1. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) The Possibility of Permanent Routing Loops  There are two cases when a router determines that a recent update may cause a permanent routing loop in its source tree.  Case 1 : Suppose router i has a path to a destination dest in its source tree such that the successor of i (i.e., next hop) is a node j with i<j.  In this case, i sends an LSU message to its neighbours.  We are assuming that the addresses of the routers are unique integers.

2. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Possibility of Routing Loops (Case 1)  The loop-prevention mechanism is implemented through the following local route selection algorithm :  Router i cannot add a link (u,v) to its new source tree choosing k on the path to (u,v) if (u,v) is not in the source tree reported by k. i u v k (u,v) must be in the source tree reported by k (in the same order) if i wants to include the link (u,v) in its source tree.

3. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Possibility of Routing Loops (Case 1) i u v k (u,v) must be in the source tree reported by k (in the same order) if i wants to include the link (u,v) in its source tree.  Each link in the topology graph can be labelled with the neighbours that have reported the link.  A link (u,v) is added in the source tree of i only if the neighbour k along the path from i to u has reported the link (u,v) in its source tree.

4. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) The Use of Case 1 K L (Minimum node) K<L I UV J  Since K is forced to choose L (K<L) as its successor in its source tree, K is forced to send an LSU and other nodes will update their source trees.  Nodes like I and J will be forced to recompute their source trees and will include either (U,V) or (V,U) in their source trees.

5. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Possibility of Permanent Routing Loops (Case 2)  The rule in Case 1 may not be sufficient to break all loops and hence we need the rule in Case 2.  Case 2: Router i sends a source-tree update after processing an input event if : – The distance from the new successor n to a destination j is longer than the distance from the previous successor m to the same destination j. i j m n

6. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Possibility of Routing Loops (Case 2) a b c d e fa b c d e fa b c d e f f a eb cd

7. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Possibility of Routing Loops (Case 2) f a eb cd a b c d e f b>a a b c d e f c>b

8. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Possibility of Routing Loops (Case 2) f a eb cd a b c d e f (b,e,1) (e,d,1) (e,f,1) a b cd e f a b c e (b,e,infinity)

9. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Possibility of Routing Loops (Case 2) a b c e (b,e,infinity) a bc a b c  Nodes a,b and c realize that there is no path to nodes d,e and f

10. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Implementation of Cases 1 and 2  A router must remember a copy of its source tree that it last notified to its neighbours.  If the new source tree includes new neighbours, then the router must send its entire source tree as an update.  If the new source tree includes the same set of neighbours as the previous source tree, the router sends only the updates necessary to get the new source tree from the previous one.

11. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) STAR Protocol Ensures Loop-free Paths  Since the network is a finite graph, any propagation of an LSU message reaches every node within a finite time.  We will assume that changes in network topology is not so fast that flooding is the only alternative.  Under these assumptions, it is easy to show that STAR ensures loop-free paths when each LSU message is processed in the order they are received.

12. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) STAR Protocol Ensures Loop-free Paths  There are three cases when a loop may form : – When a new node has joined an existing source tree – When a router is forced to choose a new successor due to the higher cost of an existing path. – When there is a link failure and a router is forced to choose a new successor to maintain the connectivity of its source tree.

13. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) When a New Node Joins an Existing Source Tree  Suppose a loop forms due to a new node n.  However, a router sends an LSU message whenever it has a new neighbour.  At least one of n´s neighbours will generate an LSU message which will propagate through the network and other nodes will update their source trees.  Hence, each node will have a loop-free source tree within a finite time.

14. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) When a Router is Forced to Choose a New Successor  Suppose a router i chooses a new successor and a loop forms due to this.  There must be at least one node in this loop that has a successor with a higher address.  We have seen in Case 1 that this smallest node will generate an LSU message and the other nodes will update their source trees.

15. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Link Failure (when Case 2 Occurs)  Each router computes its source tree by running Dijkstra´s shortest path algorithm on its partial topology graph.  Assume that the previous source tree is ST(1) and the new source tree after the link failure is ST(2) for a router i.  Since the link failure is the only event in between the computations of ST(1) and ST(2), there must be at least one node d whose distance is higher in ST(2) from i compared to ST(1).

16. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Link Failure (when Case 2 Occurs)  This is due to the fact that Dijkstra´s shortest path algorithm ensures shortest paths to each destination.  Since there is at least one destination with a higher distance, i will generate an LSU message (as we have seen in Case 2).  Other nodes will recompute their source trees due to this LSU message and they can recompute their loop-free source trees.

17. Mobile and Wireless Computing Institute for Computer Science, University of Freiburg Western Australian Interactive Virtual Environments Centre (IVEC) Performance of STAR  STAR outperforms both proactive protocols like DSDV and on-demand protocols like DSR in terms of lower number of overhead packets and higher percentage of packets delivered.  This is due to the fact that STAR has lower latency in finding routes compared to on- demand protcols and STAR need not send periodic update messages like proactive protocols.