Zipf's law

 Zipf’s Law says that the frequency of an item is inversely proportional to its rank in a frequency table.

Mathematically:

$$f(r) \propto \frac{1}{r^s}$$

• f(r) = frequency of the item ranked r

• s = Zipf exponent (a skewness factor, typically between 0.5 and 2)

• Higher s = more skewed distribution

Proven in Multiple Domains:

Zipf-like distributions have been empirically observed in:

• Web access logs

• Video-on-demand services

• CDN (Content Delivery Network) traffic

• Edge computing systems

• Cloud file sharing and storage platforms

Useful in Simulation and Modeling:

• Researchers and system designers use Zipf to simulate realistic user behaviors when testing caching algorithms, load balancing mechanisms, or data placement strategies.

 When Zipf Might Not Apply:

• In systems where access is uniformly random (e.g., randomized testing, early-stage services), Zipf might not be appropriate.

• If content popularity changes rapidly, additional models (e.g., dynamic Zipf, time-decay models, or Markov chains) may be more realistic.\

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