Performance, Pricing, and Utilization for Lambda GPU Cloud Instances
William Lorenzo, Drake Hashimoto, Albert Hickey, Syed Muhammad Arham Ali
November 20, 2025
Introduction
As a data analyst and machine learning practitioner, my primary interest in this project stems from exploring Lambda’s GPU cloud infrastructure — a platform designed to accelerate high-performance AI workloads. My background includes conducting computational experiments in both R and Python, where I’ve applied TensorFlow (Developed by Google Brain) and PyTorch (developed by Meta’s AI Research) to construct and train neural network models for predictive analytics and deep learning.
This hands-on experience has shown us how crucial GPU acceleration is in scaling AI computations efficiently. Lambda’s integration of GPU cloud instances offers a real-world framework to understand how computational hardware, pricing, and performance interact to influence accessibility and innovation in artificial intelligence.
Through this project, our team and I intend to examine how hardware specifications, benchmark performance, and pricing dynamics reflect broader trends in the AI ecosystem — particularly how users and organizations perceive and adopt advanced technologies. Understanding these relationships not only deepens our technical insight into GPU-powered computation but also highlights how cloud-based GPU platforms like Lambda are shaping the future of AI research, deployment, and public perception of emerging technologies.
William Lorenzo -Lead Data Analyst, AI Engineer @ Interlinked |Statistics, B.S.: Data Science Concentration @ California State University - East Bay
The objective of this particular study is to approximate whether hardware performance metrics such as benchmark_score, vram_gb, num_gpus, and power_watts have a measurable relationship with the hourly_price_usd of Lambda GPU cloud instances. The intention is to identify if higher performance GPUs command high hourly rental prices.
Description of Data and Variables:
The dataset, lambda_ai_gpu_instances.csv, contains approximately 300 observations of GPU instances carrying variables connected to pricing, hardware specifications, and utilization.
Variable Description Table
Variable
Description
Type
gpu_model
Type of GPU instance
Categorical
vram_gb
Video memory capacity (in GB)
Numeric
num_gpus
Number of GPUs per instance
Numeric
benchmark_score
Performance benchmark score
Numeric
power_watts
Power consumption (in watts)
Numeric
hourly_price_usd
Hourly rental price of GPU instance (USD)
Numeric (Dependent Variable)
Exploratory Data Analysis
Upon constructing further inferential analysis, the dataset was thoroughly explored from using descriptive statistics and exploratory data analysis to summarize distributions and relationships among variables.
# Loading Packageslibrary(tidyverse)
Warning: package 'ggplot2' was built under R version 4.4.3
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✔ ggplot2 4.0.0 ✔ tibble 3.2.1
✔ lubridate 1.9.3 ✔ tidyr 1.3.1
✔ purrr 1.0.2
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(broom)library(reshape2)
Attaching package: 'reshape2'
The following object is masked from 'package:tidyr':
smiths
library(knitr)
Warning: package 'knitr' was built under R version 4.4.3
# Checking for NAna_counter <-sum(is.na(df))cat("NA:", na_counter)
NA: 0
# Select only numeric columns for correlationnumeric_df <- df %>%select_if(is.numeric)# Compute correlation matrixcorr_matrix <-cor(numeric_df, use ="complete.obs")# Melt the correlation matrix for ggplotmelted_corr <-melt(corr_matrix)# Get actual range of correlations for better contrastrng <-range(melted_corr$value, na.rm =TRUE)# Plot Heatmapggplot(data = melted_corr, aes(x = Var1, y = Var2, fill = value)) +geom_tile(color ="black") +scale_fill_gradient2(low ="#3c096c", # dark purple for negativemid ="#b983ff", # light purple near 0high ="#ffb3ff", # pinkish-purple for positivemidpoint =0,limits = rng, # use actual data range, not -1 to 1name ="Correlation" ) +theme_minimal() +theme(plot.background =element_rect(fill ="black", color =NA),panel.background =element_rect(fill ="black", color =NA),panel.grid =element_blank(),axis.text.x =element_text(angle =45, vjust =1, hjust =1, color ="white" ),axis.text.y =element_text(color ="white"),axis.title =element_text(color ="white"),plot.title =element_text(color ="white", face ="bold", hjust =0.5),legend.title =element_text(color ="white"),legend.text =element_text(color ="white") ) +coord_fixed() +labs(title ="Correlation Heatmap of Lambda GPU Dataset",x ="",y ="" )
Statistical Inferences
The intention of this particular approach is to carefully examine whether GPU performance variables are crucially associated with hourly price and whether price differences exist between various GPU models.
Correlation and Simple Linear Regression
A Pearson correlation test was performed to assess the linear relationship between benchmark_score and hourly_price_usd. A simple linear regression was then fit to model hourly pricing as a function of benchmark score.
Pearson's product-moment correlation
data: df$benchmark_score and df$hourly_price_usd
t = -1.1945, df = 298, p-value = 0.2332
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.18085765 0.04455857
sample estimates:
cor
-0.06903059
# Simple Linear Regression Modellm_model <-lm(hourly_price_usd ~ benchmark_score, data = df)summary(lm_model)
Call:
lm(formula = hourly_price_usd ~ benchmark_score, data = df)
Residuals:
Min 1Q Median 3Q Max
-8.295 -4.405 0.288 4.311 8.383
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 13.7522285 1.4211753 9.677 <2e-16 ***
benchmark_score -0.0001864 0.0001560 -1.195 0.233
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 4.759 on 298 degrees of freedom
Multiple R-squared: 0.004765, Adjusted R-squared: 0.001426
F-statistic: 1.427 on 1 and 298 DF, p-value: 0.2332
The simple linear regression model is expressed as:
\[
Y = \beta_0 + \beta_1X + \epsilon
\]
Intercept:
\[
\hat{\beta}_0 = 13.7522285
\]
Slope:
\[
\hat{\beta}_1 = -0.0001864
\]
Thus, the estimated regression equation is:
\[
\hat{Y} = 13.75 - 0.0001864x.
\]
where \(Y\) is hourly_price_usd, \(X\) is the benchmark_score, \(\beta_0\) is the intercept, \(\beta_1\) is the slope, and \(\epsilon\) portrays random error.
# Linear Regression Visualizationggplot(data = df, aes(x = benchmark_score, y = hourly_price_usd)) +geom_point(col ="blue") +geom_smooth(method ="lm", se = T, col ="red", linetype ="dashed") +labs("title"="Figure 1. Relationship Between Benchmark Score and Hourly GPU Price",x ="Benchmark Score",y ="Hourly Price (USD)" ) +theme_minimal() +theme(plot.background =element_rect(fill ="black", color =NA),panel.background =element_rect(fill ="black", color =NA),panel.grid.major =element_line(color ="gray30"),panel.grid.minor =element_line(color ="gray20"),axis.text =element_text(color ="white"),axis.title =element_text(color ="white"),plot.title =element_text(color ="white", face ="bold"),legend.position ="none" )
`geom_smooth()` using formula = 'y ~ x'
The Pearson correlation has a coefficient of \(r = -0.069\) with \(p = 0.233\), thoroughly indicating a statistically insignificant negative relationship. The linear regression model produced \(\beta_1 = -0.00019\) and \(R^2 = 0.0048\), elucidating that benchmark performance explains less than 1% of price variation. Ultimately, there is insufficient evidence to conclude that GPU benchmark performance affect hourly pricing.
Two-Sample \(t\)-Test
A Welch two-sample \(t\)-test was integrated to determine whether there was a significant difference in mean hourly prices between particular GPU models (A100 and L40S).
where \(\bar{X}_1\) and \(\bar{X}_2\) are the sample means, \(S^2_1\) and \(S^2_2\) are sample variances, and \(n_1\) and \(n_2\) are the sample sizes.
substituting values into the Welch test statistic:
\[
t = \frac{0.67344}
{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
\]
Using the sample variances and sample sizes computed in R, the resulting test statistic is:
\[
t = 0.85174
\]
The degrees of freedom (Welch–Satterthwaite approximation) are:
Using the sample variances, sample sizes, and the Welch–Satterthwaite degrees of freedom \(df \approx 139.37\), the estimated standard error of the difference is
\[
SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}
\approx 0.79
\]
The critical value for a 95% confidence interval is approximately
Therefore, the 95% confidence interval for the difference in mean hourly price (A100 minus L40S) is
\[
(-0.8898,\; 2.2367).
\]
Because this interval contains 0, it is consistent with the conclusion that there is no statistically significant difference between the two mean prices.
Under the null hypothesis \(H_0 : \mu_1 - \mu_2 = 0\), the test statistic follows a \(t\)-distribution with \(df \approx 139.37\). The two-sided p-value is then defined as
\[
p = 2 \cdot P\left(T_{df} \ge |t_{\text{obs}}|\right),
\]
where \(T_{df}\) is a random variable following a \(t\)-distribution with the given degrees of freedom.
Substituting the observed values:
\[
p = 2 \cdot P\left(T_{139.37} \ge |0.85174|\right).
\]
Evaluating this probability (using R or a \(t\)-distribution table) gives:
Welch Two Sample t-test
data: hourly_price_usd by gpu_model
t = 0.85174, df = 139.37, p-value = 0.3958
alternative hypothesis: true difference in means between group A100 and group L40S is not equal to 0
95 percent confidence interval:
-0.8897991 2.2366773
sample estimates:
mean in group A100 mean in group L40S
12.99290 12.31946
# Summary Table of Meansmean_table <- gpu_subset %>%group_by(gpu_model) %>%summarise(Mean_Price =mean(hourly_price_usd),SD_Price =sd(hourly_price_usd),n =n() )kable(mean_table, digits =2, caption ="Table 1. Mean Hourly Price by GPU Model")
Table 1. Mean Hourly Price by GPU Model
gpu_model
Mean_Price
SD_Price
n
A100
12.99
4.81
69
L40S
12.32
4.63
74
\(t = 0.85\), \(df = 139.37\), and \(p-value\) = 0.396. There are no significant difference in average hourly price between A100 and L40S GPUs.
The mean hourly price for A100 was $12.99, while for L40S it was $12.32. The 95% confidence interval for the difference in means was (-0.89, 2.24), which includes zero, confirming no significant difference.
Conclusion
This analysis indicates that GPU hardware performance metrics–such as benchmark score, capacity of VRAM, number of GPUs, and power consumption–do not significantly predict hourly rental pricing in Lambda’s GPU cloud environment. Both approaches (Pearson’s Correlation and Linear Regression analyses) illustrated no statistically significant relationship between benchmark performance and price, and the \(t\)-test confirmed no significant difference between A100 and L40S pricing.
These results suggest that Lambda’s pricing model is not directly performance-driven. On the other hand, crucial variables such as geographic region, reliability, uptime, and market demand likely play a more substantial role in determining hourly rates.
