2002 Silverado 2500HD Transmission Problem

Hello all... first post with a technical question for all the experts among you... My 2002 2500HD 6.0 has an intermittent problem with the transmission that is very odd. Sometimes, when you are in drive, and you are not moving (either just putting it in drive or come to a stop in drive) the transmission lugs like it is shifting to a higher gear. The RPM's drop, and as long as you hold on the brakes, it lugs a while, the comes out of it, and starts to idle normally. If you take your foot off the brake when it's lugging, The truck will take off, like it's in a higher ratio gear. If you tap the gas, it will come out of it, and act normal. It does it in reverse as well... Some days it will do it a lot, and some days it won't do it at all. I'm not positive it's in the transmission, but it's related I guess. I thought it might be a vaccum issue or something? Anyone with help on this I would really appreciate it. Thanks!

Is this an Allison, or 4l80e?

I know it's not the Allison... That was only offered with the Duramax or the big block gas burner at the time I bought it. I'm not sure of the number, I'm assuming you are right with the model number. On the window sticker it said "HD 4 speed automatic transmission" Thanks