Yes — the Tesla P4 8GB (8 GB GDDR5) can run Llama-3.1-8B-Instruct. At Q4 with the default 8K context it needs ≈ 7.0 GB VRAM (weights 4.4 GB + KV cache 1.6 GB + 1 GB runtime overhead), which fits within 8 GB. Decode at Q4/8K: ≈ 15.3 tok/s (estimated, batch 1). FP16 needs ≈ 18.6 GB — does not fit on this card. Estimates come from memory-bandwidth math; rows tagged measured override estimates. Relative ranking is more reliable than absolute tok/s. Methodology. Buy Tesla P4 8GB on Amazon →
Fit & speed by quant and context
Quant
Context
VRAM needed
Fits?
tok/s (decode)
Q4
4K
6.2 GB
Yes
15.3±est.
Q4
8K default
7.0 GB
Yes
15.3±est.
Q4
32K
11.8 GB
No
19.9±est.
FP16
4K
17.8 GB
No
2.4±est.
FP16
8K default
18.6 GB
No
2.2±est.
FP16
32K
23.4 GB
No
1.4±est.
Fits = weights + KV(ctx) + 1 GB overhead ≤ 95% of VRAM. Measured anchors are context-agnostic; the fit verdict is recomputed per context. A missing tok/s means the model is far beyond this card (offload-only territory).