When Two Hops Beat One

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

ADA · CALCULATION AUDIT

When Two Hops Beat One

A three-node chain, S → R → GW, loses relay R, and HWMP has to decide whether to heal onto a weaker direct link or find another route. The chapter’s own worked example pits two solid 130 Mbit/s hops against one weak 6 Mbit/s direct link, under its own rule that each extra same-channel hop roughly halves throughput. This audit asks the question that comparison invites: how much longer does the weak direct link actually hold the channel than the two clean hops, and does that gap explain why airtime routing prefers two hops over one?

Companion to the chapter Lab: Wi-Fi Mesh and Self-Healing — every number here comes from that chapter.

Ada: The worked example says HWMP’s airtime metric prefers two solid 130 Mbit/s hops over one weak 6 Mbit/s direct link, even though hop-counting picks the direct link. Let me put numbers on “airtime” to show the gap is not close.

• Sending a fixed frame of L bits takes L / rate of channel time (L is illustrative; it cancels below). The direct one-hop path costs L / 6.
• The two-hop relay path transmits the same frame once per link: L / 130 + L / 130 = 2L / 130 = L / 65.
• Dividing, the weak direct link occupies the channel (L / 6) / (L / 65) = 65 / 6 ~= 10.8x longer than the two clean hops - and that is before its retries, which only widen the gap.

That factor of about 11 is why a shared radio routes for least airtime, not fewest hops. The same store-and-forward accounting explains the chapter’s “each extra same-channel hop roughly halves throughput” rule: one delivery now occupies the channel for two transmissions instead of one. Keeping hop depth shallow and links fast is how self-healing lands on a path that is still fast, not merely still connected.

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