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Equation 1 · Part 5 · Building a Production-Grade MCP Server

=

tn=random ⁣(0, min⁡ ⁣(tmax⁡, tbase⋅2n)),t_n = \mathrm{random}\!\left(0,\ \min\!\left(t_{\max},\ t_{\mathrm{base}} \cdot 2^{n}\right)\right),
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Server-side deduplication only pays off if the retry that triggers it is well behaved, and naive retry timing defeats itself. If every failed client retries after exactly the same fixed delay, the retries arrive in synchronized waves and can overload a server that was only briefly struggling. AWS’s widely adopted answer is to randomise the delay rather than only grow it, and the simplest of the algorithms it documents, full jitter, is stated as tn=random ⁣(0, min⁡ ⁣(tmax⁡, tbase⋅2n))t_n = \mathrm{random}\!\left(0,\ \min\!\left(t_{\max},\ t_{\mathrm{base}} \cdot 2^{n}\right)\right). drawing the wait before attempt n uniformly between zero and a capped exponential ceiling, rather than sleeping for the ceiling itself [ 8 ] . The reasoning given is about contention, not just delay: without jitter, “N clients…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.