How long between the acceptance and proof correction of Elsevier? My paper has beed accepted by Elsevier's International Journal of Electronics and Communications (AEUE).

I want to know how long I should expect to wait until I receive the notice of online proof correction.
You can answer this question is to look at the date stamps sequences on some of the existing papers.  Many journals (including the one you have asked about), include all of the major dates in the publication process, e.g., "Received Date1, Accepted Date2, Available Online Date3," as well as the final date of publication.

Note that the "Available Online" and final date of publication may often be very different, but except in rare cases it is "Available Online" that you should care about because that is when people begin to be able to get your paper.  However, some journals do not do all of the final proof correction until closer to the date of publication, but essentially just have your preprint up online for quite some time!

Applying this analysis to this particular journal, one can find the following:


Acceptance to available online looks like 1-3 weeks
Final publication happens ~6 months later


So you will probably get contacted about the proof very quickly (if they follow the normal method of proofing before online availability), or not for several months (if they do late-binding proofing).