for the dynamic programming formulation