Consider a segment where only one router, RTA, is eligible to become a DR. When it first comes up,it will run the DR election process. Here is what happens as per the steps in section 9.4 of RFC2328 (the numbers correspond to the corresponding step numbers in section 9.4).
1. There is no current DR or BDR.
2. Since no other routers will have declared themselves BDR, RTA will consider itself the BDR for now.
3. Since no other routers will have declared themselves DR, RTA will assign the Designated Router to be the same as the newly elected Backup Designated Router, which happens to be itself. So at this point, RTA considers itself both a DR and a BDR.
4. At this point, since RTA is now newly both the DR and the BDR, it has to repeat steps 2 and 3.
2 - Repeat. This step says:"Only those routers on the list that have not declared themselves to be Designated Router are eligible to become Backup Designated Router". Since RTA considers itself to be the DR, it is no longer eligible to be the BDR as per the previous statement. Therefore, since there are no other DR-eligible routers on the segment, RTA will decide that the segment has no BDR>
3 - Repeat. RTA has to choose the DR from among those routers that have declared themselves DR. In this case, it's only RTA so it will now declare itself DR.
So here's what the repetition of steps 2 and 3 do.
- at the end of the first iteration, RTA considers itself both DR and BDR
- at the end of the second iteration, RTA considers itself just the DR and there is no BDR on the segment.
Step 4 make sure that the same router (i.e. RTA) does not consider itself both DR and BDR.
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