The Real Price of a Bigger Zone

The Real Price of a Bigger Zone

Ada re-derives this chapter’s own numbers step by step, at full precision

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calculation-audit
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Ada ADA · CALCULATION AUDIT

The Real Price of a Bigger Zone

On a 150-node campus mesh, ZRP’s zone radius is the tuning knob: moving from radius 2 to radius 3 spends an extra 106 MB/hour of periodic update traffic to eliminate about 844 reactive route discoveries an hour. Divide one by the other and the trade has an exact price: 126 KB per discovery removed. This audit rebuilds both overhead ledgers and asks whether that 126 KB exchange rate is worth paying, or just a bigger zone dressed up as an upgrade.

Companion to the chapter ZRP Hybrid Zone Routing — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is extra periodic traffic. The middle card applies this page's rule. The green card is cost per discovery removed. 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 extra periodic traffic, so the numeric fixture does not switch without explanation.

Extra periodic traffic changes cost per discovery removed An input card leads through the rule cost = extra MB/hour x 1,000 / 844 discoveries/hour to the cost per discovery removed result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. A larger proactive zone spends recurring bytes to avoid each reactive discovery.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 106 MB/hour.

  2. 2

    Name the relationship. cost = extra MB/hour x 1,000 / 844 discoveries/hour

  3. 3

    Substitute with units. 106 x 1,000 / 844 = 125.6 KB/discovery

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change extra periodic traffic

Try Predict the direction of cost = extra MB/hour x 1,000 / 844 discoveries/hour. Test another extra periodic traffic, then compare cost per discovery removed.

106 MB/hour
Chapter baseline
Cost per discovery removed

Observe A larger proactive zone spends recurring bytes to avoid each reactive discovery. Reset extra periodic traffic to 106 and compare cost per discovery removed.

Explain A larger proactive zone spends recurring bytes to avoid each reactive discovery.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only extra periodic traffic moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only extra periodic traffic. It is not a field prediction.

Ada: The campus example weighs zone radius 2 against radius 3 and ends on a single decisive number: 126 KB of extra control traffic per discovery the larger zone eliminates. That figure is what tells an engineer whether covering more of the building proactively is worth it, so it has to be exact. Let me rebuild both overhead ledgers for the 150-node network from the chapter’s own inputs (50 bytes/route entry, 240 updates/hour, 30 packets/hour/node, 1,800 bytes/discovery; decimal MB).

  • rho = 2 proactive: 24 routes x 50 B = 1,200 B; x 240/hr = 288 KB/node; x 150 = 43.2 MB/hr.
  • rho = 3 proactive: 84 routes x 50 B = 4,200 B; x 240/hr = 1,008 KB/node; x 150 = 151.2 MB/hr.
  • rho = 2 reactive: 150 x 30 x 0.4375 = 1,968.75 discoveries/hr; x 1,800 B = 3.54 MB/hr.
  • rho = 3 reactive: 150 x 30 x 0.25 = 1,125 discoveries/hr; x 1,800 B = 2.025 MB/hr.
  • Totals: rho 2 = 43.2 + 3.54 = 46.74 MB/hr; rho 3 = 151.2 + 2.025 = 153.225 MB/hr.
  • Extra overhead: 153.225 - 46.744 = 106.481 MB/hr.
  • Discoveries eliminated: 1,968.75 - 1,125 = 843.75/hr.
  • Cost per eliminated discovery: 106.481 MB / 843.75 = 0.1262 MB = 126.2 KB — matching the chapter’s 126 KB.

The arithmetic confirms the trade and names what the number means: moving from rho 2 to rho 3 spends an extra 106 MB/hour of periodic update traffic to save 844 reactive discoveries, and 126 KB is the exchange rate between them. Whether that price is worth paying depends on how latency-sensitive the traffic is — the ledger turns the ZRP tuning decision into an explicit purchase rather than a default.

Every number above is taken from the chapter’s own material and re-derived step by step.

TryRebuild proactive and reactive overhead for zone radii 2 and 3.
ObserveRadius 3 spends 106.481 MB/hour extra to remove 843.75 discoveries/hour.
ExplainThe exchange rate is 126.2 KB per eliminated discovery; workload value decides whether it is worthwhile.
Technical boundaries. The audit assumes fixed route counts, update frequency, discovery probability, discovery bytes, and decimal units. It does not model topology churn, packet loss, bordercast overlap, contention, route quality, memory limits, energy, or latency saved per discovery.
Audit result

The 126.2 KB exchange rate is correct for the stated fixture; it is not a universal optimal zone radius.