1. Network-Coding Multicast Networks With QoS Guarantees Yuanzhe Xuan and Chin-Tau Lea, Senior Member, IEEE IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 19, NO. 1, FEBRUARY 2011 Speaker: Lin-You Wu

2. Outline I. INTRODUCTION II. OPTIMAL ROUTING FORMULATION III. SOLVING THE OPTIMAL ROUTING PROBLEM IV. NUMERICAL RESULTS V. CONCLUSION

3. I. Introduction It is well known that without admission control, network congestion is bound to occur. However, to implement admission control is difficult in IP-based networks, which are constructed out of the end-to-end principle.

4. Even if routers can perform admission control internally, the path computation and the state updating activities required for setting up and tearing down each flow will overwhelm the network. A new QoS architecture, called a nonblocking network, has been proposed recently, and it requires no internal admission control and can still offer hard QoS guarantees.

5. In this architecture, as long as each edge node admits not more than a specified amount of traffic, the network will never experience link congestion. For multicast networks, the main problem with this approach is low throughput.

6. Multicast architectures with hard QoS intentions can be divided into two types. One performs multicast at the network layer [Fig. 1(a)], and multicast is done by the routers (IP or MPLS type). The other, like a content distribution network (CDN), performs multicast at the application layer [Fig. 1(b)], and multicast is done by the servers.

8. Data transmission in both architectures consists of two parts: Transmission in the backbone network –covers a long distance –bandwidth is more expensive Transmission between a client and its local server –handle by LANs –bandwidth is relatively ample

9. Local data transmissions can also be tackled with the P2P technology as in a hybrid P2P network. The focus of this paper will be on the QoS guarantees in the backbone network.

10. It is well known that without admission control, congestion inside a network is bound to occur, but to implement admission control in a high- speed IP-based network is difficult. One reason is that IP-based networks are constructed out of the end-to-end principle and major signaling protocols. –meaning that a signaling message’s semantics can only be interpreted by the signaling servers located at the edge of the network [see Fig. 1(a)].

12. Another reason is that even if every node understands the semantics of a signaling message, as it is the case in Fig. 1(b) where each node is a server, the activities of checking bandwidth availability and setting up the paths for each flow can overwhelm the network.

13. A new QoS architecture has been proposed recently that requires no admission control inside the network and can still guarantee the congestion-free property. It applies to both shortest-path-routing (IP-like) and explicit-routing (MPLS-like) networks.

14. The most salient property of the network is the following: As long as the traffic of the ingress and egress directions admitted by edge node I is less than a i and b i respectively, the network will be congestion-free and none of its links will experience overflow.

16. Suppose that the network in Fig. 1(a) is a nonblocking network with a i = b i =900 Mb/s for all edge routers. Suppose also that each edge router connects to three video servers, and each server is allocated 300 Mb/s (even allocations are not a requirement).

17. Routing in a conventional network is based on the assumption that the traffic matrix T = {t ij } is given, where t ij represents the traffic rate from edge node I to edge node J. However, a i and b i are given in a nonblocking network (this pattern is called a hose-model pattern.)

18. For a unicast network, this means that only the row and column sums of T are known (a i =Σ j t ij and b i = Σ j t ji ),but not its t ij. For a multicast network, the relationship between the traffic matrix T and(a i, b i ) is more complicated (see Section II-A).

19. Finding an efficient routing algorithm for a nonblocking network is not a simple task because there are infinite traffic matrices that can satisfy the constraint (a i, b i ), and a feasible routing scheme must guarantee the congestion- free property for all of them. The task becomes even harder if the network needs to support multicast traffic.

20. As far as a nonblocking network is concerned, the most significant benefit of network coding is that it allows us to treat a multicast connection with q destinations as q unicast connections in formulating the flow optimization problem. we are able to prove two important results in this paper. Both results apply to explicit-routing and shortest-path routing networks.

21. 1.The optimal paths between a source–destination pair in a nonblocking unicast network are also the optimal paths for the pair in a nonblocking multicast network with network coding. 2.An immediate consequence of the result of 1) is that a nonblocking multicast network can admit the same amount of traffic as in a nonblocking unicast network.

22. II. OPTIMAL ROUTING FORMULATION The formulation of the optimal routing problem of a nonblocking multicast network with network coding is given in this section. The discussion applies to both explicit routing (MPLS-like) and shortest-path routing (IP-like) networks.

23. A. Traffic Unevenness A network can be described as a directed G(V,E) where V is the set of vertices and E is the set of links.