Our Paper Leaves Open Several Interesting Avenues for Further Research. 6 Discussion 5 Loss of Nacks and Retransmitted Cells

It is interesting to investigate other topologies, in particular those which allow us to model the dependencies between cell losses for neighboring nodes. Can we take into account the fact that cells are typically lost in batches? How can information about transmission of previous packets be used to tune the redundancy factor? On the more practical side, much work is left to do on designing the protocols which exploit IDA inside an implementation of reliable multicast, defining the exact protocols for session management, flow control and transmission. Start: send m cells; pointer := 0; t := 1; for j := 1 to lg m counter(j) := 0; repeat receive a message; if NACK(j t ; m(t)) then if counter(j t) < 2d) then m s := 2 jt+1 ; else m s := 2m(t); counter(j t) := counter(j t) + 1; if (m s L) send m s cells starting at cell(pointer) to all receivers; pointer := (pointer + m s) mod L; else goto Start t := t + 1; until false; Figure 4: Algorithm CUP: Pseudocode for the sender in the unreliable case Proof: We note, that for any node in i 2 S j , after the sender retransmits 2d times 2 j+1 cells in response to NACKS sent from S j , i has obtained its missing cells with probability 1 ? O(n ?2). Therefore, for any 1 j dlg re, the probability that there exists a node i 2 S j with m i > 0 is bounded by 1 ? (1 ? (2q c L) 2d) jSjj 1 ? O(exp(?1=n)) = O(1=n) : Thus, with probability 1?O(1=n) the sender retransmits at most 2d P dlg re j=0 2 j+1 = d 16r cells. A new scheme for reliable multicast using IDA was presented as well as randomized algorithms minimizing the number of rounds and the amount of receiver-to-sender traffic. These algorithms were shown to be optimal, by proving lower bounds on the number of negative acknowledgments and time. 14 the probability that node i sends at least one NACK in the first (s ? 1) phases. Since the algorithm is non-uniform, these probabilities may now be different for different nodes. Let q(s) = 1 jS H j jSHj X i=1 q i (s) be the average success probability of a node in S H in phase s, and q(s ? 1) = 1 jS …