Hi Ashok,
I am afraid you are not entirely correct.
You are right that for E1 routes originated from other areas, the total cost is calculated as the cost from the particular router to the ABR (LSA-1 and LSA-2) plus the cost from the ABR to the ASBR (LSA-4) plus the cost of the redistributed route (LSA-5), while for E2 routes, its cost is directly taken from the LSA-5 and is not incremented in the OSPF domain. However, if two or more ASBRs advertise an E2 route with the same cost, OSPF tries to choose the path to the nearest ASBR, and to calculate that, you need to revert to the sum of the costs to reach the ABR (LSA-1 and LSA-2) plus the cost of reaching the ASBR (LSA-4). So even for E2 routes, metric information in LSA-4 is required even though it is not directly reflected in the E2 cost.
There is, however, a more profound need for the LSA-4. To explain, we first need to focus on a specific property of LSA-5. An LSA-5 is in fact the only LSA from the standard LSA set (types 1 through 5) that is flooded unmodified across all regular areas of an OSPF domain. Every LSA-5 is associated with the ASBR that originated it by the value of the Advertising Router ID in its header. This association is of utmost importance because if the Forwarding Address in an LSA-5 is zero (which, for the most cases, truly is) then the originating ASBR is to be used as the next hop for this particular external route. Therefore, every router processing such LSA-5 must know the location of the ASBR to be able to compute the shortest path to it, and through it, to the external route.
Now, in the area where the ASBR resides, every router immediately knows who the ASBR is because its LSA-1 is known to every router in the area. However, after the LSA-5 is flooded to another area, routers in that area have no clue - just by looking at the LSA-5's Advertising Router ID - who the ASBR is and how to reach it because its LSA-1 is known in the ASBR's own area only. In other words, in every other area, routers are unable to associate the LSA-5 with its orginating router because they do not know it and so they cannot compute the shortest path to it, and through it, to the external route.
This is where the LSA-4 comes in. An LSA-4 itself is originated by the ABR and it tells every router in the other area: "Hey, if you want to go to this particular ASBR, you can go through me and it will cost you this much." Now, every router in that other area knows that to reach the ASBR that originated the particular LSA-5, they first need to reach the particular ABR, and now the shortest path computation can be completed.
In graph theory terms, an LSA-4 is necessary in other areas to make the graph connected; otherwise, LSA-5 would constitute disconnected, unreachable components of the graph, thereby excluded from the shortest path calculation.
Best regards,
Peter
