Packet-Network Resilience Calculation Audit
Packet-Network Resilience Calculation Audit
Ada checks path-diversity reliability, packet size, and the exponential scale claim
ADA · CALCULATION AUDIT
Packet-Network Resilience Calculation Audit
The chapter shows three independent 90%-reliable paths deliver 99.9% of the time — a 9.9-point gain — and compares an ARPANET packet of 1,008 bits (126 bytes) with a 1,500-byte Ethernet frame, nearly 12x larger. The history is really a set of engineering checks. This audit works packet-network resilience, from path diversity to byte ceilings.
Companion to the chapter History of the Internet: From ARPANET to IoT — every number here comes from that chapter.
Packet switching became convincing because the arithmetic matched the physics of real links: independent paths reduce shared failure risk, while finite packet and buffer sizes force every network to account for bytes.
See the relationship before changing it
The figure reads from left to right. The blue card is independent paths. The middle card applies this page's rule. The green card is delivery probability. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only independent paths, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 3 paths.
- 2
Name the relationship. delivery = (1 - (1 - 0.90)^paths) x 100
- 3
Substitute with units. (1 - 0.10^3) x 100 = 99.9%
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change independent paths
Try Predict the direction of delivery = (1 - (1 - 0.90)^paths) x 100. Test another independent paths, then compare delivery probability.
Observe Independent paths reduce the chance that every available route fails at the same time. Reset independent paths to 3 and compare delivery probability.
Explain Independent paths reduce the chance that every available route fails at the same time.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Redundant paths turn failure probability into a power term
The chapter's example gives three independent paths, each with 90% reliability. One path fails with probability 1 - 0.90 = 0.10. All three fail only if the failures happen together:
The absolute improvement over one 90% path is 99.9 - 90.0 = 9.9 percentage points. The relative improvement is (0.999 / 0.900 - 1) x 100 = 11.0%.
2. Packet size is a physical resource budget
The chapter notes that an ARPANET packet carried 1,008 bits, while a standard Ethernet frame carries 1,500 bytes. Converting the older packet to bytes makes the comparison audit-ready:
| Claim | Arithmetic | Audited result |
| ARPANET packet size | 1,008 bits / 8 bits per byte | 126 bytes |
| Ethernet versus ARPANET packet payload scale | 1,500 / 126 = 11.904... | Rounds to 11.9x, so "nearly 12x" checks out |
| 12 KB IMP memory scale | 12 x 1024 / 126 = 97.523... if KB is read in the usual memory sense | About 97.5 packet-sized chunks before real buffers and code overhead |
3. The scale claim is exponential notation, not a slogan
A throughput increase of 109 means nine factors of ten:
What the audit buys you: the history is not only a timeline. It is a set of engineering checks: path diversity changes delivery probability, byte ceilings shape packet design, and layered protocols survived because those budgets could scale without changing the core idea.
The displayed reliability assumes independent paths; shared conduits, correlated outages, routing convergence, congestion, headers, buffers, and retransmissions remain outside this derivation.
Work the audit first, then check the displayed derivation.
Every number above is taken from this chapter's own worked example and re-derived step by step.