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Multi-Scale Datacenter Power Modulation

Akshay Sreekumar, Nicolas Christianson, Fiodar Kazhamiaka, Ram Rajagopal

arXiv:2609.17809v1eess.SYcs.SY

TL;DR

Datacenters must modulate power under changing grid and infrastructure constraints without neglecting service impact. This paper coordinates delayed server transitions with fast worker throttling through a hierarchical receding-horizon controller. Across realistic power-cap trajectories, it reports lower cost than throttling-only and server-only baselines while satisfying power limits in real time.

  • Problem

    Datacenters must coordinate server states and worker throttling under time-varying power constraints, while minimizing the impact on hosted services.

    Source: §I · p. 1, A. Finite-Horizon Dynamic Control… · p. 5

  • Method

    A hierarchical receding-horizon controller separates slow server control from fast throttling recourse, using dual decomposition for the service-level convex problem and ranked-prefix search for server actions.

    Source: A. Contributions · p. 2

  • Results

    Across realistic power-cap trajectories, the controller reduces cost relative to throttling-only and server-only baselines while satisfying power limits in real time.

    Source: §VIII · p. 9

  • Takeaways & Limitations

    The controller is tractable at realistic datacenter sizes, and its performance typically approaches exact MPC on smaller instances.

    Source: §VIII · p. 9

    The framework remains a candidate for extension to richer models, including heterogeneous accelerator workloads, different service classes, and more detailed performance models.

    Source: §VIII · p. 9

Abstract

from arXiv · show

Cloud datacenters must increasingly modulate power in response to time-varying grid and infrastructure constraints. We study this problem as finite-horizon control of a networked hybrid dynamical system, where datacenter power and service capacity depend on interactions between servers, workers, and hosted services. Power can be reduced through fast continuous worker throttling, which acts immediately but degrades service capacity, and slow discrete server transitions, which provide deeper savings but evolve with delay. Coordinating these mechanisms yields a high-dimensional mixed-integer dynamic optimization problem which is intractable to solve at scale. We propose a hierarchical receding-horizon controller that separates slow server reconfiguration from fast throttling recourse. For fixed server states, the throttling layer reduces to a service-level convex recourse problem solved efficiently by dual decomposition. The server layer then uses a ranked-prefix search that evaluates candidate configurations through the recourse value over the planning horizon. Experiments on realistic instances with over 15,000 servers, 200,000 workers, and 1,400 services show that the controller satisfies time-varying power caps with no violations and substantially lower service impact than fast-only or slow-only baselines. Our method offers significant speedups compared to standard optimization solvers, computing near-optimal plans within a 20 second real-time control interval.

I. INTRODUCTION

Datacenters face growing grid and infrastructure constraints, while power reductions must balance savings against service capacity. The paper models this as a networked hybrid control problem and proposes a hierarchical controller coordinating fast worker throttling with slower server transitions.

I. INTRODUCTION

  • Grid load growth and infrastructure constraints motivate datacenters to modulate power, but power reductions must respect service performance and availability.Fast worker throttling responds immediately but degrades service capacity; slower server transitions save more power by eliminating base power, but require advance action.Source: §I · p. 1

II. SYSTEM MODEL

  • The paper formulates datacenter power modulation as finite-horizon hybrid control, capturing topology, power and capacity characteristics, and service-level impact.The modeled setting coordinates server transitions and worker throttling under time-varying exogenous power constraints.Source: A. Contributions · p. 2, §II · p. 3

A. Contributions

  • The hierarchical receding-horizon controller separates slow server control from fast throttling recourse for scalable, real-time operation.The formulation targets joint optimization of worker throttles and server states while satisfying power constraints and minimizing service impact.Source: A. Contributions · p. 2, §I · p. 2
  • Worker throttling is reduced to a service-level convex recourse problem that can be solved by dual decomposition.This addresses the large-scale throttle optimization required for fixed server states.Source: A. Contributions · p. 2, §I · p. 2
  • A ranked-prefix heuristic scores candidate server configurations using downstream recourse value over the planning horizon.The paper reports experiments on realistic datacenter simulations with time-varying power constraints to evaluate scalability and near-optimality.Source: A. Contributions · p. 2
  • The controller achieves the lowest episode cost across step, ramp, and oscillatory power-cap trajectories, with no budget violations and within the 20s planning constraint.The proposed approach coordinates server reconfiguration with throttling recourse to satisfy time-varying power constraints.Source: A. Contributions · p. 2

B. Related Work

  • Prior work spans power capping, dynamic capacity management, grid-facing flexibility, and hybrid optimization, but does not address their combination at datacenter scale.The paper focuses on coordinating fast throttling and slow server configuration under exogenous power budgets while limiting service impact.Source: B. Related Work · p. 2

A. Datacenter Topology and Control Dynamics

The model fixes worker-to-server and worker-to-service assignments over the control horizon, while servers move through delayed boot and shutdown states and workers are throttled by normalized CPU frequency. Server power includes baseline and throttle-dependent worker power, with worker power modeled as a service-parameterized convex quadratic.

A. Datacenter Topology and Control Dynamics

  • Worker throttles α_w represent normalized CPU frequency, range from the service threshold to 1, and yield no power or useful capacity at the threshold.Worker-to-server and worker-to-service assignments remain fixed over the control horizon.Source: A. Datacenter Topology and Control… · p. 3
  • Servers transition between ON, OFF, BOOT(k), and SHUT(k); transition states draw power but provide no capacity, and server actions are restricted by state.Booting is allowed only from OFF and shutdown only from ON; no further action is allowed until a transition completes.Source: A. Datacenter Topology and Control… · p. 3, Figure 1 · p. 3

B. Worker Power Model

  • While ON, server power includes baseline power and throttle-dependent worker power; each worker’s power is modeled as a convex quadratic in throttle.The power-model coefficients are determined by the worker’s service.Source: Figure 1 · p. 3, B. Worker Power Model · pp. 3–4

C. Worker Capacity Model

Worker capacity depends on throttle with diminishing returns, and active-server workers’ capacity is aggregated by service. The model also aggregates server power to datacenter power and estimates service impact from sampled load distributions.

C. Worker Capacity Model

  • Worker capacity is concave in throttle, with ρ_w representing assigned cores times per-core capacity and γ_w capturing diminishing returns from frequency scaling.The model parameters can be estimated from service profiling, throttling telemetry, or workload-class models.Source: C. Worker Capacity Model · p. 4

D. Datacenter Power Aggregation

  • Datacenter power scales aggregate IT power by a constant PUE and adds fixed background power independent of control actions.PUE does not model delayed cooling-power response to IT-load changes.Source: D. Datacenter Power Aggregation · p. 4

E. Service Capacity Aggregation

  • Service capacity aggregates workers across servers, but only workers hosted on ON servers contribute capacity.Workers of the same service may be distributed across multiple servers.Source: E. Service Capacity Aggregation · p. 4

F. Impact Model

  • Insufficient-capacity impact is estimated from empirical service-load distributions built by aggregating and binning worker utilization traces; the resulting function is convex and nonincreasing in capacity.It approaches 1 as capacity approaches zero and is zero when capacity exceeds all load samples.Source: F. Impact Model · p. 4

G. Deviation Model

The controller uses a finite-horizon MPC problem with power-budget and throttle constraints, balancing service impact against deviation from a nominal configuration. Its stagewise structure separates fixed-state throttle recourse from server decisions coupled over time, but realistic-scale optimization remains challenging.

G. Deviation Model

  • A deviation penalty biases the controller toward the fully provisioned nominal state after a power excursion and favors fewer idle servers and less throttling among equally low-impact actions.The nominal state is all servers ON with workers at α = 1, though another specified nominal configuration can be used.Source: G. Deviation Model · p. 4

A. Finite-Horizon Dynamic Control Problem

  • The H-step MPC optimizes server actions and worker throttles under power-budget and throttle-bound constraints, applies only the first actions, then updates the state and forecast before resolving.Service priority weights reflect operational importance, while a small weight applies to the deviation penalty.Source: A. Finite-Horizon Dynamic Control… · p. 5

B. Stagewise Reduction and α-Recourse Value Function

  • For a fixed post-action server state, worker throttles form a convex within-step recourse problem; states with no feasible throttle are assigned value +∞.Server decisions remain coupled across time through delayed transitions, unlike throttles, which have no intertemporal dynamics.Source: B. Stagewise Reduction and α-Recourse… · p. 5
  • With m servers and horizon H, the server action space grows as approximately 2^(mH), while repeated recourse evaluations over hundreds of thousands of worker variables can take several seconds with standard solvers.A typical instance has mH ≈ 90,000, making generic convex solvers too slow for online candidate scoring.Source: B. Stagewise Reduction and α-Recourse… · p. 5
  • The proposed hierarchy reduces worker throttling to a service-level convex problem solved by dual decomposition, then scores ranked-prefix server configurations through recourse values over the planning horizon.The recourse solver is used within the receding-horizon server controller.Source: B. Stagewise Reduction and α-Recourse… · p. 5

IV. AN EFFICIENT ALGORITHM FOR LARGE-SCALE

The α-recourse solver exploits symmetry and separability to evaluate candidate server configurations efficiently. Under the stated within-service homogeneity and aggregate-capacity assumptions, worker-level throttle variables can be reduced to one throttle per service without changing the optimal value.

IV. AN EFFICIENT ALGORITHM FOR LARGE-SCALE

  • The α-recourse algorithm exploits symmetry and separability to evaluate candidate server configurations efficiently and in a highly parallelizable way.Its evaluations feed the receding-horizon controller’s server-configuration scoring.Source: §IV · p. 5

A. Variable Reduction

  • The reduction preserves the extended optimal value when same-service active workers share throttle thresholds, power and capacity models, and impact depends only on aggregate service capacity.The result guarantees an optimal solution with one throttle variable per service when the recourse value is finite.Source: A. Variable Reduction · p. 6
  • Assigning a common throttle to active workers of each service preserves feasibility and optimality, reducing variables from O(|W|) to O(|Q|).This replaces one throttle per worker with one per service.Source: A. Variable Reduction · p. 6

B. Dual Decomposition via Bisection

Fixing server states reduces throttling to a service-level convex resource-allocation problem with a single aggregate power constraint. Nested bisection solves the coordinating power price and the independent service subproblems in parallel.

B. Dual Decomposition via Bisection

  • With fixed server states, the recourse problem has one throttle variable per service and a separable convex objective coupled only by the aggregate power budget.Fixed server and transition power is subtracted from the cap to form the reduced budget.Source: B. Dual Decomposition via Bisection · p. 6
  • The convex recourse problem is solved by dual decomposition: a scalar power-price multiplier coordinates independent one-dimensional service subproblems.For a fixed multiplier, evaluating the dual function requires solving one scalar minimization per service.Source: B. Dual Decomposition via Bisection · p. 6
  • Bisection updates the outer multiplier because induced power is nonincreasing in the single dual variable.The resulting supergradient is scalar and monotone.Source: B. Dual Decomposition via Bisection · p. 6
  • Each convex service subproblem is also solved by bisection, with independent solves run in parallel; the multiplier acts as an internal power price.Higher prices penalize power more strongly, while lower prices favor larger throttles to reduce service impact.Source: B. Dual Decomposition via Bisection · p. 6

V. A STRUCTURED RECEDING-HORIZON ALGORITHM FOR SERVER CONTROL

Server control is computationally difficult because the action space grows exponentially and delayed transitions affect future states and feasible actions. The proposed receding-horizon heuristic searches ranked-prefix actions and scores them using horizon-wide throttle recourse.

V. A STRUCTURED RECEDING-HORIZON ALGORITHM FOR SERVER CONTROL

  • Arbitrary server subsets create an exponentially large action space, and delayed transitions affect current and future power, capacity, and admissible actions.Even after separating convex recourse, exact reduced MPC remains impractical at datacenter scale.Source: §V · pp. 6–7

A. Ranked-Prefix Receding-Horizon Approximation

  • The controller evaluates a candidate current server action with an H-step rollout, assuming no later server actuation, and replans at each time step.Each rollout score includes the induced throttle-recourse value across the horizon.Source: §V · p. 7, A. Ranked-Prefix Receding-Horizon… · p. 7
  • A cheap static proxy ranks servers by weighted nominal capacity relative to baseline power, while the dynamic rollout score makes the final choice.The rollout accounts for delayed server dynamics and downstream throttle recourse.Source: A. Ranked-Prefix Receding-Horizon… · p. 7
  • Ranked-prefix search reduces each boot or shutdown choice to acting on the top k eligible servers, alongside a no-action option.The controller excludes arbitrary mixed boot/shutdown subsets.Source: A. Ranked-Prefix Receding-Horizon… · p. 7

B. Geometric Depth Search

The ranked-prefix depth search uses geometric probes followed by local refinement. It avoids assuming rollout scores are monotone or unimodal, since changing depth trades capacity against power headroom and throttle recourse.

B. Geometric Depth Search

  • Rollout scores need not be monotone or unimodal because every prefix reoptimizes throttle recourse, trading removed capacity against power headroom.Booting trades restored capacity against additional power consumption.Source: B. Geometric Depth Search · p. 7
  • A coarse-to-fine geometric search probes small, medium, and large depths with logarithmically many rollout evaluations.The probe sequence runs forward for shutdowns and in reverse for boots.Source: B. Geometric Depth Search · p. 8
  • Probing stops after ν consecutive failures to improve or when eligible servers are exhausted, then uniformly spaced depths around the best coarse probe are evaluated.The selected depth has the minimum rollout score among all evaluations.Source: B. Geometric Depth Search · p. 8

VI. EXPERIMENTAL SETUP

The evaluation uses realistic-scale instances for closed-loop performance and scalability, plus small synthetic instances for comparison with exact solutions. It compares real-time heuristics with optimization baselines and a dynamic-programming oracle.

1) Realistic Instance:

  • The realistic instance has 15,360 servers, 207,674 workers, and 1,422 services, with 20-second time steps and a 20-second decision deadline.It uses a six-step planning horizon and a 30-step episode.Source: 1) Realistic Instance · p. 8

2) Synthetic Instances:

  • Synthetic instances use 3–7 servers and roughly three services per server, enabling validation against exact methods across random seeds.These instances use a four-step horizon and 10-step episodes.Source: 2) Synthetic Instances · p. 8

B. Controllers and Baselines

5) GurobiMICP:

6) Dynamic Programming (DP) MPC:

  • The small-instance exact oracle uses dynamic programming over a time-expanded server-state graph, with throttle-recourse costs as transition costs.The reduced finite-horizon server-control problem can be solved exactly for small instances.Source: 5) GurobiMICP · p. 8, 6) Dynamic Programming (DP) MPC · p. 8

C. Scenarios

The evaluation covers step, ramp, and oscillating power caps, then assesses closed-loop performance, scalability, and near-optimality. The conclusion presents a tractable controller that coordinates worker throttling with server reconfiguration, while identifying richer datacenter models as future work.

C. Scenarios

  • The scenarios use three power-cap trajectories: a step drop and recovery, a ramp down and recovery, and a cosine-shaped oscillation followed by recovery.The step changes at T/4 and recovers at 3T/4; the ramp descends from 2T/5 and the oscillation spans the first 4T/5 slots.Source: C. Scenarios · p. 8

A. Closed-Loop Performance on Realistic Sizes

  • Across step, ramp, and oscillatory power caps, RankedPrefix has the lowest episode cost, no budget violations, and stays within the 20s planning constraint.On an oscillatory trajectory, it balances fewer server shutdowns with moderate throttling.Source: Table I · p. 9, A. Closed-Loop Performance on… · p. 9

B. Computational Scalability and Empirical Optimality

  • Under the 20s per-step limit, RankedPrefix scales beyond centralized baselines, while GurobiMICP returns poor or no incumbents as instances grow.GurobiFixedAlpha scales further but incurs higher cost relative to RankedPrefix because it omits throttling recourse.Source: B. Computational Scalability and… · p. 9
  • On 100 random small instances with varying topologies, service placements, and power-cap trajectories where dynamic programming is tractable, RankedPrefix’s optimality-gap distribution is concentrated near zero, and it is usually optimal or near-optimal.Source: B. Computational Scalability and… · p. 9

VIII. CONCLUSION

  • The controller uses service-level convex throttling recourse solved by dual decomposition and evaluates ranked-prefix server actions using downstream recourse value over the forecast horizon.This provides an online alternative to solving the mixed-integer dynamic optimization directly.Source: §VIII · p. 9
  • The framework remains open to extension to heterogeneous accelerator workloads, different service classes, and more detailed performance models.The paper identifies these richer datacenter models as future work.Source: §VIII · p. 9

APPENDIX I BASELINE AND ORACLE FORMULATIONS

The appendix describes exact dynamic programming for small instances and two optimization baselines that replan after each applied action. It also details their rollout formulations and reports controller comparisons.

A. Exact MPC via Dynamic Programming

  • Exact dynamic programming computes optimal remaining cost by a Bellman recursion over feasible server states and admissible actions, with zero terminal cost.The stage cost is the α-recourse value.Source: A. Exact MPC via Dynamic Programming · p. 9

B. Optimal One-Step Fixed Throttle Controller

  • GurobiFixedAlpha selects one admissible server action per server using binary action variables.The selected action is applied for the current step before replanning.Source: B. Optimal One-Step Fixed Throttle… · pp. 9–10
  • GurobiFixedAlpha precomputes rollout indicators for each action, then applies only the current optimal server action and replans at the next step.The rollout formulation includes epigraph variables for sampled expected-shortfall terms.Source: B. Optimal One-Step Fixed Throttle… · pp. 9–10
  • On an oscillatory power trajectory, RankedPrefix satisfies the budget and has 63.7% lower final cumulative cost than AlphaOnly and 89.7% lower than ServerOnly.The figure attributes the balance to avoiding aggressive throttling and excessive server shutdowns.Source: Figure 2 · p. 10

C. Optimal One-Step Mixed Integer Convex Controller

  • Unlike GurobiFixedAlpha, GurobiMICP optimizes service-level throttles over the rollout alongside server actions.It maintains one throttle per service and rollout step and introduces auxiliary variables for realized throttles, worker power, and capacity.Source: C. Optimal One-Step Mixed Integer… · p. 10
  • Under a 20s per-step limit, RankedPrefix closely matches exact MPC on 100 small instances, with median and mean episode-cost gaps of 0.0% and 0.4%.The scalability figure also marks whether plans finish within the limit, yield a feasible incumbent, or find no feasible plan.Source: Figure 3 · p. 11
  • GurobiMICP linearizes the action-dependent throttle constraint and imposes constraints on service capacity and total power.The formulation defines realized service capacity as the sum of capacity contributions across servers.Source: C. Optimal One-Step Mixed Integer… · pp. 10–11

APPENDIX II DETAILS ON INSTANCE GENERATION

The instance-generation details describe both a power-driven datacenter simulator and procedurally generated small instances for exact-method validation.

Instance generation

  • The realistic simulator samples and places servers from a catalog until a power budget is met, then creates services and workers to reach target core utilization.Service priorities are sampled from a heavy-tailed distribution, and worker placement respects per-server core capacity.Source: APPENDIX II DETAILS ON INSTANCE… · p. 11
  • Per-worker utilization traces combine a flat baseline, daily and weekly seasonalities, and Gaussian noise, then are aggregated into per-service load histograms.The histograms support sampling loads for the impact-function approximation.Source: APPENDIX II DETAILS ON INSTANCE… · p. 11

Small synthetic instances

  • Small validation instances use fixed-power, fixed-core servers and services sampled across three priority tiers, biased toward low-priority services.The number of services in each tier scales with the target server count.Source: APPENDIX II DETAILS ON INSTANCE… · p. 11
  • Small-instance services are placed on random subsets of servers, and their demand samples are Gaussian, clipped at zero.Random seeds vary service placements and demand realizations across instances.Source: APPENDIX II DETAILS ON INSTANCE… · p. 11

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