Estimate the average and peak QPS behind a million support tickets a month

Work it in three small steps. First, count the calls, not the tickets. Each ticket triggers 2 LLM calls, so the month produces 1,296,000 x 2 = 2,592,000 calls. Second, count the seconds. A 30 day month has 30 x 86,400 = 2,592,000 seconds. The numbers match on purpose: 2,592,000 calls over 2,592,000 seconds is exactly **1 call per second** on average. Third, apply the peak factor. Support traffic clusters in business hours, and the problem says peaks run 10x the average, so you plan for 10 calls per second. The takeaway is bigger than the arithmetic. A million-plus tickets a month sounds like a scaling crisis, but it averages out to one call per second, which any provider handles easily. The numbers that actually matter are the peak rate, because that is what you provision and rate-limit for, and later the tokens per second behind each call, because providers meter tokens, not just requests.

Convert the monthly number to a per-second rate, then plan for the peak. $$\lambda_{avg} = \frac{1{,}296{,}000 \times 2}{30 \times 86{,}400} = \frac{2{,}592{,}000}{2{,}592{,}000} = 1 \text{ call/s}$$ With the stated 10x peak to average ratio, the capacity planning number is **10 QPS**, not 1. Averages describe billing; peaks describe the infrastructure you must stand up, the rate limits you must negotiate, and the queue depth you must absorb. Two habits make this estimate reliable under interview pressure. Count the right unit first: tickets are not calls, and here the 2x multiplier doubles the answer. And keep the seconds-in-a-month constant handy: 86,400 seconds a day, about 2.6 million a month. Monthly volumes divided by 2.6 million turn intimidating totals into honest per-second rates almost instantly. The natural follow-up, and worth volunteering, is that QPS alone understates load for LLM systems. Ten calls per second at 3,000 input and 500 output tokens each is 30,000 prefill plus 5,000 decode tokens per second, and provider rate limits are written in tokens per minute as much as requests per minute. The QPS estimate is step one of the capacity chain, not the conclusion.