01 deck
Look at the deck
Every trip needs room. The deck is the GPU's memory, and other passengers may already be sitting on it.
p = 1 - free / total
granted07@kolkata:~/research$ cat gamma
How long would you wait for a fuller ferry?
A GPU answers questions in groups. Bigger groups are cheaper per person, but everyone waits for the boat to fill. I am teaching it to decide, live.
scroll
02 dock
Look at the dock
A long line means every extra minute of waiting costs more than it did a moment ago.
ρ = arrivals / what one trip can carry
03 crowd
Look at the crowd
Fifty people trickling in is easy. Fifty arriving together is a different day.
V = (cₐ² + cₛ²) / (1 + cₛ²)
04 price
Put a price on space
One number, γ: how many milliseconds of waiting is one megabyte of deck worth right now? A tight deck makes space dear. A long line or a wild crowd makes it cheaper. Then smooth it, so the price never flickers.
γ = base · (1 + (G-1)·s(p)) / (1 + κ·V·ρ²)
05 rail
Keep the rail
Whatever the price says, a hard limit stops the ferry from sinking. The price is a preference. The rail is a promise.
B_eff = min(B, ⌊(free - reserve - m₀) / k⌋)
06 plan
Ask the planner
BatOpt, the published method this builds on, picks the trip size with the smallest waiting plus price times space.
b* = argmin E(W_b) + γ·(k·b + m₀)
07 again
Then look again
The size it chose becomes the starting point for the next look. Round and round.
b → next cycle
still open
?The starting numbers are educated guesses. Finding the right ones is the real work.
?The line may be counted twice. I am testing whether that part earns its place.
?The crowd fix is a patch, not a theory.
?All of it runs in a simulator first, on timings measured from a real GPU.