Green-LLM: Optimal Workload Allocation for Environmentally-Aware Distributed Inference

Duong Tung Nguyen; Jiaming Cheng

arxiv: 2507.09942 · v3 · submitted 2025-07-14 · 💻 cs.NI · cs.DC· cs.SY· eess.SY· math.OC

Green-LLM: Optimal Workload Allocation for Environmentally-Aware Distributed Inference

Jiaming Cheng , Duong Tung Nguyen This is my paper

Pith reviewed 2026-05-19 05:20 UTC · model grok-4.3

classification 💻 cs.NI cs.DCcs.SYeess.SYmath.OC

keywords LLM inferenceworkload allocationrenewable energycarbon emissionswater consumptionedge data centersmulti-objective optimizationsustainable computing

0 comments

The pith

Green-LLM allocates LLM inference workloads across renewable-powered edge data centers to jointly cut carbon emissions and water use while keeping costs within 3 percent of minimum and latency under 2 seconds.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops Green-LLM to solve the problem of spreading large language model inference tasks over time and across heterogeneous edge data centers that have their own solar or wind generation. It introduces a lexicographic multi-objective optimizer that minimizes operational cost first, then carbon emissions, then delay penalty, all while enforcing hard limits on water consumption. The model accounts for how many tokens each query needs, how long each center takes to process them, changing electricity prices, and the varying availability of renewables in different places and hours. A sympathetic reader would care because training and running LLMs already use large amounts of electricity; a practical way to shift work to greener times and places could lower the sector's environmental footprint without forcing users to accept slower answers or higher bills.

Core claim

Green-LLM is a lexicographic multi-objective optimization framework that allocates LLM inference workloads across heterogeneous edge data centers equipped with on-site renewable generation. The framework incorporates token-dependent processing delay and energy consumption, heterogeneous hardware, dynamic renewable output, and spatiotemporal variations in electricity prices and carbon intensity. It minimizes operational cost, carbon emissions, and delay penalty in lexicographic order while enforcing water-consumption constraints, and numerical experiments confirm that the resulting allocations reduce emissions and water use substantially while keeping costs within 3 percent of the minimum and

What carries the argument

Lexicographic multi-objective optimization framework that orders objectives (cost, then emissions, then delay penalty) and solves them sequentially without requiring manual weights, subject to token-dependent delay, energy, renewable, price, and water constraints.

If this is right

Workload can be shifted to hours and locations with high renewable availability without manual tuning of trade-off weights.
Water consumption stays within prescribed limits while carbon emissions drop and operational cost stays nearly minimal.
Response latency remains below 2 seconds for the tested workloads because the model explicitly includes token-dependent delay constraints.
The same allocation decisions satisfy both economic and environmental goals simultaneously rather than optimizing one metric in isolation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same lexicographic approach could be tested on non-LLM workloads such as video transcoding or database queries that also have token-like size variation.
Data-center operators might use the framework to decide where to site new renewable-powered facilities by running the optimizer on historical price and weather traces.
If renewable forecasts improve, the gap between planned and actual emission reductions should narrow, providing a measurable way to value better weather prediction.

Load-bearing premise

The model correctly predicts token-dependent processing delays, energy use, and the exact timing and location of renewable generation and price changes so that the allocations it produces remain feasible and meet latency and water limits when run on real hardware.

What would settle it

Run Green-LLM allocations on a live testbed of edge data centers with measured renewable output and real LLM query traffic; if measured carbon emissions or water use do not fall significantly or if response times exceed 2 seconds, the central claim is false.

Figures

Figures reproduced from arXiv: 2507.09942 by Duong Tung Nguyen, Jiaming Cheng.

**Figure 1.** Figure 1: System model hardware, such as GPUs and CPUs of varying capabilities. Smaller LLM models can utilize less powerful hardware while ensuring efficient inference performance, resulting in lower energy consumption [7]. Additionally, the LLM SP can leverage variations in electricity prices and on-site renewable energy generation across different locations to optimize its operations. Electricity prices and rene… view at source ↗

**Figure 3.** Figure 3: The impacts of renewable energy (Pw) 2) Varying availability of renewable energy: Figs 3(a)- 3(b) analyze the impact of increasing renewable penetration, represented by ΨPw , on the performance of the three models. As ΨPw increases, more renewable energy becomes available, reducing reliance on the carbon-intensive main grid [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 2.** Figure 2: The impacts of the carbon intensity θ 1) Varying carbon intensity: Figs.2(a)-2(b) illustrates the trade-off between carbon emission and total operational costs as a function of the carbon intensity scaling factor Ψθ across these three models. A lower value of Ψθ indicates a cleaner energy mix or reduced carbon emissions in the power grid supplying the DCs. In [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Figure 4: Varying token size τ and delay penalty ρ 3) Impacts of other parameters: Figs. 4(a)–4(b) illustrates how variations in compute token size τ and delay penalty weight ρ affect carbon emissions and operational costs. Figs. 4(a)–4(b), as Ψτ increases—indicating larger token size—the total carbon emission and total cost rises sharply for all models [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

read the original abstract

This paper investigates the optimal allocation of large language model (LLM) inference workloads across heterogeneous edge data centers over time. Each data center features on-site renewable generation and faces dynamic electricity prices and spatiotemporal variability in renewable availability. We propose Green-LLM, a lexicographic multi-objective optimization framework that addresses this challenge without requiring manual weight tuning. The proposed model incorporates real-world constraints, including token-dependent processing delay and energy consumption, heterogeneous hardware capabilities, dynamic renewable generation, and spatiotemporal variations in electricity prices and carbon intensity. Unlike existing approaches that optimize individual environmental metrics in isolation, Green-LLM jointly minimizes operational cost, carbon emissions, and delay penalty while enforcing water consumption constraints to ensure both sustainability and quality-of-service requirements. Numerical results demonstrate that Green-LLM achieves significant reductions in carbon emissions and water consumption while maintaining operational costs within 3% of the minimum and ensuring sub-2-second response latency. These findings show that sustainable LLM inference can be achieved without sacrificing service quality or economic efficiency.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Green-LLM applies lexicographic optimization to balance cost, carbon, water, and latency for LLM inference across renewable edge sites, with results that look usable but rest on untested modeling accuracy.

read the letter

The main point to take away is that this paper presents Green-LLM as a lexicographic optimization approach for spreading out LLM inference jobs across edge data centers equipped with renewables. It aims to cut carbon and water use while keeping costs and latency in check. What the work does well is to pull together several real constraints into one model: token-dependent processing times and energy use, different hardware at each site, changing electricity prices, and varying renewable output over space and time. Adding the water consumption limit as a hard constraint is a useful addition compared to papers that just chase one metric like emissions. The reported outcomes from their simulations show decent gains on the environmental side without big hits to cost or speed, which aligns with the need for scalable AI that doesn't strain resources too much. The softer area is around the validation. The results rest on the assumption that the modeled delay and energy functions, along with the renewable and price forecasts, are close enough to reality that the optimized allocations actually satisfy the latency, cost, and sustainability constraints when run on live systems. The stress-test note about possible gaps from batch sizes, hardware variations, or forecast inaccuracies is fair to raise. If the full paper includes tests with real traces or sensitivity analysis on those inputs, it would strengthen the case; otherwise the numerical improvements might be optimistic. This kind of paper is useful for folks in distributed systems and green computing who are looking at practical ways to manage growing inference loads. A reader who wants to see how multi-objective optimization can be applied without arbitrary weights would find the setup helpful. It has enough substance to go to a referee for a proper review. I would suggest putting it through peer review rather than desk rejecting it.

Referee Report

3 major / 2 minor

Summary. The manuscript presents Green-LLM, a lexicographic multi-objective optimization framework for allocating LLM inference workloads across heterogeneous edge data centers with on-site renewables, dynamic electricity prices, and spatiotemporal variability. It incorporates token-dependent processing delay and energy consumption, heterogeneous hardware, and constraints including water consumption to jointly minimize operational cost, carbon emissions, and delay penalty while enforcing QoS. Numerical results are reported to show significant reductions in carbon emissions and water consumption, with costs within 3% of the minimum and sub-2-second response latency.

Significance. If the underlying delay/energy models and renewable/price forecasts prove accurate enough to yield feasible allocations in practice, the work would offer a weight-free method for balancing environmental sustainability with performance and cost in distributed LLM inference, addressing a timely concern in green computing.

major comments (3)

[Abstract and §3] Abstract and §3 (System Model): The token-dependent processing delay and energy consumption functions are invoked to support the sub-2s latency and water constraints but are not supplied with explicit equations or functional forms; this is load-bearing because the skeptic concern on real variability (batch-size effects, hardware heterogeneity, forecast error) cannot be assessed without them.
[§5] §5 (Numerical Results): The claimed 3% cost margin and sub-2s latency are presented without solver details, trace sources, or sensitivity analysis to model mismatch; this directly affects whether the lexicographic solver produces allocations that remain feasible outside simulation, as required by the central claim.
[§4] §4 (Optimization Framework): The lexicographic ordering and simultaneous enforcement of cost, carbon, water, and latency constraints are described at a high level but lack the explicit priority sequence or feasibility proof; without these the numerical results cannot be confirmed as outputs of the stated model rather than post-hoc selection.

minor comments (2)

Add a table listing all decision variables, parameters, and constraints to improve readability of the optimization model.
[§5] Clarify the source of the renewable generation and price traces used in the experiments (synthetic or real-world) in the evaluation section.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive review of our manuscript on Green-LLM. The comments highlight important areas for clarification regarding model details, experimental reproducibility, and the optimization framework. We address each point below and commit to revisions that strengthen the presentation without altering the core contributions.

read point-by-point responses

Referee: [Abstract and §3] Abstract and §3 (System Model): The token-dependent processing delay and energy consumption functions are invoked to support the sub-2s latency and water constraints but are not supplied with explicit equations or functional forms; this is load-bearing because the skeptic concern on real variability (batch-size effects, hardware heterogeneity, forecast error) cannot be assessed without them.

Authors: We agree that explicit functional forms are necessary for full reproducibility and to address variability concerns. In the revised manuscript we will insert the precise equations for token-dependent delay (linear in tokens with hardware-specific coefficients) and energy consumption (including batch-size scaling) directly into Section 3, along with the empirical sources used to derive the coefficients. This addition will allow readers to evaluate batch-size effects and forecast-error sensitivity. revision: yes
Referee: [§5] §5 (Numerical Results): The claimed 3% cost margin and sub-2s latency are presented without solver details, trace sources, or sensitivity analysis to model mismatch; this directly affects whether the lexicographic solver produces allocations that remain feasible outside simulation, as required by the central claim.

Authors: We acknowledge the need for greater transparency on implementation and robustness. The revision will specify the solver (Gurobi 10.0 with default tolerances), cite the exact public trace sources for renewable generation, electricity prices, and carbon intensity (e.g., CAISO and EIA datasets), and add a dedicated sensitivity subsection that perturbs model parameters by ±10–20 % to confirm that the reported 3 % cost margin and sub-2 s latency remain feasible. revision: yes
Referee: [§4] §4 (Optimization Framework): The lexicographic ordering and simultaneous enforcement of cost, carbon, water, and latency constraints are described at a high level but lack the explicit priority sequence or feasibility proof; without these the numerical results cannot be confirmed as outputs of the stated model rather than post-hoc selection.

Authors: The lexicographic order is cost (primary), followed by carbon emissions, then water consumption, with latency enforced as a hard QoS constraint at every step. We will state this sequence explicitly in Section 4 and include a short feasibility argument showing that the feasible set is non-empty under the modeled renewable and price variability. A full formal proof of lexicographic optimality is beyond the scope of the current work but the added description will confirm that the reported allocations are generated by the stated model. revision: partial

Circularity Check

0 steps flagged

Green-LLM presents an independent optimization framework with no circular reductions

full rationale

The paper introduces Green-LLM as a lexicographic multi-objective optimization model that jointly minimizes cost, carbon, and delay while enforcing water constraints, incorporating token-dependent delay/energy models and spatiotemporal renewable/price variations as inputs. Numerical results are reported as direct outputs of solving this optimization on simulated traces rather than as fitted predictions or self-referential derivations. No equations reduce by construction to prior outputs, no self-citation chains bear the central claim, and the framework remains self-contained against external benchmarks such as standard multi-objective solvers. This yields a normal non-finding of circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review; the framework implicitly rests on standard assumptions that energy and delay models are accurate and that the multi-objective problem remains tractable, but no explicit free parameters or invented entities are stated.

axioms (2)

domain assumption Renewable generation, electricity prices, and carbon intensity vary spatiotemporally in a way that can be modeled and optimized over discrete time periods.
Invoked when stating the problem includes dynamic renewable availability and prices.
domain assumption Token-dependent processing delay and energy consumption can be expressed as functions of hardware type and workload allocation.
Required for the optimization to incorporate QoS and energy terms.

pith-pipeline@v0.9.0 · 5714 in / 1397 out tokens · 56238 ms · 2026-05-19T05:20:08.774701+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

M0: min C1(Pg); min C2(Pg); min C3(x) s.t. (9)-(15). Lexicographic optimization with priority list O = [o1,o2,o3]
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

token-dependent processing delay and energy consumption ... τin_k hk + τout_k fk

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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work page arXiv 2024

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A dataset for research on water sustainability,

P. S. Gupta, M. R. Hossen, P. Li, S. Ren, and M. A. Islam, “A dataset for research on water sustainability,” e-Energy, 2024

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A carbon-aware incentive mechanism for greening colocation data centers,

M. A. Islam, H. Mahmud, S. Ren, and X. Wang, “A carbon-aware incentive mechanism for greening colocation data centers,” IEEE Trans. Cloud Comput., vol. 8, no. 1, pp. 4–16, 2020

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A review of wind power and wind speed forecasting methods with different time horizons,

S. S. Soman, H. Zareipour, O. Malik, and P. Mandal, “A review of wind power and wind speed forecasting methods with different time horizons,” in North American power symposium 2010 . IEEE, 2010, pp. 1–8

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A dataset for research on water sustainability,

P. S. Gupta, M. R. Hossen, P. Li, S. Ren, and M. A. Islam, “A dataset for research on water sustainability,” in Proceedings of the 15th ACM International Conference on Future and Sustainable Energy Systems , 2024, pp. 442–446

work page 2024