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REVIEW 4 major objections 4 minor 2 cited by

Carbon- and Precedence-Aware Scheduling for Data Processing Clusters

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A scheduler that weighs task precedence against grid carbon can cut data-processing emissions by up to 39.7 percent, while keeping end-to-end completion time nearly unchanged.

desk verdict PCAPS is a real systems contribution, but the theory is bookkeeping and the paper's central assumption—that softmax probability tracks task criticality—is asserted, not validated. read the letter →

arxiv 2502.09717 v1 pith:6VSEEFKX submitted 2025-02-13 cs.DC cs.CYcs.SYeess.SY

Adam Lechowicz , Rohan Shenoy , Noman Bashir , Mohammad Hajiesmaili , Adam Wierman , Christina Delimitrou This is my paper · ORCID
classification cs.DCcs.CYcs.SYeess.SY
keywords carbon-awareschedulingprecedence-constrainedDAGsdataprocessingclustersreinforcementlearningschedulercarbonstretchfactorthreshold-basedonlinealgorithmsApacheSparkKubernetes
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that carbon-aware scheduling for data-processing clusters should use both the time-varying carbon intensity of the grid and the precedence structure of each job's task graph. It proposes PCAPS, a scheduler that wraps an existing machine-learned probabilistic scheduler and decides at each scheduling event whether to run the sampled task or idle it until a cleaner period. The decision uses a relative-importance score: tasks the learned scheduler considers critical run even during high-carbon hours, while less important tasks wait. In a 100-node Spark/Kubernetes prototype and a high-fidelity simulator, a moderately carbon-aware PCAPS cuts carbon by about a third to 39.7 percent while raising end-to-end completion time by only a few percent, at the cost of substantially longer average per-job completion times. The paper also gives analytical bounds on the carbon-versus-completion-time trade-off for PCAPS and for a simpler provisioning-only variant, CAP.

What carries the argument

The load-bearing object is the relative-importance ratio $r_{v,t} := p_{v,t}/\max_{u\in A_t} p_{u,t}$, computed from the probability distribution over ready tasks generated by a machine-learned scheduler, together with the exponential threshold function $\Psi_\gamma(r)$ that turns this ratio into a run-or-defer decision. When the current carbon intensity $c(t)$ exceeds $\Psi_\gamma(r_{v,t})$ and at least one machine is busy, the sampled task is idled rather than executed; otherwise it runs. Because $\Psi_\gamma(1)=U$, the highest-importance task is always allowed to run regardless of carbon, which is the mechanism that protects the DAG's critical path. The proofs also lean on Graham's list-scheduling bound, which turns deferrals into a bounded makespan increase and yields the carbon stretch factor. CAP, by contrast, uses a k-search-inspired threshold set to set a cluster-wide resource quota, so it captures the carbon-shifting half of the idea but not the per-task precedence half.

What would settle it

Run PCAPS on a test batch where the scheduler's highest-probability tasks are known not to lie on the critical path, or replace its importance scores with random permutations while keeping the same deferral thresholds; if the carbon-versus-ECT trade-off does not degrade, then relative importance is not what is producing the savings.

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Extended reading notes

Core claim

The central claim is that fine-grained, precedence-aware deferral is what makes carbon-aware scheduling worthwhile for data processing. PCAPS assumes that the softmax probabilities produced by a probabilistic scheduler such as Decima contain implicit information about which tasks are bottlenecks: the ratio $r_{v,t} = p_{v,t}/\max_{u\in A_t} p_{u,t}$ measures how much the scheduler wants task $v$ to run now. An exponential threshold function $\Psi_\gamma(r)$, parameterized by a carbon-awareness knob $\gamma$ and bounded by the known minimum and maximum carbon intensities, determines whether $v$ is dispatched to a machine or deferred. Critical tasks (those with $r$ near 1) are always dispatched; tasks with low relative importance are delayed when carbon intensity is high, and the freed capacity is used later. The paper proves that this filter gives PCAPS a carbon stretch factor of $1 + \frac{D(\gamma,c)K}{2 - 1/K}$, characterizes its carbon savings, and demonstrates experimentally that the idea beats both a carbon-agnostic ML scheduler and a uniform resource-quota wrapper (CAP) on the carbon-versus-end-to-end-time frontier.

Load-bearing premise

PCAPS's benefit rests on treating the probabilities emitted by the learned scheduler as a reliable ranking of how costly it is to delay each task, and the paper does not directly verify that high-probability tasks are the true bottlenecks.

Editorial extensions

If this is right

  • A moderately carbon-aware PCAPS reduces carbon emissions by up to 39.7% in the simulator and 32.9% in the prototype, with average end-to-end completion time increasing by only 4.5% in the simulator and 1.3% in the prototype.
  • The same setting raises average job completion time by 38.1% in the prototype and about 119% relative to Decima in the simulator, so the carbon savings come from queue build-up during high-carbon periods rather than from faster execution.
  • CAP, which only scales cluster resources without looking at task dependencies, achieves smaller carbon savings (up to 25.1%) and pays more end-to-end time for the same carbon reduction, confirming that per-task precedence information is the differentiator.
  • The trade-off is tunable: $\gamma=0$ reproduces the carbon-agnostic scheduler, $\gamma=1$ is maximally carbon-aware, and the achievable carbon savings grow with the variability of the grid's carbon intensity.
  • On grids with stable, mostly coal-based intensity (ZA in the paper's data), the schedulers defer little and save little; on renewable-dominated grids with strong diurnal swings (CAISO), they wait for solar hours and save more.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the softmax probability is a faithful criticality proxy, then PCAPS is a drop-in carbon filter for any probabilistic DAG scheduler, not just Decima; a natural stress test is to replace the learned probabilities with critical-path slacks and compare the frontier.
  • The large gap between average JCT and ECT suggests PCAPS is effectively trading fairness across jobs for aggregate throughput; in settings with per-job service-level objectives, the deferral policy would need a deadline or a per-job slack guardrail.
  • The prototype's 32.9% carbon cut at 1.3% ECT cost implies that under internal carbon pricing, such a filter could pay for itself largely as an accounting change, but the realized cost saving depends on how tightly the carbon price tracks grid intensity.
  • A direct ablation—running PCAPS with random importance scores while keeping the same threshold function—would isolate how much of the benefit is due to precedence information rather than to the carbon-triggered idling alone.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes PCAPS, a carbon-aware scheduler for precedence-constrained data processing workloads, and CAP, a simpler resource-provisioning wrapper. PCAPS augments a probabilistic ML scheduler (e.g., Decima) with a threshold filter: using the ratio r_{v,t} = p_{v,t}/max_u p_{u,t} as a proxy for task importance, it runs high-importance tasks even during high-carbon periods and defers low-importance ones. CAP instead varies the cluster resource quota according to carbon intensity while leaving the underlying scheduler unchanged. The authors give analytical results on carbon stretch factor and carbon savings (Theorems 4.3–4.6), and evaluate both schedulers in a Spark-on-Kubernetes prototype on 100 executors and in a Spark simulator across six carbon-intensity traces and TPC-H/Alibaba workloads. The headline results are a 32.9% average carbon reduction in the prototype with near-neutral ECT relative to the default, and up to 39.7% carbon reduction in the simulator with modest ECT increases.

Significance. If the core mechanism is valid, the paper offers a practical, configurable way to reduce data-processing carbon footprint without severely degrading cluster throughput, and it provides one of the few evaluations of carbon-aware scheduling on a real 100-node Spark cluster. The prototype and the six-grid simulator study are substantial, the code is made available, and Appendix A.1.2 honestly documents the simulator/prototype baseline differences. The main limitation is that the distinguishing mechanism—interpreting Decima's softmax probability ratio as precedence-driven criticality—is an unverified proxy, and several analytical results are definitional rather than substantive. The contribution is therefore promising but not yet fully supported.

major comments (4)
  1. [§4.1, Definition 4.2 and Algorithm 1] The paper's distinguishing mechanism treats the softmax probability ratio r_{v,t} = p_{v,t} / max_{u in A_t} p_{u,t} as 'precedence-driven importance' and uses it to decide which tasks run during high-carbon periods. This identification is an assumption, not a derived property of Decima or of any probabilistic scheduler. The only direct evidence, Fig. 13, compares PCAPS to CAP-Decima on one grid (DE), one batch size (50 TPC-H jobs), and without confidence intervals, and the two systems differ in more than the r computation (fine-grained per-task deferral vs. cluster-level quotas). If r does not track criticality, PCAPS may defer exactly the tasks that block downstream DAGs, and the claimed small ECT increase will not generalize. I recommend a direct validation of the proxy: for example, compare deferral decisions against critical-path or descendant-count measures of task importance, and run an ablation in which r is replaced by random or anti-correlated priorities across several grids and batch sizes.
  2. [§4.1, Proof of Theorem 4.3 (Appendix B.1.1)] The proof bounds the total number of deferrals by E[D] <= n-1, arguing that at least one machine is active at all times. This does not bound D_v: a task can be sampled and deferred many times, especially because Algorithm 1 treats carbon-intensity changes as scheduling events, so the same ready task can be deferred repeatedly during a long high-carbon interval. Moreover, D(γ,c) is defined post hoc from E[D] and the longest task runtimes, so the 'carbon stretch factor' formula is an identity that holds for any scheduler and any γ; it carries no predictive content unless D(γ,c) is bounded a priori in terms of γ, K, L, U, and the DAG. Please either prove such a bound or recast Theorem 4.3 as a definition/measurement rather than a theorem.
  3. [§4.2, Proof of Theorem 4.5 (Appendix B.2.1)] The chain CAPK(J | M) <= AG_M(J) assumes that having additional machines and time-varying quotas cannot hurt. This is not generally true for list scheduling: Graham's anomalies show that adding processors can increase makespan for precedence-constrained jobs, and dynamic quota changes can fragment the schedule. Since Theorem 4.5 is presented as an analytical bound on CAP's carbon stretch factor, the monotonicity step needs a proof or a counterexample-free justification; otherwise the theorem should be stated under explicit assumptions on the scheduler and quota dynamics.
  4. [§4.1–4.2, Theorems 4.4 and 4.6 (Appendices B.1.2, B.2.2)] The carbon-savings results are exact algebraic rearrangements of Definition 3.2 after defining W, s_-, s_+, and c(T,T') in terms of the schedules being compared. They therefore cannot fail and do not, by themselves, establish that any particular scheduling policy saves carbon; the sign of the savings depends entirely on whether the weighted intensities satisfy s_- > s_+ + c(T,T'). I recommend presenting these as accounting identities and moving the burden of the trade-off claim to the empirical evaluation and to a priori bounds on the deferred work W.
minor comments (4)
  1. [Abstract and §6.3, Table 2] The abstract's 'up to 32.9%' is an average over traces and trials in Table 2, not a maximum; also the text in §6.3 reports 32.8% for PCAPS while Table 2 reports 32.9% (and 24.6% vs. 24.7% for CAP). Please align the wording and the numbers.
  2. [§6.5] The takeaway 'reduces carbon emissions by up to 39.7%' is again an average over the six carbon traces in Table 3, not a per-trace maximum; please state it as an average or report the actual maximum separately.
  3. [Definition 3.2 and Appendix B.1.2] The carbon-savings definition is written with integrals, while the proofs use discrete sums; state explicitly that the integrals are over the continuous time model and the sums are the discretized analogue.
  4. [Fig. 13] The cubic polynomial fit is used to compare PCAPS and CAP-Decima, but the fit is shown without confidence intervals and is extrapolated to regions with sparse trials; please report per-parameter-point means and standard errors or another uncertainty measure.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the theoretical bounds are parameterized applications of external list-scheduling results, and the headline carbon/ECT trade-off is an empirical measurement rather than a definitional or fitted prediction.

full rationale

The derivation chain in Sections 3-4 and Appendix B does not reduce the paper's central claims to its inputs. Theorems 4.3 and 4.5 are genuine applications of Graham's list-scheduling bound to deferral/provisioning parameters D(gamma,c) and M(B,c); they state conditional bounds, not empirical predictions, and the parameters are not fitted from the reported carbon savings. Theorems 4.4 and 4.6 decompose Definition 3.2 into W and weighted-average carbon intensities; this is an algebraic accounting identity, and the paper explicitly notes the savings can be negative (e.g., strictly increasing carbon traces), so the identity is not used as a self-fulfilling guarantee. The relative-importance score r_{v,t} (Definition 4.2) is an unvalidated proxy for precedence criticality, and the Fig. 13 ablation is limited; this is a correctness/robustness concern, not circularity, because r is taken from a JCT-trained scheduler and is not fitted to carbon outcomes, so Algorithm 1's decisions are not definitionally equal to the measured carbon reductions. Self-citations appear only as background for bounded carbon signals and threshold design; the load-bearing bounds come from external sources (Graham [25], k-search [45], Decima [48]). Prototype and simulator results are measurements against real traces and baselines, so the headline trade-off does not collapse into an input.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

No new physical or theoretical entities are proposed. PCAPS and CAP are software artifacts with released code and their own experimental falsifiable handles. The central claims rest on standard scheduling analysis (Graham's list scheduling), domain assumptions about bounded carbon signals and the linear c(t)E(t) model, and two ad hoc-to-paper design choices: the relative-importance proxy and the time scaling factor.

free parameters (4)
  • gamma (PCAPS carbon-awareness hyperparameter) = 0.5 (moderate config used for headline results)
    Hand-chosen in prototype and simulator experiments to represent 'moderate' carbon-awareness; the reported 32.9% and 39.7% carbon reductions depend on this setting, and results vary substantially with gamma (Figures 7 and 11).
  • B (CAP minimum resource quota) = 20 executors out of 100 (moderate config)
    Hand-chosen to balance carbon savings and ECT for the headline CAP results; the trade-off is sensitive to B (Figures 8 and 12).
  • theta (GreenHadoop adaptation parameter) = 0.5
    Tunable carbon-awareness parameter in the adapted GreenHadoop baseline (Appendix A.1.1); affects the baseline comparison but not the central PCAPS/CAP claims.
  • time scale factor = 1 real minute = 1 experiment hour
    All job durations are scaled by 1/60 (Section 6.1) so that hourly carbon intensity granularity is meaningful for multi-hour jobs; this makes carbon deferral possible and shapes the empirical savings.
assumptions (7)
  • standard math Graham's list scheduling bound: makespan on K identical machines is at most (2 - 1/K) times optimal.
    Used in the proofs of Theorem 4.3 (Appendix B.1.1) and Theorem 4.5 (Appendix B.2.1), cited as [25].
  • domain assumption Carbon intensity c(t) is bounded by known L and U over the relevant horizon.
    Section 2.1, following prior work [5,33]; required for the threshold functions Psi_gamma and Phi to be well-defined and for the k-search thresholds in CAP.
  • domain assumption Carbon footprint of a schedule is C(t) = c(t)E(t), linear in the number of active executors, excluding idle power, cooling, and embodied carbon.
    Section 3 defines C_ALG(t) := c(t)E_ALG(t); all reported carbon savings use this linear accounting model.
  • domain assumption A carbon-agnostic probabilistic scheduler (e.g., Decima) is an instance of list scheduling with a random list.
    Appendix B.1.1 relies on this to apply Graham's bound to the PB baseline; it presumes a single task is greedily assigned per idle machine without preemption.
  • ad hoc to paper The relative importance r_{v,t} = p_{v,t} / max_u p_{u,t} measures the precedence-driven importance of task v.
    Definition 4.2 and Algorithm 1; this is the load-bearing design assumption for PCAPS's deferral decisions and is not directly validated against critical-path metrics.
  • ad hoc to paper Experimental time scaling of 1 real minute = 1 experiment hour keeps hourly carbon granularity meaningful for job durations.
    Section 6.1 scales all job durations by 1/60; this modeling choice is specific to this paper's evaluation setup.
  • domain assumption Each job is a DAG of precedence-constrained tasks (stages) scheduled non-preemptively onto K machines.
    Section 2.1 formalizes the job model; inherited from Spark and prior DAG scheduling work.

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Cite this review

Pith. "Pith review of Carbon- and Precedence-Aware Scheduling for Data Processing Clusters." pith.science (2026). https://pith.science/paper/6VSEEFKX

@misc{pith2026250209717,
  author       = {Pith},
  title        = {Pith review of: Carbon- and Precedence-Aware Scheduling for Data Processing Clusters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6VSEEFKX}},
  note         = {Machine review of arXiv:2502.09717}
}
abstract

As large-scale data processing workloads continue to grow, their carbon footprint raises concerns. Prior research on carbon-aware schedulers has focused on shifting computation to align with availability of low-carbon energy, but these approaches assume that each task can be executed independently. In contrast, data processing jobs have precedence constraints (i.e., outputs of one task are inputs for another) that complicate decisions, since delaying an upstream ``bottleneck'' task to a low-carbon period will also block downstream tasks, impacting the entire job's completion time. In this paper, we show that carbon-aware scheduling for data processing benefits from knowledge of both time-varying carbon and precedence constraints. Our main contribution is $\texttt{PCAPS}$, a carbon-aware scheduler that interfaces with modern ML scheduling policies to explicitly consider the precedence-driven importance of each task in addition to carbon. To illustrate the gains due to fine-grained task information, we also study $\texttt{CAP}$, a wrapper for any carbon-agnostic scheduler that adapts the key provisioning ideas of $\texttt{PCAPS}$. Our schedulers enable a configurable priority between carbon reduction and job completion time, and we give analytical results characterizing the trade-off between the two. Furthermore, our Spark prototype on a 100-node Kubernetes cluster shows that a moderate configuration of $\texttt{PCAPS}$ reduces carbon footprint by up to 32.9% without significantly impacting the cluster's total efficiency.

Figures

Figures reproduced from arXiv: 2502.09717 by the authors.

Figure 1
Figure 1. Four scheduling policies for a motivating DAG and 18-hour-long carbon intensity trace (on the left hand side). [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. PCAPS interfaces with a probabilistic (PB) schedul￾ing policy. Given a probability distribution over nodes ➊, PCAPS computes a relative importance score ➋ that is used to determine which nodes should run based on the current carbon intensity ➌ – e.g., bottleneck nodes impeding job com￾pletion run regardless of carbon ➍, while less important nodes can be deferred for lower carbon periods ➎. 4.1 PCAPS From the discuss… view at source ↗
Figure 3
Figure 3. Illustrating PCAPS’s carbon-awareness filter. Jobs A and B are DAGs found in TPC-H queries and Alibaba traces, respectively [1, 60]. Highlighted nodes explain two schedul￾ing outcomes. In job A, the sampled node has low relative importance, so it is deferred. In contrast, job B’s sampled node is a bottleneck task with high relative importance: even when the current carbon intensity is high, such tasks are scheduled … view at source ↗
Figures from the paper (14 more)
Figure 5
Figure 5. Figure 5: Time-varying carbon intensity for six grids (detailed [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Visualizing executor usage over time for three schedulers, [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Relative carbon footprint and end-to-end completion [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: Relative carbon footprint and end-to-end completion [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 11
Figure 11. Figure 11: Relative carbon footprint and end-to-end com [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: Relative carbon footprint and end-to-end comple [PITH_FULL_IMAGE:figures/full_fig_p011_12.png]
Figure 13
Figure 13. Figure 13: Relative carbon footprint vs. end-to-end com [PITH_FULL_IMAGE:figures/full_fig_p012_13.png]
Figure 15
Figure 15. Figure 15: Executor usage (left) and number of jobs in the system (right) for an identical group of 50 TPC-H jobs in both the [PITH_FULL_IMAGE:figures/full_fig_p018_15.png]
Figure 16
Figure 16. Figure 16: plots the average carbon reduction, end-to-end completion time, and average per-job completion time with respect to FIFO for PCAPS, Decima, and CAP on top of FIFO in the simulator environment, using experiments with 12, 25, 50, 100, and 200 jobs. We find that the rela…
Figure 17
Figure 17. Figure 17: (a) Carbon reduction, (b) end-to-end completion time, and (c) average job completion time achieved by PCAPS, CAP, and Decima (relative to the Spark/Kubernetes default) in a single grid region for varying experiment sizes. Shaded regions denote the standard deviation a…
Figure 18
Figure 18. Figure 18: (a) Carbon reduction, (b) end-to-end completion time, and (c) average job completion time achieved by PCAPS, CAP-FIFO, and Decima (relative to FIFO) in a single grid region for varying Poisson interarrival times. Shaded regions denote the standard deviation across the…
Figure 19
Figure 19. Figure 19: (a) Carbon reduction, (b) end-to-end completion time, and (c) average job completion time achieved by PCAPS, CAP, and Decima (relative to the Spark/Kubernetes default) in a single grid region for varying Poisson interarrival times. Shaded regions denote the standard d…
Figure 20
Figure 20. Figure 20: (a) Average latency with N jobs in the queue and (b) average normalized time in the scheduler for PCAPS, CAP-FIFO, Decima, and FIFO in a single grid region for varying experiment sizes. Shaded region denotes the standard deviation across all 1000 trials. B Deferred An…
Figure 21
Figure 21. Figure 21: An example to contextualize how the optimal makespan differs when a job is given different amounts of machines. In [PITH_FULL_IMAGE:figures/full_fig_p026_21.png]

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Pith tools

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