Capacity planning

Serving capacity is priced by the node, not the request: cards rent by the hour and bill whether busy or idle, so the job is to size the fleet to the peak minute you intend to survive. The inputs are measured, not guessed: the peak arrival rate, how long a request holds its seat from admission to completion, and how many concurrent requests one card can grant given its KV cache budget. The seats, not the tokens, decide the node count.

The arithmetic is one multiplication and one ceiling division. Arrival rate times time-in-system gives the resident request count at the peak - which is a queueing identity, not a coincidence, and it is why the same formula warns of saturation from the other direction when queue depth is measured instead. Divide the resident count by seats per card, round up to whole cards, and decide how much headroom to rent for a card loss or an arrival spike.

What separates a good plan from a spreadsheet is honesty about the distributions behind the averages. Peak is not the mean - launches land in bursts, agent traffic multiplies tokens per request, and a pool sized to the average bills cheaply until the one hour a month that pays the whole invoice. So the plan states its percentile: cover the 99th-percentile minute and accept the idle rent the other 98.9 percent of minutes pay for, or design shedding around what you chose not to cover.

A tier sees a peak of 10 requests per second, each request holds its seat for 2 seconds end to end, and each replica grants 10 concurrent seats. One card rents at $2.50 per hour.

1. Resident demand at the peak: arrival rate x time in system = 10 x 2 = 20 concurrent requests.
2. Replicas: 20 / 10 = 2, plus one spare for a card loss, so the run set is 3 cards.
3. Bill: 3 x $2.50 = $7.50 per hour, and $7.50 x 24 x 30 = $5,400 a month for the standing fleet.

Peak arrivals x sojourn time fixes demand at 20 seats, which is 2 replicas plus a spare, $5,400 a month - capacity is arithmetic until the arrival distribution is a judgment call.

Where this shows up

• Buying the FleetThe third serving job is the balance sheet: the product found users, the token demand no longer fits on a demo pod, and the interview question becomes procurement. Do you buy the fleet, rent it month to month, or route the overflow through a frontier API's meter? The model is one month. Demand is stated in terabytes of tokens (10T a month is a serious product, 1000T is frontier traffic), a month is 730 hours, and each card contributes an aggregate tokens/sec rate a well-fed, batched steady state sustains: an H100 carries about 10,000 tokens/sec on an 8B chat and 700 on a 70B premium, a B200 is 2.4x either, and a used A100 is 0.45x an H100. Three dollar lines then price the month. Owned cards bill their card-month no matter what flows - about $2,100 to $2,900 for the modern chips once the capex is amortized over 36 months and power, colo, network, and staff are added - rented cards bill the cloud's roughly 1.35x premium on the same floor, and the API bills per token at retail: $0.20 per 1M for the 8B chat, $2.50 for the 70B premium. Notice what that ordering says: ownership beats renting on the per-token rate everywhere, because the cloud premium is the margin it takes for owning. So the question is never "own or rent on rate" - it is utilization. An owned GPU idling is a mortgage payment, and the idle check lets at most 15% of owned capacity sit unused; sizing the fleet to a story about growth instead of the demand curve is how a $441M bet runs 71% idle. The margin check says self-hosting must beat the API by a real quarter - blended cost at most 75% of the API's price - because owning takes financing risk a rental does not: a failed chip generation or a slower model year erases a thin saving. The overflow check caps the API's share at 10% of needed tokens, because the API is metered per token at retail while rented cards bill wholesale: at sustained volumes, 40% of a big month's shortfall bills more than the whole rented cloud would. The sim's three stories are the used-chip bargain that was cheap per card and expensive per token, the shiny chip bet that bought for a demand curve that had not arrived, and the API tax where the overflow meant to catch the spike swallowed the month. The three challenges below work the model: the tokens a fleet carries, the whole rented cards that fill the shortfall, and the dollars the API meter bills on its share.
• Fleet Efficiency & EvictionWhen a serving pool grows past a handful of cards, someone has to judge the cards, and that job is a real interview subject: a senior inference-gateway role lists it as fleet-efficiency work, autoscaling and scoring a rented fleet, evicting underperformers, all aimed at peak tokens per dollar. The model in this topic is one month of one rented pool. Every card in the pool is the same class, but not the same card: each draws a quality lottery ticket at boot, a true serving rate for the rated number, and rides silent dips, rate blips that cost part of the window while they last. The autoscaler never sees the truth. It sees a measured score read through a measurement window, and the window is a lever: over one hour a card can look 25% better or worse than it is, over a day 5%, over a week 2%. The month's bill has three parts: the cards the run set keeps warm bill their rent in full, the cards the score evicts bill 15% of a node-month on the way out (a churned card holds reserved capacity while it drains), and the cards outside the run set never bill at all. Three checks judge the month, and the interview version of this topic is knowing which failure each check can see. The capacity check reads the delivered tokens against demand, because no eviction policy repairs a rate shortage; the convergence check reads the real bill against the ideal operator's bill, the perfect selection with no churn fees sized to the demand shape, because that is what an autoscaler is actually judged on; and the eviction check counts wrong evictions, the cards whose true rate sat at or above the fleet median when the score threw them out, because a wrong eviction is the one failure that refunds nothing. The three presets are the month's three verdicts, and all three pass at least one check, which is why each is dangerous as an incident report: the golden idler bills $69,940 keeping 26 flagship cards warm for a 60,000 tok/s average and burns $44,348 of it on capacity that moved no tokens, yet shows zero unmet demand and zero wrong evictions; the noise evictor scores through the hour window and evicts 12 of 32 cards on a 25% error, 4 of them healthy, 33% wrong; the bargain shortfall bills a tempting $28,840 and covers only 61,015 of 90,000 tok/s, a 32% shortage the bill never could buy back. The fixes carry verified numbers too: the idler on steady mode bills $25,740 for the same demand and converges at 90.9%; the evictor moving to the day window at a 10% eviction share converges at 97.9% with no wrong evictions, and the shortfall swap to flagships covers 90,000 tok/s for $35,360 at 95.6% convergence. The three challenges below work the arithmetic the autoscaler acts on: the tokens-per-dollar score of one card, the whole-card greedy that sizes a run set, and the eviction policy that decides who leaves.
• Design ChatGPT: Tiers & Rate LimitsDesign ChatGPT is the most-cited systems design question at AI companies, and it is really one question: when everyone arrives at once, who gets served, who waits, and who is told no, all without the paying tier ever noticing. The answer interviewers grade against has three parts. First, three pools: a small provisioned pool whose cards exist for one tier only, a larger shared pool where paid requests carry priority over free ones, and the queue itself, which lives in card memory, not in a message broker. Second, a token-bucket rate limiter at the gateway, held in Redis for atomicity under concurrent writers, that admits free arrivals at a chosen share of demand and reconciles the token count after each grant, so a burst of arrivals is answered instantly without consulting a GPU. Third, shedding: a request refused at the gateway with a 429 costs nothing; the same request admitted into a saturated pool holds an expensive seat and lengthens every wait behind it, which is why the tail wait punishes utilization non-linearly, and why an incident that removes 30% of capacity can turn a 97 millisecond paid wait into an 850 millisecond one. Interviewers test this because every knob in the design is a money or trust decision: renting burst capacity for a launch day, tightening the bucket over a jammed pool, or letting the free tier shed so the subscribers do not notice an outage. The three challenges below work the mechanics: the admit count a token bucket grants, the queue wait the utilization formula quotes, and the shed arithmetic that keeps the shared pool from jamming.

Related terms