Can anyone elaborate about Proportional fair scheduler for LTE?

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I want to know formulated explanation..Basic is clear for me. How to implement it for LTE..any document and white paper links are welcomed. I am working on C Language.

posted Nov 19, 2013
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Each carrier in LTE is 15khz so in a calculation i found that useful symbol time = 1/15khz = 66.6 mircosec

wrt to this
Each symbol duration is calculated like this
Normal Cyclic Prefix length = 4.69 microsec --- so each symbol in this = 66.6 + 4.69 = 71.29 microsec
Extended Cyclic Prefix length = 16.67 microsec ----so each symbol in this = 66.6 + 16.67 = 83.27 microsec

So Normal cyclic prefix Slot (7 symbols) duration = 71.29 * 7 = 499.03 microsec(0.49903 millis)
and Extended cyclic prefix Slot (6 symbols) duration = 83.27 * 6 = 499.63 microsec (0.49963 millis)

But slot duration is fixed as 0.5 ms ...

So does this slight difference creates any problem ???
How real time it works ???