 Hello and welcome to a lecture on optimality principle learning outcomes by the end of this session student will be able to illustrate optimality principle and will be able to illustrate intra domain and inter domain routing before we proceed to the content you may pause here the video and answer this question the question is what are the desired properties of a routing algorithm the desired properties of routing algorithm are correctness and simplicity robustness and stability fairness and optimality correctness and simplicity it should be correct and it should be simple so that it could be easily understood and rectified if any problems are there it should be robust because so many devices constitute the network and once if any of the device fail then it should be robust to that failure it should be stable it should be fair enough to provide the chances for transmission to each and every router or the device of the network today we will focus on optimality principle before proceeding to the optimality principle we should first know what is the metric or cost associated with the network we know network consists of so many routers whenever router receives a packet from one of its input it should know to which of the network it should be forwarded or it should be passed on or through which network it should be forwarded to the destination network the forwarding or the passing on decision is based on the optimization which of the available path is optimal path for the packet to reach the destination ok. So, this decision is based on the optimization the first approach is to assign a cost for passing through a particular network ok we call this cost as a metric metric something high cost can be believed as a something bad and a low cost metric is something believed to be good ok. Let us say what are the metrics suppose we are using a throughput as our metric then high throughput means low cost and low throughput means high cost a throughput is nothing but the amount of data transferred from network or from source to destination between a specified time interval if we are using delay as our metric then low delay is a low cost which is good and high delay is a high cost which is considered as a bad. So, other than throughput and delay bandwidth then queuing delay transmission rate and the communication cost in terms of money associated through the network are some of the metrics. So, we will proceed to the optimality principle ok. We go in the next sessions into specific algorithms it will be helpful for us to note down one statement which is a general statement about optimal routes how to decide the optimal route ok. We should not bother about the network topology or the traffic through the network going on ok. This kind of a general statement is known as optimality principle. What is that statement? If router j is on a optimal path from router i to k then the optimal path from j to the router k also falls along the same route if we try to understand this suppose this is your router i this is your router j and this is your router k. The statement or the optimality principle is that if the router j if the router j is on a optimal path between router i and router k then the optimal path between j and k also falls along the same route. Suppose we are calling this segment between i and j router as r 1 and we are calling j to k section as r 2 then r 1 r 2 r 2 as it is a optimal route for i to k. So, j to k which is also optimal path falls along the same this is generalised optimality principle ok. If you say there is another router j through which you can reach the router k and if it is if this j to k section is j to k section r route is better than an r 2 then the optimal path from i to j could have been r 1 r 3 ok. So, this statement is contradict to the optimality principle. So, r 1 r 2 is the optimal path from i to j and on this path the router j falls. So, it is also optimal path for between j to k. As a result of optimality principle the set of optimal routes from all the sources to a given destination form a tree which is rooted at the destination. Such tree which is rooted at the destination is called as sink tree. Here we have a general subnet this is our general subnet where number of routers are interconnected to form a internal. Here it shows a sink tree for router B means which is rooted at router B as our destination is B ok. Here the thing to note is the sink tree is not necessarily to be unique. Other trees may also exist with different path lengths. As this is a tree it will does not have any of the loops. Goal of the all routing algorithms is to realize and use these sink trees for all the routers. The sink trees are indeed a tree so it does not contain any loops. So, each packet will be delivered within a finite and limited number of hopes means the packet will not keep on circulating through the network for indefinite time. But practically it is not the case it is not that much simple ok. At any time any link or the router can go down and come back up during the operations. So, the different routers may have different ideas about the current topologies. Routing protocols routing protocols are created to fulfill the demands of dynamic routing tables. The dynamic routing tables are used by dynamic routing protocols and these dynamic routing protocols are based on the adaptive routing algorithms. So, these protocols are used to update the routing tables. What is the routing protocol? Routing protocol is nothing but a blend of rules and procedures that allows the routers in the network inform each other about the changes happening in the network. That change may be about the status of the link whether it is down or up or whether it may be or it could be a status of a neighbor router which may be dead or which may be alive. Routing protocols not only allows the router to share whatever they know about the network or about their neighbors, but also it provides the procedures for combining the information received from other routers as well. Routing protocol can be categorized in the two forms. First is interior protocol and other is exterior protocol. An interior routing protocol handles intra-domain routing and exterior routing protocol handles inter-domain routing. Let us see what is intra-domain and inter-domain routing. We know the internet is made up of large number of networks, small, small networks, routed together as well as number of routers. So, a single routing protocol cannot handle the type of routing task of updating the routing tables for all the routers. So, an internet is divided into autonomous systems. What is autonomous system? Autonomous system is nothing but a group of networks and routers which falls under the authority of a single administration. This figure number 2 shows the two autonomous system. This autonomous system is numbered 101 while this is numbered as 110. Here we have two autonomous system. Autonomous system is nothing but a group of routers or network which falls under a single authority. The routing inside the routing inside this autonomous system is referred as intra-domain routing and the routing between these two autonomous system is referred as inter-domain routing. An autonomous system can have multiple intra-domain routing protocols to update their routing tables. The intra-domain routing protocols are RIP which is routing information protocol, OSPF, and short test path first and others. While the routing between the two autonomous system is called as inter-domain routing which is handled by exterior routing protocols. One of the example is BGP, border gateway protocol which is responsible for routing between two autonomous systems. These are the references. Thank you.