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Equation 9 · Part 2 · Measuring Tool Protocols and the Model Context Protocol: Evidence, Benchmarks, and Uncertainty

Symbol n

T(n)≈T0+n tˉ.T(n) \approx T_0 + n\,\bar{t}.
nn

What this part means

n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

A simple linear model makes the assumption underneath that spread explicit. If a system prompt costs T0T_0 tokens before any tools are added, and each of n tools costs on average tˉ\bar{t} tokens to describe, total schema overhead is approximately T(n)≈T0+n tˉT(n) \approx T_0 + n\,\bar{t}. Under a fixed context budget B , the largest catalogue that fits is roughly nmax⁡n_{\max} ≈\approx (B - T0T_0)/tˉ\bar{t} . The model is a reasonable first approximation, and it is also the…

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