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.
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 = 6.5xthe 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.