| vars | n | mean | sd | median | trimmed | mad | min | max | range | skew | kurtosis | se | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| uptime_hours | 1 | 300 | 1011.09 | 554.24 | 1021.00 | 1001.58 | 726.47 | 116.0 | 1999.00 | 1883.00 | 0.11 | -1.26 | 32.00 |
| reliability_score | 2 | 300 | 94.94 | 2.98 | 94.90 | 94.93 | 3.85 | 90.0 | 100.00 | 10.00 | -0.01 | -1.23 | 0.17 |
| avg_utilization_% | 3 | 300 | 75.27 | 14.92 | 75.85 | 75.29 | 19.20 | 50.2 | 100.00 | 49.80 | -0.06 | -1.25 | 0.86 |
| hourly_price_usd | 4 | 300 | 12.09 | 4.76 | 12.44 | 12.12 | 6.47 | 4.1 | 19.97 | 15.87 | -0.05 | -1.32 | 0.27 |
| num_gpus | 5 | 300 | 3.51 | 2.63 | 2.00 | 3.26 | 1.48 | 1.0 | 8.00 | 7.00 | 0.80 | -0.85 | 0.15 |
Performance, Pricing, and Utilization for Lambda GPU Cloud Instances
Albert Hickey, Drake Hashimoto, William Lorenzo, Syed Muhammad Arham Ali
December 8, 2025
Introduction
The growth of modern AI systems has made clear just how essential GPU acceleration is for handling large-scale computations and managing data-intensive workloads. Lambda’s GPU cloud offerings create an applied environment where we can observe how hardware capabilities, pricing structures, and performance benchmarks interact in practical settings, and how these relationships shape the usability and adoption of cutting-edge AI technologies.
In this project, my team investigates how variations in GPU specifications, benchmark results, and cost structures correspond to broader patterns within the AI landscape: particularly the ways students, researchers, and industry professionals weigh performance against affordability. By analyzing these relationships, strengthen our understanding of GPU-driven computation, and gain insight into how cloud-based GPU platforms like Lambda influence the direction of AI development, experimentation, and real-world implementation.
- Albert Hickey – Data Science student @ California State University, East Bay
Experience with R, Python, SQL, SAS, with a focus on data visualization, exploratory data analysis (EDA), and statistical inference for real-world data problems.
Objective of the Study
The objective of this study is to examine whether GPU hardware features—such as benchmark_score, vram_gb, num_gpus, and power_watts—are related to the hourly_price_usd of Lambda GPU instances. In other words, we want to see if higher-performance GPUs tend to cost more and how these technical factors help explain differences in pricing.
Variable Description Table
| Variable | Description | Type |
|---|---|---|
uptime_hours |
Total operational hours of the GPU instance | Numeric |
reliability_score |
Reliability rating based on stability metrics | Numeric |
avg_utilization_pct |
Average GPU utilization percentage | Numeric |
hourly_price_usd |
Hourly rental price of GPU instance (USD) | Numeric (Dependent Variable) |
num_gpus |
Number of GPUs included in the instance | Numeric |
Data Exploration
| uptime_hours | reliability_score | avg_utilization_% | hourly_price_usd | num_gpus | |
|---|---|---|---|---|---|
| uptime_hours | 1.00 | -0.05 | 0.05 | 0.05 | 0.03 |
| reliability_score | -0.05 | 1.00 | -0.04 | 0.02 | -0.07 |
| avg_utilization_% | 0.05 | -0.04 | 1.00 | 0.06 | 0.11 |
| hourly_price_usd | 0.05 | 0.02 | 0.06 | 1.00 | 0.01 |
| num_gpus | 0.03 | -0.07 | 0.11 | 0.01 | 1.00 |
Since the sample size for all relevant variables is well above 30, the Central Limit Theorem applies. This ensures that statistical tests involving sample means are valid even if the underlying distributions are not perfectly normal. Therefore, we can confidently proceed with the planned inferential analyses.
Statistical Inferences
The statistical analyses in this study focus on understanding how key performance and reliability metrics relate to the pricing of Lambda GPU cloud instances. Specifically, we examine whether GPUs with higher reliability scores tend to command higher hourly prices and whether uptime demonstrates a measurable association with rental cost.
Are High-Reliability GPUs Priced Higher?
We split reliability_score at the sample median (94.9). Instances with
reliability_score ≥ 94.9 form the High group, and those below the median form the Low group.
We compare mean hourly price across the two groups.
Hypotheses
\[ H_0: \mu_{\text{High}} = \mu_{\text{Low}} \qquad\text{vs.}\qquad H_a: \mu_{\text{High}} \ne \mu_{\text{Low}}. \]
Sample Summaries
From the dataset:
High-reliability group:
\(n_1 = 152,\quad \bar{x}_1 = 12.1786,\quad s_1 = 4.7244\)
Low-reliability group:
\(n_0 = 148,\quad \bar{x}_0 = 11.9922,\quad s_0 = 4.8163\)
Test Statistic (Welch)
The formula for the Welch t-statistic is:
\[ t = \frac{\bar{x}_1 - \bar{x}_0} {\sqrt{\frac{s_1^2}{n_1} + \frac{s_0^2}{n_0}}}. \]
Compute the standard error:
\[ SE = \sqrt{ \frac{s_1^2}{n_1} + \frac{s_0^2}{n_0} } \]
Substitute the values:
\[ \begin{aligned} SE &= \sqrt{ \frac{4.7244^2}{152} + \frac{4.8163^2}{148} } \\[4pt] &= \sqrt{0.1468 + 0.1560} \\[4pt] &= \sqrt{0.3028} \\[4pt] &\approx 0.551. \end{aligned} \]
Compute the t-statistic:
\[ \begin{aligned} t &= \frac{\bar{x}_1 - \bar{x}_0}{SE} \\[4pt] &= \frac{12.1786 - 11.9922}{0.551} \\[4pt] &= \frac{0.1864}{0.551} \\[4pt] &\approx 0.338. \end{aligned} \]
Degrees of Freedom (Welch Approximation)
\[ df = \frac{ \left( \frac{s_1^2}{n_1} + \frac{s_0^2}{n_0} \right)^2 }{ \frac{ \left( \frac{s_1^2}{n_1} \right)^2 }{n_1 - 1} + \frac{ \left( \frac{s_0^2}{n_0} \right)^2 }{n_0 - 1} }. \]
Substituting values gives:
\[ df \approx 297.37. \]
p-Value and Confidence Interval
The two-sided p-value is:
\[ p = 2P(T_{297.37} \ge |0.338|) \approx 0.74. \]
A 95% confidence interval for \(\mu_{\text{High}} - \mu_{\text{Low}}\) is:
\[ \begin{aligned} (\bar{x}_1 - \bar{x}_0) \pm t_{0.975,297.37}\,SE &= 0.1864 \pm (1.968)(0.551) \\ &\approx 0.1864 \pm 1.084 \\ &\approx (-0.90,\ 1.27). \end{aligned} \]
Welch Two Sample t-test
data: hourly_price_usd by rel_group
t = 0.33829, df = 297.37, p-value = 0.7354
alternative hypothesis: true difference in means between group High Reliability and group Low Reliability is not equal to 0
95 percent confidence interval:
-0.897921 1.270698
sample estimates:
mean in group High Reliability mean in group Low Reliability
12.17862 11.99223 
Conclusion
Since the p-value is much larger than \(\alpha = 0.05\):
\[ p \approx 0.74 \gg 0.05, \]
we fail to reject \(H_0\). There is no statistically significant evidence that high-reliability GPUs are priced higher than low-reliability GPUs in this dataset, meaning that Lambda’s pricing does not meaningfully differ between high-reliability and low-reliability GPUs.
Does Uptime Correlate With Price?
To examine whether uptime is associated with hourly price, we compute Pearson’s correlation coefficient between uptime_hours and hourly_price_usd.
Sample Correlation
From the dataset, the sample correlation is
\[ r = 0.04928. \]
This indicates a very weak positive linear association between uptime and price.
Hypothesis Test
We test
\[ H_0: \rho = 0 \qquad \text{vs.} \qquad H_a: \rho \ne 0, \]
where () is the true population correlation.
The test statistic for Pearson’s correlation is
\[ t = \frac{r\sqrt{n-2}}{\sqrt{1 - r^2}}. \]
Substituting the values:
\[ \begin{aligned} t &= \frac{0.04928\sqrt{300 - 2}}{\sqrt{1 - (0.04928)^2}} \\[6pt] &= \frac{0.04928 \cdot \sqrt{298}}{\sqrt{1 - 0.00243}} \\[6pt] &= \frac{0.04928 \cdot 17.262}{\sqrt{0.99757}} \\[6pt] &= \frac{0.8508}{0.9988} \\[6pt] &\approx 0.852. \end{aligned} \]
Degrees of freedom:
\[ df = n - 2 = 298. \]
p-Value
The two-sided p-value is
\[ p = 2P(T_{298} \ge |0.852|) \approx 0.395. \]
Confidence Interval for the Correlation
Using Fisher’s ( z )-transformation, the 95% confidence interval for () is
\[ (-0.060,\; 0.158). \]
Pearson's product-moment correlation
data: lambda$uptime_hours and lambda$hourly_price_usd
t = 0.85168, df = 298, p-value = 0.3951
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.06432302 0.16161575
sample estimates:
cor
0.04927675 
Conclusion
Because the sample correlation coefficient is extremely small (\(r = 0.049\)), the 95% confidence interval for the correlation includes \(0\), and the p-value is much greater than \(\alpha = 0.05\) (\(p \approx 0.395\)), the data provides no statistically significant evidence of a linear relationship between uptime and hourly price, meaning that Lambda GPU pricing appears to not be influenced by GPU uptime.
Discussion and Conclusions
Overall, our analyses show that neither reliability nor uptime has a meaningful impact on the hourly price of GPU instances in this dataset. The t-test comparing high and low-reliability groups found no significant difference in average price, and the confidence interval included zero, and the correlation between uptime and price was very small and not statistically significant. These results suggest that Lambda’s GPU pricing is not strongly influenced by reliability or uptime. Other factors such as GPU model, memory size, or performance benchmarks are likely playing a larger role in determining rental prices. Future studies could explore these additional variables to better understand what determines GPU rental costs.