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IV · Queueing theory

M/M/1 queue

What it is

Single server, Poisson arrivals (rate λ), exponential service (rate μ). Average wait W = 1/(μ−λ).

Where it lives

Initial latency models for any single-bottleneck system. The clean baseline before reality intrudes.

The key insight

The (μ−λ) denominator: as utilisation approaches 1, wait time → ∞. You cannot run a server at 99% utilisation.

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Across the foundations
V Memory hierarchy Physics & hardware limits V Landauer principle Physics & hardware limits V Amdahl's law Physics & hardware limits VI One-way functions Cryptographic foundations VI Discrete log Cryptographic foundations VI Birthday attack Cryptographic foundations VI AEAD Cryptographic foundations VII P vs NP Computational complexity
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