It seems that regions like Japan or Singapore travel the long way around the globe and go from US to EU and then reach destinations in Middle-East.
What is the best region? Do you have any first hand experience or statistics?
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I don't think it is possible for anyone to guarantee that a certain location will be better since amazon does not have a node in middle-east nor is it one of their priority locations.
I do not have any first hand experience, but in theory EU should be the best option for you. Though parts of east asia may be geographically closer, bandwidth routing in asia is generally very tough due to lack of peering and transit options. Related to that, bandwidth in asia is extremely expensive. So, even if you had a host in asia, you'll often see routes going all the way to USA then all the way back to the neighboring country. As such, routes like Asia -> US -> EU -> ME is not rare at all.
If latency is highly sensitive, you should try to get one actually in middle-east. Or you can seek getting a service in europe that's catered to having good connection to the middle-east.
Consider having a look at internet cables map to know how internet flow from one country to another. http://submarinecablemap.com/
The answer to your question vary depending on which country you are targeting. Dubai for example has direct connection to India so you should use EC2 server in India / Mumbai.
The other route is to go from Dubai down to Djiboti then up to Egypt, then to France then to UK then to Ireland. on the other hand if you are targeting Egypt then Ireland might be a better option in this case than Singapore.
Hope that helps
Now AWS provides service in the Middle East from Bahrain