Incoprea Theory
Volume IX · 44

Theory 37/Society, Computation & Engineering /Software reliability

Depth Beats Count

Complexity is counted in services. The failure probability multiplies along the path.

The claim

System availability is set by the depth of the dependency chain rather than by the number of services, so a shallow system with many services can be more reliable than a deep one with few.

01The evidence

Outages propagate along call chains, and the propagation length correlates with the depth of the dependency graph rather than with service count.

02The tension

Architecture reviews count services, which predicts reliability from the number of components and misses the serial multiplication along the deepest path.

03The mechanism

A request must traverse a chain. If each hop has availability a, the chain has availability a to the depth, so depth dominates.

That makes the deepest path the determinant, and predicts downtime should track depth rather than count.

04What this is not

Component-count reliability

Count models multiply independent failures. This multiplies along the path, which is the serial case.

05Predictions

  • P1Downtime should track dependency depth.
  • P2Shallow many-service systems should outperform deep few-service ones.
  • P3Reducing depth should improve availability.

06Refutation

Downtime tracking service count at controlled depth would favour count models.

07What it changes

It would change architecture review criteria.