When a Zone Radius Quietly Turns ZRP Into DSDV

When a Zone Radius Quietly Turns ZRP Into DSDV

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

ADA · CALCULATION AUDIT

When a Zone Radius Quietly Turns ZRP Into DSDV

A 15-node emergency-response mesh runs ZRP at zone radius 10 in a network only 8 hops across, burning 4200 control packets a minute and 850 KB of tables where radius 3 would need 650 and 180 KB — an 85% overhead reduction and 79% memory saving on paper. Those percentages read like a tuning win. This audit re-checks them and asks whether the real story is the savings, or that a radius of 10 past an 8-hop diameter has quietly turned the hybrid into pure DSDV.

Companion to the chapter Lab: Ad-Hoc Networks and Quiz — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is radius-3 control traffic. The middle card applies this page's rule. The green card is traffic reduction. 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 radius-3 control traffic, so the numeric fixture does not switch without explanation.

Walk the arrows. A smaller zone cuts control traffic because the oversized zone has become nearly proactive everywhere.

Derive the baseline in four named moves

1. 1

   Name the input. The chapter baseline is 650 packets/min.

2. 2

   Name the relationship. reduction = (1 - radius-3 traffic / 4,200) x 100

3. 3

   Substitute with units. (1 - 650 / 4,200) x 100 = 84.5%

4. 4

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

Predict, then change radius-3 control traffic

Try Predict the direction of reduction = (1 - radius-3 traffic / 4,200) x 100. Test another radius-3 control traffic, then compare traffic reduction.

Radius-3 control traffic

650 packets/min

Chapter baseline

Traffic reduction

Observe A smaller zone cuts control traffic because the oversized zone has become nearly proactive everywhere. Reset radius-3 control traffic to 650 and compare traffic reduction.

Explain A smaller zone cuts control traffic because the oversized zone has become nearly proactive everywhere.

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 radius-3 control traffic moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only radius-3 control traffic. It is not a field prediction.

Ada: The zone-radius scenario above compares rho = 10 against rho = 3 and quotes an “85% overhead reduction” and “79% memory savings.” Let me check those, then name the structural thing the numbers are pointing at.

The two reductions, from the scenario’s own figures:

• Overhead: (4200 - 650) / 4200 = 3550 / 4200 = 0.845 = 84.5%, reported as ~85%
• Memory: (850 - 180) / 850 = 670 / 850 = 0.788 = 78.8%, reported as ~79%
• As a ratio, the large zone costs 4200 / 650 = 6.5x the control traffic

Both check out. But the real finding is why rho = 10 is so expensive, and it is a comparison, not a division: the network diameter is 8 hops, and 10 > 8, so every node already sits inside the zone. When the zone swallows the whole network, the reactive half of ZRP — the bordercast discovery that justifies the hybrid — never fires, and the protocol degenerates into pure proactive DSDV, paying full table-maintenance cost for zero hybrid benefit.

The design meaning is that ZRP’s tuning knob has a hard cliff the overhead numbers only hint at: once the zone radius reaches the network diameter the hybrid collapses to its proactive extreme, so the radius must stay a fraction of the diameter — the scenario’s 30-50% coverage rule — or you are running DSDV while believing you configured a hybrid.

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

TryRecalculate control-traffic and memory savings for radius 3 versus radius 10.

ObserveThe savings are 84.5% and 78.8%, while radius 10 exceeds the 8-hop diameter.

ExplainThe key defect is structural: the oversized zone eliminates the reactive half of ZRP.

Technical boundaries. The audit uses one fixed topology diameter, packet count, and memory total. It does not model topology change, uneven node degree, bordercast cost, update loss, route quality, latency, energy, or alternative proactive protocols.

Audit result

Because 10 exceeds the 8-hop diameter, every node is intra-zone; the fixture has become fully proactive regardless of the percentage savings.