The Second Node Buys Uptime, Not Capacity

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

ADA · CALCULATION AUDIT

The Second Node Buys Uptime, Not Capacity

This chapter’s smart building runs 4,000 devices and must hit 99.9% uptime — no more than about 8.76 hours of downtime a year. The chapter is blunt that a single broker handles the traffic easily, yet one node at a typical 99.5% uptime still misses that target, so the design pays for a second node. This audit checks the availability arithmetic to ask what that extra node actually buys, since it adds no capacity the building needs.

Companion to the chapter MQTT Production Operations — every number here comes from that chapter.

Ada: Step 2 already showed one broker handles this building’s load, yet the design still specifies two nodes. Let me audit the availability arithmetic that justifies the extra node, because it is the whole reason to pay for redundancy the throughput does not need.

First the target. A 99.9% SLA allows 0.001 x 365.25 x 24 = 0.001 x 8766 = 8.77 hours of downtime per year. A single node at a typical 99.5% uptime is down 0.005 x 8766 = 43.83 hours/year, failing the target by nearly 5x.

Now two independent nodes; the cluster is down only when both are:

• Cluster availability: 1 - (1 - 0.995)^2 = 1 - 0.005^2 = 1 - 0.000025 = 0.999975, i.e. 99.9975%
• Cluster downtime: 0.000025 x 8766 = 0.219 hours = 13.1 minutes/year

That is an improvement of 43.83 / 0.219 = 200x (equivalently 0.005 / 0.000025), and it clears the 8.77-hour budget with roughly a 40-fold margin. The point the numbers make is that the second node contributes no throughput the building requires, since Step 2 proved one node suffices, so its entire job is to convert a single point of failure into 200x less downtime. Redundancy here is bought for availability, and the per-device cost of that insurance is $175 / 4000 = $0.044/device/month.

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