Equation 12 · The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol
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the fixed cost of operator instructions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Put the three costs together and a deployment question comes into focus: given a fixed context window, how many tools can actually be offered before something has to give? A simple ceiling model makes the trade-off explicit. Let C be the model’s usable context window, the fixed cost of operator instructions, and a reserved allowance for the user’s message and the model’s own answer. If every tool schema costs on average tokens and all of them are injected in full on every turn, the maximum number of tools a deployment can nominally offer before it must start pruning or retrieving is
Sources cited in the article section
- [1] Model Context Protocol Specification (2025-06-18) ↗
- [11] Efficient Memory Management for Large Language Model Serving with PagedAttention ↗
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