As you can see traffic is bi-directional. You have made changes on the Mumbai end to route outbound Internet traffic via Chennai to USA. I don't know if you are running BGP with the ISP in Chennai. Are you using the same ISP at both Chennai and Mumbai and if you are that improves your chances of influencing traffic coming in. You may want to work the ISP(s) to see if there is anyway they can influence traffic from the USA into your network prefer the Chennai link.
If this is the situation in your Office Network, say all Users are accessing the Internet after getting validated at Proxy at US.
Normally, from MUMBAI to US the static will be pointed to Proxy in US to reach directly for HTTP Traffic Validation. In this case, for the failover you can write a static with higher metric for the Proxy IP Segments in US, pointing the traffic to Chennai Internet Router. Since the Chennai Internet Router has direct connectivity to the US and it must have route available for the PROXY Server.
So, for the User's in MUMBAI if the MUM-US fails the traffic will flow via MUM-CHN and to reach the Proxy for having the Internet Access it will go via CHN-US
We don't have all the information to make the best recommendation to address your routing situation.
Let's say you want all traffic from US to Mumbai (10.8.1.0) to be routed via Chennai then configure a static route in the US router, that terminates the p-t-p links, to point to the router in Chennai as it's next hop. Instead, if you want all traffic between US and India routed via Mumbai with the exception of communication between the 10.3.0.0/16 and 10.8.1.0/24 networks to use Chennai link then you may have to setup policy routing in the US router. PBR provides the flexibility of routing traffic based on several different criteria unlike normal routing which goes by destination address.
All traffic between the 10 networks needs to be on the primary link.
Users in 10.8.1.0 subnet are accessing the internet from the customer network, we dont have any proxy address, just the default route,the routing to internet is done within the 10.3 network not managed by us. Our demarcation is the US router which is the gateway for 10.3 network to our network.
All traffic the is destined to the internet and is coming back from the internet needs to be on the secondary link.
I agree with you idea of using PBR, not sure how I'd filter the internet traffic though.
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