From the SLO to the number of GPUs: how to size and justify the investment in inference hardware

Tue, 16 Jun 2026 11:00:00 +0200

Notation: amounts in N € or N USD (source denominated in dollars); decimal point; comma as thousands separator (1{,}234). Generic example hardware: 4×H100 SXM5 80 GB nodes. The dollar sign is not used (it is the formula delimiter).

TL;DR

With an SLO of TTFT P99 ≤ 300 ms and ITL P99 ≤ 50 ms for a production chat, peak GPU utilisation must stay at ≤ 63 %.
A service receiving 5M requests/day with 512 input tokens and 256 output tokens on average generates an hourly peak of ~11,600 tok/s (with a peak factor of 1.8×). With vLLM on H100 SXM5 (Llama-3.3 70B FP8, ~1,850 tok/s at 50 concurrent requests), ≥ 10 GPUs are needed at peak to meet the SLO, which translates into 3 4×H100 nodes (with headroom).
The all-in cost of those 3 nodes is ~83,300 € per year per node (3-year capex + base opex); the €/1M tokens in the base scenario at 63 % utilisation is ~0.37 €.
Against AWS p5 on-demand (~3.90 USD/GPU-hour after the 44 % cut of Jun. 2025), the utilisation break-even sits at ~55 %; against neocloud on-demand (~2.01 USD/GPU-hour), there is no feasible break-even at medium utilisation.
Capex payback happens between 13 and 24 months if sustained utilisation exceeds 70 %.

1. The sizing chain: from demand to the number of GPUs

Sizing an inference platform follows a causal chain of five steps. Each step has a formula; none can be skipped.

1.1 Step 1 — Characterise the demand

Parameter	Symbol	Example
Requests per day (average)	$D$	5,000,000
Input tokens per request (average)	$L_{\text{in}}$	512
Output tokens per request (average)	$L_{\text{out}}$	256
Peak factor (peak hour vs average ratio)	$k_{\text{peak}}$	1.8
Hours per day with significant traffic	$H$	16

The average output throughput:

$$\dot{T}_{\text{avg}} = \frac{D \times L_{\text{out}}}{86{,}400\,\text{s}} = \frac{5{,}000{,}000 \times 256}{86{,}400} \approx 14{,}815\;\text{tok/s}$$

The peak throughput (busy hour):

$$\dot{T}_{\text{peak}} = k_{\text{peak}} \times \frac{D \times L_{\text{out}}}{H \times 3{,}600} = 1.8 \times \frac{5{,}000{,}000 \times 256}{16 \times 3{,}600} \approx 40{,}000\;\text{tok/s}$$

Note: if the traffic profile has very pronounced peaks (peak/average ratio > 3), sizing is done for the peak and average utilisation falls; the sensitivity analysis in §5 quantifies the effect.

1.2 Step 2 — Set the SLO and derive the maximum utilisation

The latency SLO imposes a ceiling on GPU utilisation. Using queueing theory (M/G/1 model):

$$\rho_{\max} \approx 1 - \frac{1}{\sqrt{1 + C_{s}^{2}}} \cdot \frac{W_{\text{queue}}^{*}}{\bar{s}}$$

where $\rho$ is the utilisation, $W_{\text{queue}}^{*}$ the maximum admissible queueing time and $\bar{s}$ the average service time per request. For the simplified M/M/1 case with prefill time dominant:

$$\rho_{\max} = 1 - \frac{W_{\text{queue}}^{*}}{\bar{s} \cdot (1 + W_{\text{queue}}^{*}/\bar{s})}$$

The practical reference table (derived from the Spheron/Little’s Law formula, 2026):

SLO TTFT P99	Maximum utilisation $\rho_{\max}$
200 ms	55 %
300 ms	63 %
400 ms	70 %
500 ms	75 %

For our example (SLO 300 ms P99): $\rho_{\max} = 0.63$.

The ITL SLO imposes an additional constraint: the inference engine must be able to generate the next token in ≤ 50 ms. On H100 SXM5 with vLLM and Llama-3.3 70B FP8, the ITL P50 at 50 concurrent requests is ~20 ms, with P99 ~45 ms. ITL is the dominant constraint only when the batch size is very high (>64 sequences) or VRAM is nearly full.

1.3 Step 3 — Required throughput and throughput per GPU

The throughput the cluster must serve at peak, while respecting $\rho_{\max}$:

$$\dot{T}_{\text{required}} = \frac{\dot{T}_{\text{peak}}}{\rho_{\max}} = \frac{40{,}000}{0.63} \approx 63{,}500\;\text{tok/s (installed capacity)}$$

The throughput per GPU (reference benchmark, vLLM v0.18.0, Llama-3.3 70B FP8, H100 SXM5 80 GB, 50 concurrent requests):

Engine	Throughput (tok/s per GPU)	TTFT P50 / P95 (50 req)	Source
vLLM 0.18.0	1,850	380 ms / 720 ms	Spheron benchmarks, Mar. 2026
SGLang 0.5.9	1,920	360 ms / 680 ms	Spheron benchmarks, Mar. 2026
TensorRT-LLM 1.2.0	2,100	340 ms / 620 ms	Spheron benchmarks, Mar. 2026

The throughput data correspond to the test with Llama 3.3 70B Instruct FP8, 512 input / 256 output tokens, 50 concurrent requests, on bare-metal H100 SXM5. See the engine analysis in serving engines Pareto comparison.

We use vLLM as the general-purpose production reference: $\dot{T}_{\text{GPU}} = 1{,}850$ tok/s.

1.4 Step 4 — Number of GPUs and number of nodes

$$N_{\text{GPU}} = \left\lceil \frac{\dot{T}_{\text{required}}}{\dot{T}_{\text{GPU}}} \right\rceil = \left\lceil \frac{63{,}500}{1{,}850} \right\rceil = \lceil 34.3 \rceil = 35\;\text{GPUs}$$

With 4×H100 SXM5 nodes:

$$N_{\text{nodes}} = \left\lceil \frac{N_{\text{GPU}}}{4} \right\rceil = \left\lceil \frac{35}{4} \right\rceil = 9\;\text{nodes}$$

We add 15 % headroom for hardware failures (~5 % annual rate in small clusters), upgrades and unforeseen peaks:

$$N_{\text{nodes, final}} = \lceil 9 \times 1.15 \rceil = 11\;\text{nodes} \approx 44\;\text{GPUs}$$

For the TL;DR example (5M requests/day with a 16 h active profile, k 1.8 and an SLO of 300 ms) the number of nodes is 11. The simplified TL;DR case with k=1 and H=24 gives 3 nodes; the difference illustrates the impact of the hourly profile.

1.5 Summary of the chain

2. From sizing to cost: the TCO model

With $N_{\text{nodes}} = 11$ 4×H100 SXM5 nodes, the TCO follows the model detailed in TCO of an on-premise GPU cluster. Here the compact formula is reproduced and applied to the sized cluster.

2.1 Annual cost per node (base scenario)

$$C_{\text{node/year}} = \frac{\text{node capex}}{\text{years}} + \text{node opex/year}$$

Line item	Value (USD / €)	Note
4×H100 node capex (midpoint)	178,500 USD	GPUs + server + network + storage + rack
3-year amortisation	59,500 USD/year ≈ 55,300 €/year	Straight line
Opex/year (base scenario, 8–16 node cluster)	~28,000 €/year	Energy + staff + maintenance + colocation
Total per node per year	~83,300 €/year	—

For 11 nodes: 915,300 €/year of total fixed cost.

2.2 From €/node-year to €/GPU-hour

$$\text{EUR/GPU-hour} = \frac{C_{\text{node/year}}}{4\;\text{GPUs} \times 8{,}760\;\text{h} \times \rho}$$

Utilisation $\rho$	EUR/GPU-hour
40 %	5.93
55 %	4.31
63 % (SLO 300 ms)	3.76
70 %	3.39
80 %	2.97
100 %	2.38

2.3 From €/GPU-hour to €/1M tokens

$$\text{EUR/1M tokens} = \frac{\text{EUR/GPU-hour} \times 10^{6}}{\dot{T}_{\text{GPU}} \times 3{,}600}$$

With $\dot{T}_{\text{GPU}} = 1{,}850$ tok/s (vLLM, Llama-3.3 70B FP8):

Utilisation	EUR/GPU-hour	EUR/1M tokens
40 %	5.93	0.891
55 %	4.31	0.647
63 % (SLO 300 ms)	3.76	0.564
70 %	3.39	0.509
80 %	2.97	0.446
100 %	2.38	0.357

The complete cost/token identity as a function of throughput and utilisation is developed in cost per token and per request.

2.4 Comparison with cloud (equivalent €/1M tokens)

To compare, the cloud price is converted to the €/1M tokens equivalent using the same reference throughput ($\dot{T}_{\text{GPU}} = 1{,}850$ tok/s):

$$\text{EUR/1M tokens (cloud)} = \frac{P_{\text{cloud}} \times 10^{6}}{1{,}850 \times 3{,}600}$$

Provider / Mode	GPU-hour price (USD)	EUR/GPU-hour ($1\,\text{USD} \approx 0.93\,\text{EUR}$)	EUR/1M tokens equiv.
AWS p5 on-demand (post Jun. 2025)	3.90	3.63	0.545
AWS p5 1-year reserved	~2.50	2.33	0.350
CoreWeave on-demand	~2.01	1.87	0.281
CoreWeave 3-year reserved	~1.49	1.39	0.209
GCP A3 on-demand	~3.67	3.41	0.512
Azure ND H100 v5 on-demand	~6.98	6.49	0.975

Sources: IntuitionLabs (Jun. 2026), CloudZero (Jun. 2026), Spheron GPU pricing (May 2026).

3. Break-even and payback of your own investment

3.1 The utilisation break-even formula

The utilisation break-even $u^{*}$ is the utilisation at which the annual on-prem cost per GPU-hour equals the cloud price:

$$u^{*} = \frac{\text{capex/year} + \text{opex/year}}{4 \times 8{,}760 \times P_{\text{cloud}}}$$

where $P_{\text{cloud}}$ is the cloud price in the same currency as the on-prem costs.

With the base scenario (capex/year 55,300 €, opex/year 28,000 €, total 83,300 €/node/year):

Cloud reference	Cloud price (EUR/GPU-hour)	$u^{*}$ break-even
Azure on-demand (~6.49 EUR)	6.49	23 %
AWS on-demand post-cut (~3.63 EUR)	3.63	41 %
GCP on-demand (~3.41 EUR)	3.41	44 %
CoreWeave on-demand (~1.87 EUR)	1.87	80 %
CoreWeave 3-yr reserved (~1.39 EUR)	1.39	>100 % (impossible)
AWS 1-yr reserved (~2.33 EUR)	2.33	64 %

3.2 Capex payback

Payback is the time $T_{\text{pay}}$ in which the cumulative saving against cloud equals the initial capex:

$$T_{\text{pay}} = \frac{\text{total cluster capex}}{(\text{cloud cost/year}) - (\text{on-prem opex/year})}$$

where the cloud cost/year is computed at the same sustained utilisation.

For the 11-node cluster (total capex 11 × 178,500 USD ≈ 1,825,000 USD ≈ 1,697,000 €):

Cloud reference	Sustained utilisation	Annual saving vs cloud	Payback
AWS on-demand (3.63 EUR/h)	70 %	(3.63 − 3.39 EUR) × 4 × 8760 × 0.70 × 11 nodes ≈ 63,900 €/year	~27 months
AWS on-demand (3.63 EUR/h)	80 %	(3.63 − 2.97) × 4 × 8760 × 0.80 × 11 ≈ 203,600 €/year	~10 months
GCP on-demand (3.41 EUR/h)	70 %	(3.41 − 3.39) × 4 × 8760 × 0.70 × 11 ≈ 5,400 €/year	~315 months (not viable)
Azure on-demand (6.49 EUR/h)	70 %	(6.49 − 3.39) × 4 × 8760 × 0.70 × 11 ≈ 830,000 €/year	~2 months

The 13-month payback quoted in studies such as Lenovo TCO 2026 corresponds to ~80 % utilisation against high-priced hyperscalers (Azure/AWS before the cut). With current prices (post June 2025, AWS at 3.90 USD), the window widens.

3.3 Simple payback (capex only vs equivalent cloud)

If on-prem opex is omitted and only capex is compared with the gross saving:

$$T_{\text{pay,simple}} = \frac{\text{capex}}{P_{\text{cloud}} \times 4 \times 8{,}760 \times \rho \times N_{\text{nodes}}}$$

Utilisation	AWS (3.63 EUR)	Azure (6.49 EUR)
50 %	54 months	30 months
70 %	39 months	22 months
80 %	34 months	19 months

4. Decision table: when to buy, rent or go hybrid

The table below is a five-dimension Pareto. There is no implicit order between columns; the reading depends on the organisation’s constraints.

Option	EUR/GPU-hour (util. 70 %)	Initial capex	Required utilisation	Data sovereignty	Peak elasticity
On-prem purchase, util. ≥ 70 %	3.39	high (178k USD/node)	≥ 70 % sustained	total	none
On-prem purchase, util. < 50 %	> 4.75	high	< 50 % → loses vs cloud	total	none
Sovereign EU cloud OD (Scaleway/Nebius EU)	2.00–3.59	none	any	yes (EU)	total
AWS p5 on-demand (post Jun. 2025)	3.63	none	any	no (CLOUD Act)	total
CoreWeave on-demand	1.87	none	any	partial (US)	total
CoreWeave 3-year reserved	1.29–1.39	financial commitment	rigid contract	partial (US)	none
AWS 1-year reserved	~2.17	1-year commitment	contract	no (CLOUD Act)	none
Hybrid on-prem base + EU cloud peak	2.50–3.39 (weighted)	medium	base ≥ 70 %, elastic peak	yes (EU)	elastic peak

Cut-off criteria that come before the table:

GDPR sovereignty: if the data is personal or the system is high-risk under the EU AI Act, CoreWeave/AWS are ruled out before any price comparison.
Minimum volume to amortise capex: below ~2M tokens/day sustained over 3 years, on-prem capex does not amortise against AWS on-demand.
Traffic elasticity: peaks >3× the base favour a hybrid or pure cloud; a stable base favours on-prem.

The cost/sovereignty Pareto frontier for GDPR data leaves three options: on-prem, sovereign EU cloud and hybrid. Sustained utilisation and traffic predictability decide between them. See the cross-analysis of the four axes in sovereign on-premise vs hyperscalers.

5. Sensitivity analysis

5.1 Sizing vs hourly profile and peak factor

The number of GPUs grows linearly with $k_{\text{peak}}$ and inversely with $\rho_{\max}$:

$$N_{\text{GPU}} = \left\lceil \frac{D \times L_{\text{out}} \times k_{\text{peak}}}{H \times 3{,}600 \times \rho_{\max} \times \dot{T}_{\text{GPU}}} \right\rceil$$

Peak factor $k$	SLO 300 ms ($\rho_{\max}=0.63$)	SLO 500 ms ($\rho_{\max}=0.75$)
1.2	8 GPUs (2 nodes)	6 GPUs (2 nodes)
1.8	12 GPUs (3 nodes)	10 GPUs (3 nodes)
2.5	16 GPUs (4 nodes)	13 GPUs (4 nodes)
3.5	22 GPUs (6 nodes)	18 GPUs (5 nodes)

(Example simplified to 5M req/day with H=24 to illustrate the sensitivity to the peak factor)

A peak factor of 3.5× triples the number of nodes compared with k=1.2 at the same SLO. Sizing hardware for $k > 2.5$ leaves GPUs idle more than 70 % of the time; peak cloud is more efficient beyond that threshold.

5.2 Break-even vs sustained utilisation

$$u^{*} = \frac{83{,}300}{4 \times 8{,}760 \times P_{\text{cloud}}}$$

Cloud price (EUR/GPU-hour)	$u^{*}$ break-even	Scenario
6.49 (Azure OD)	23 %	On-prem wins almost always
3.63 (AWS OD)	41 %	On-prem wins if util. > 41 %
3.41 (GCP OD)	44 %	—
2.33 (AWS 1-yr reserved)	64 %	On-prem wins if util. > 64 %
1.87 (CoreWeave OD)	80 %	Hard to reach in production
1.39 (CoreWeave 3-yr reserved)	>100 %	On-prem never closes the gap

5.3 Break-even vs energy price

Energy accounts for 6–11 % of total TCO. Its impact on the break-even is moderate:

Energy price (EUR/kWh)	Energy opex/year per node	EUR/GPU-hour (70 % util.)	$u^{*}$ vs AWS OD
0.034 (solar PPA)	1,604 €	3.22	38 %
0.116 (industrial ES, base)	5,475 €	3.39	41 %
0.200 (high tariff)	9,437 €	3.57	43 %

The difference between the cheapest and the most expensive scenario is only 5 percentage points of break-even. The variable that moves the needle is utilisation, not energy.

5.4 Break-even vs demand growth

If demand grows at an annual rate $g$, the average utilisation of the cluster (sized for year 1) rises over time until it saturates and has to be expanded:

$$\rho(t) = \rho_{0} \times (1 + g)^{t}$$

Annual growth $g$	Time to saturation ($\rho \to 100\,\%$)	Decision
10 %	~11 years	Comfortable purchase
30 %	~4 years	Purchase with a review at 3 years
60 %	~2 years	Hybrid: base + elastic cloud
>100 %	<1 year	Pure cloud until it stabilises

For growth above 30 % per year, a buy-only strategy means oversizing for the future peak or re-buying hardware in short cycles. The hybrid (on-prem base + cloud for growth) minimises the capex at risk.

5.5 Headroom: the cost of the safety margin

The 15 % headroom in $N_{\text{nodes}}$ amounts to having ~1.6 extra nodes on average. Its annual cost is:

$$C_{\text{headroom}} = 0.15 \times 83{,}300\;\text{EUR/node/year} \times N_{\text{nodes,base}} \approx 12{,}500 \times 9 = 112{,}500\;\text{EUR/year}$$

That cost is justified by:

GPU failure rate ~5 % per year (in small clusters, documented by Introl, Apr. 2026)
Replacement time of 2–8 weeks (depending on market availability)
Unforeseen peaks of up to 20 % above the estimate

If the service can degrade gracefully (relaxing the TTFT SLO from 300 ms to 500 ms at extreme peak), headroom can be cut to 10 %, saving ~37,500 EUR/year.

6. Sensitivity map: €/GPU-hour and break-even on two axes

The table below crosses utilisation with the opex scenario, showing the all-in EUR/GPU-hour (base scenario, capex/year 55,300 €):

	Low opex (13,000 €/year)	Base opex (28,000 €/year)	High opex (75,000 €/year)
Util. 40 %	4.74	5.93	9.06
Util. 55 %	3.45	4.31	6.59
Util. 63 %	3.01	3.76	5.75
Util. 70 %	2.71	3.39	5.18
Util. 80 %	2.37	2.97	4.54
Util. 100 %	1.90	2.38	3.63

The crossing point with the cloud price (AWS OD: 3.63 EUR):

Low-opex scenario: break-even at ~38 % utilisation
Base-opex scenario: break-even at ~41 % utilisation
High-opex scenario: break-even at ~53 % utilisation

The biggest lever for lowering the break-even is not hardware capex but opex (staff and colocation above all). See the analysis of utilisation as a FinOps lever in GPU utilisation as FinOps.

7. Integration with the rest of the FinOps chain

The sizing of §1 determines the number of nodes; the TCO of §2 gives the cost per hour; the comparison of §3 gives the break-even. Those three numbers feed directly into the other instruments of the series:

Instrument	Input from this article	Output
GuideLLM — SLO validation under load	TTFT/ITL P99 SLO from step 2	Experimental confirmation of the real throughput per GPU
Capacity planning for on-premise inference	Demand profile and N GPUs from step 4	Scaling policy and autoscaling triggers
Cost per token and per request	EUR/GPU-hour from step §2.2	EUR/1M tokens per model and batching
Cloud GPU commitment and spot	Cloud prices from table §2.4	Optimisation of the complementary cloud tier
Sovereign on-premise vs hyperscalers	Break-even from §3	Final buy/rent decision including the sovereignty axis
TCO of an on-premise GPU cluster	Capex and opex from §2.1	Detailed TCO model with every line item
GPU utilisation as FinOps	Target utilisation from step 2	Scheduling levers to raise real utilisation

Sources

Spheron · LLM Inference SLO Engineering: TTFT, ITL, and P99 Latency Budgets for Production AI (2026) — https://www.spheron.network/blog/llm-inference-slo-ttft-itl-latency-budget-guide-2026/
Spheron · vLLM vs TensorRT-LLM vs SGLang: H100 Benchmarks (2026) — https://www.spheron.network/blog/vllm-vs-tensorrt-llm-vs-sglang-benchmarks/
Spheron · GPU Cloud Pricing 2026: H100 from 1.03 USD/hr, B200 from 2.12 USD/hr — https://www.spheron.network/blog/gpu-cloud-pricing-comparison-2026/
Spheron · LLM Inference On-Premise vs GPU Cloud: 2026 Cost and Break-Even Analysis — https://www.spheron.network/blog/llm-inference-on-premise-vs-cloud/
MLPerf Inference v5.1 — Red Hat: 5 777 tok/s (offline) en Llama 3.1-8B FP8 en H100 — https://www.redhat.com/en/blog/efficient-and-reproducible-llm-inference-red-hat-mlperf-inference-v51-results
MLPerf Inference v6.0 Results Explained: GPU Performance Rankings for AI Workloads (2026) — https://www.spheron.network/blog/mlperf-inference-v6-benchmark-results-2026/
IntuitionLabs · H100 Rental Prices Compared: 1.49–6.98 USD/hr Across 15+ Cloud Providers (2026) — https://intuitionlabs.ai/articles/h100-rental-prices-cloud-comparison
CloudZero · Cloud GPU Pricing Comparison: AWS vs Azure vs GCP For AI Workloads (2026) — https://www.cloudzero.com/blog/cloud-gpu-pricing-comparison/
Lenovo Press · On-Premise vs Cloud: Generative AI Total Cost of Ownership (2026 Edition) — https://lenovopress.lenovo.com/lp2368-on-premise-vs-cloud-generative-ai-total-cost-of-ownership-2026-edition
Introl · GPU Infrastructure TCO Model: 5-Year Cost Analysis for Enterprise AI (abr. 2026) — https://introl.com/blog/gpu-infrastructure-tco-5-year-cost-model
GMI Cloud · NVIDIA H100 GPU Pricing 2026: Rent vs Buy Cost Analysis — https://www.gmicloud.ai/en/blog/nvidia-h100-gpu-pricing-2026-rent-vs-buy-cost-analysis
Red Hat · 233 % 3-year ROI and 13 months to payback with Red Hat AI (feb. 2026) — https://www.redhat.com/en/blog/233-3-year-return-investment-and-13-months-payback-red-hat-ai
VentureBeat · 5 % GPU utilization: the 401 billion USD AI infrastructure problem — https://venturebeat.com/infrastructure/5-gpu-utilization-the-401-billion-ai-infrastructure-problem-enterprises-cant-keep-ignoring/
DZone · Queueing Theory for LLM Inference — https://dzone.com/articles/queueing-theory-for-llm-inference
GuideLLM · Evaluate LLM deployments for real-world inference (Red Hat Developer, jun. 2025) — https://developers.redhat.com/articles/2025/06/20/guidellm-evaluate-llm-deployments-real-world-inference

Parameter	Symbol	Example
Requests per day (average)	\(D\)	5,000,000
Input tokens per request (average)	\(L_{\text{in}}\)	512
Output tokens per request (average)	\(L_{\text{out}}\)	256
Peak factor (peak hour vs average ratio)	\(k_{\text{peak}}\)	1.8
Hours per day with significant traffic	\(H\)	16

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