Figure 1: IP multicast not available.
Figure 2: IP multicast available.
Figure 3: Smart routers available.
packets to different branches at different rates. As a result, all destination nodes will receive packets at the rate $x_o^s (= \max_{d \in D^s} x_{o,d}^s)$ if there are no packet losses. Fig. 2 explains this situation. Clearly, this may cause a receiver to receive packets at a rate larger than the intended rate. However, as we will show shortly, our algorithm can observe this through measurements and lead to a rate allocation to the overlay nodes to minimize such redundancy. In fact, at the operating point $x^*$ we have $x_{o,d}^s = x_o^{s*}$ for all $d \in D^s$.
Suppose that the routers possess additional intelligence and are capable of forwarding packets to downstream branches at different rates that are specified by the network (Network Model-III). Then, it is possible to forward packets to each destination $d$ at the selected rate $x_{o,d}^s$ as shown in Fig. 3. This allows source nodes to exercise more fine-grained control over the rates $x_s = (x_{o,d}^s, o \in O^s, d \in D^s)$.
Note that under these models, overlay nodes can be viewed as content delivery servers that store a portion of the original content to be distributed. The objective is to distribute the content to these servers in such a way that the usage of network resources is optimized. Our goal is to minimize the total network cost defined to be the summation of all link costs in the network, by balancing the traffic load among multiple paths. However, the relationship between the rate assignments and the link loads depends on the adopted network model, which effectively alters behavior of the algorithm.
3.2 Link Loads
In this subsection we describe how the link loads are computed based on the rate allocations $x = (x_s, s \in S)$.
3.2.1 Network Model-I
This model represents the traditional IP network with routers without IP multicast functionality. We assume that packets are encoded using a Digital Fountain code at the source. A source node forwards the encoded packets to overlay nodes at the required rate, and overlay nodes create a unicast session and forward packets to each destination at the specified rate $x_{o,d}^s$.
Let $V_{n_2}^{n_1} \subset \mathcal{L}$ be the set of links in the default path from node $n_1$ to node $n_2$. Given