Lord Shree Rama ruled his kingdom for 11000 years?

Question

How is it possible to rule a kingdom for so many years?

Or was it like his kingdom followed his dynasty for so many years?

Ravana lived more than Lord Shree Ram as per this link. How is this possible?

What I assume is Ram Rajya was there for 11000 years, he created such a robust living style that it was continued for 11000 years.

Answer 1

Yes.

http://www.valmikiramayan.net/utf8/baala/sarga1/balasans1.htm#Verse97

raamaraajyam upaasitvaa = Rama having served the kingdom dashavarSasahasraaNi = for ten thousand years; dashavarShashataani ca = and also for thousand years; brahmalokam gamiShyati = will go to the abode of Brahma.

"Having served the kingdom for ten thousand years and another one thousand years, i.e. for a total of eleven thousand years, Rama will go to the abode of Brahma... [1-1-97]

If you don't believe it is possible for humans to live this long, I empathize with you, so let us be really scientific for a moment.

Do you believe Rama existed ? Yes or No ?
If Yes, did you see him personally ? Yes or No ?
If No, then what is your basis/proof for the belief that he existed ?

We all know about Rama only through Valmiki muni's Ramayan.
If you believe Rama existed just because it is said so in Ramayan (meaning you have faith in the book Ramayan), then you should also believe Rama ruled for 11,000 years just because it is said so in Ramayan.
Similarly, if you reject the 11000-year life based on 'common sense' (you don't see anyone living for more than 100+ years nowadays), then you should also reject Rama's existence based on common sense (you don't see Rama nowadays).
If you neither accept nor reject the 11000 year-rule, then you should neither accept nor reject Rama's existence. All you can scientifically say is "I do not know enough about either claim to confirm or deny it".

Apply the same level of belief OR non-belief on an evidence. If you want to be scientific, you cannot accept one part of an evidence based simply on faith, and reject another part of an evidence based on 'common sense', which is subjective.

Answer 2

Figure of 11000 years, is likely a case of bad translation.
Following is the verse, which is not specified in the Qn:

दशवर्षसहस्राणि दशवर्षशतानि च । रामो राज्यमुपासित्वा ब्रह्मलोकं प्रयास्यति ।। [source]

In Sanskrit the word "सहस्र / Sahastra" is translated as "many/several" or "thousand". An accurate number like "thousand" is least likely to be the right word for such verses.
However, some people would strictly translate as following:

दशवर्षसहस्राणि = 10 thousand years
दशवर्षशतानि = 10 hundred years
Total = 10000 + 1000 = 11000 years!

This is not only irrational, but is also not sensible even from Ramayana perspective itself.

• Archaeology: As per recent survey, RAmAyana happened 7000 years back (i.e. killing of RAvana). In that sense, RAma must be living till now!
• RAmAyana: Just imagine if the ages were 10000 years, then would Kaikeyi make RAma to exile for just 14 years!? 14 years in 10000 years is as good as 51 days in 100 years. :-)

So here is more sensible interpretation:

After serving the kingdom for several decades and ten years after [the age of] hundred, RAma proceeded towards Brahmaloka (highest of all planes).

So RAma's life span can be 110+/- years. During that, he ruled the kingdom for few decades (5-7).

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Here is another misinterpretation of Dasaratha's age depicted as 60000 years!

षष्टिः वर्ष सहस्राणि जातस्य मम कौशिक ... [Valmiki Ramayana- Verse-10]
Sixty thousand years have passed from my birth, ...

In 60000 years, 14 years of exile of RAma would have felt like 9 days! It's unbelievable, that Dasharatha would have died in grief of just short span!
Now here is how one should interpret:

षष्टिः = 60 
सहस्र = many or several (not thousand)

[1] Six decades of years have passed from my birth, ...
[2] As many as Sixty years have passed from my birth, ...

Refer this post for some more information on the same topic.