Let's make the model explicit before answering. Suppose it has 32 attention layers, eight KV heads per layer, head dimension 128, and bf16 K and V. No sliding window, compression, prefix sharing or tensor-parallel sharding. A cached token costs 2 × 32 × 8 × 128 × 2 = 131,072 bytes, or 128 KiB. The first 2 is for K and V. The last 2 is bytes per bf16 element. At 32,768 cached tokens, one conversation consumes 4 GiB. Six consume exactly 24 GiB. vLLM's cache implementation and configuration account for KV shapes and dtype, while its PagedAttention design explains block-based allocation.

So the practical admission answer is no. The 24 GiB is a KV budget, not a promise that every byte is available for six fully occupied sequences plus their future output. If each chat generates 256 more tokens, that adds 32 MiB per chat, or 192 MiB across six, even before block rounding and allocator metadata. If “32K conversation” already includes a hard maximum total length and generation is forbidden beyond it, the six static caches fit the ideal arithmetic. That is not the interactive workload the question describes.

For production I would reserve decode growth and a block-allocation margin, set admission based on currently reserved and projected tokens, and specify what happens when output exceeds the estimate. Prefix reuse may reduce physical KV consumption when requests truly share a compatible prefix. Tensor parallelism may distribute KV heads differently. Other architectures, mixed layer types and KV quantization change the formula. Do the derivation from the actual checkpoint and serving backend rather than applying this number to every GQA model.

An interviewer may ask whether lowering max_model_len alone fixes it. It limits a worst-case sequence but does not tell you how many active sequences and output tokens share the pool. Show the current occupancy, free blocks and expected growth, then decide whether to admit, queue or preempt. What is actually in the KV cache, and why does it fill up? explains what the KV cache stores. KV memory is allocated in blocks. Why can short requests waste so much of it? covers waste inside allocated blocks. This is the arithmetic and admission decision an engineer should be able to do on a whiteboard.