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DataCenterGym: A Physics-Grounded Simulator for Multi-Objective Data Center Scheduling
Nilavra Pathak, Samadrita Biswas, Nirmalya Roy
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 95%
Last extracted: 4/27/2026, 6:25:20 PM
Summary
DataCenterGym is a physics-grounded, Gymnasium-compatible simulation environment designed for evaluating multi-objective scheduling in geo-distributed data centers. It integrates complex physical couplings between compute workloads, thermal dynamics (using an RC model), HVAC control (via PID), and power consumption. The paper introduces a Hierarchical Model Predictive Control (H-MPC) algorithm that performs joint job placement and thermal setpoint optimization, outperforming various baseline policies (Random, Greedy, Thermal-Aware, and Power-Aware) by accounting for thermal inertia and delayed physical effects.
Entities (9)
Relation Signals (5)
PID Controller → controls → Cooling Power
confidence 100% · tracked by local PID controllers that determine the resulting cooling power
DataCenterGym → uses → Alibaba cluster trace dataset
confidence 100% · Workload arrivals are instantiated from the Alibaba cluster trace dataset [1]
DataCenterGym → integrates → Lumped Thermal RC Model
confidence 95% · The simulator integrates compute queueing, building thermal dynamics, localized HVAC behavior...
DataCenterGym → integrates → RC Model
confidence 95% · The simulator integrates compute queueing, building thermal dynamics, localized HVAC behavior...
H-MPC → improves → Scheduling Performance
confidence 90% · we demonstrate how H-MPC improves scheduling performance relative to baseline schedulers.
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Abstract
Abstract:Modern datacenters schedule heterogeneous workloads across geo-distributed sites with diverse compute capacities, electricity prices, and thermal conditions. Compute utilization, heat generation, cooling demand, and energy consumption are tightly coupled, yet most existing schedulers abstract these effects and treat them independently. We present \textit{DataCenterGym}, a physics-grounded simulation environment for job scheduling in geo-distributed data centers, designed as a reusable testbed for future research. The simulator integrates compute queueing, building thermal dynamics, localized HVAC behavior, and temperature-dependent service degradation within a Gymnasium-compatible interface. We also develop a Hierarchical Model Predictive Control (H-MPC) scheduling algorithm that performs distributed job placement while explicitly accounting for thermal and power dynamics. Through experiments on nominal operation and workload sensitivity, we demonstrate how H-MPC improves scheduling performance relative to baseline schedulers.
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- Source: https://arxiv.org/abs/2604.15594v1
- Canonical: https://arxiv.org/abs/2604.15594v1
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DataCenterGym: A Physics-Grounded Simulator for Multi-Objective Data Center Scheduling Nilavra Pathak1, Samadrita Biswas2, and Nirmalya Roy3 Abstract Modern datacenters schedule heterogeneous workloads across geo-distributed sites with diverse compute capacities, electricity prices, and thermal conditions. Compute utilization, heat generation, cooling demand, and energy consumption are tightly coupled, yet most existing schedulers abstract these effects and treat them independently. We present DataCenterGym, a physics-grounded simulation environment for job scheduling in geo-distributed data centers, designed as a reusable testbed for future research. The simulator integrates compute queueing, building thermal dynamics, localized HVAC behavior, and temperature-dependent service degradation within a Gymnasium-compatible interface. We also develop a Hierarchical Model Predictive Control (H-MPC) scheduling algorithm that performs distributed job placement while explicitly accounting for thermal and power dynamics. Through experiments on nominal operation and workload sensitivity, we demonstrate how H-MPC improves scheduling performance relative to baseline schedulers. I Introduction The rapid expansion of hyperscale and edge data centers is driven by growing demand for large-scale AI training, cloud services, and latency-sensitive applications. These facilities account for a substantial and rising share of global electricity consumption, posing significant challenges in thermal management, energy provisioning, and sustainable operations [14, 10]. Operators must continuously adapt to fluctuating workloads and heterogeneous infrastructure while maintaining thermal safety, hardware reliability, and performance across geographically distributed sites. Traditional resource managers were designed to optimize utilization and latency, but largely ignore the environmental interactions. Job execution generates heat proportional to resource consumption, raising internal temperature and driving cooling demand. Due to thermal inertia, these effects unfold over minutes to hours rather than instantaneously [18]. Hence, schedulers optimizing for short-term throughput can inadvertently cause thermal violations. This delayed effects can harm the hardware devices over time. Geographic distribution further amplifies these challenges. A GPU workload executed in Phoenix during summer requires substantially more cooling than the same workload in Seattle. Most production schedulers model data centers as interchangeable capacity pools, without explicitly accounting for thermal and power dynamics [26, 9]. High-density accelerators further exacerbate the problem: GPU clusters generate approximately 33–4×4× higher heat density per node than CPU clusters [20, 32], placing increased stress on cooling systems and increasing the risk of thermal throttling under sustained load. This simultaneously increases the energy usage, and hence the carbon footprint and cost of operations. The Challenge: Prior work has explored power-aware scheduling [27] and control-theoretic approaches to thermal management in data centers [12]. However, there is no comprehensive dataset or evaluation framework that jointly captures the full range of environmental and operational interactions in modern data centers. As a result, simulation-based platforms have emerged as a practical means to evaluate control-theoretic and reinforcement learning approaches for scheduling [13]. Existing simulators, however, do not support closed-loop physical dynamics. Consequently, the interactions among scheduling decisions, temperature evolution, cooling demand, and thermal throttling under temperature spikes cannot be fully explored. Evaluating policies that explicitly reason about these inter-dependencies requires a unified simulation environment that integrates workload dynamics, thermal physics, and cooling control. This setting introduces several fundamental challenges: • Coupled objectives: Scheduling decisions must balance throughput, latency, energy efficiency, and thermal safety under shared physical constraints, where improving one objective can degrade others. • Delayed physical effects: Thermal inertia and cooling response times induce delayed thermal stress. The impact of a scheduling decision may emerge gradually over time. • Heterogeneity and scale: Geo-distributed data centers exhibit diverse climate conditions, hardware characteristics, power limits, and electricity pricing, resulting in location-dependent thermal and cost profiles for identical workloads. • Realistic workload modeling: Synthetic or simplified job traces fail to capture key characteristics of real workloads. They miss hardware affinity constraints and the temporal arrival patterns observed in production systems. Our Contributions. This paper presents DataCenterGym, a physics-aware simulation environment for geo-distributed data centers. It enables the evaluation of scheduling policies under coupled thermal, power, and workload dynamics. Our contributions are as follows: 1. Simulator modeling heat generation, thermal evolution, localized HVAC control, and thermal throttling across heterogeneous compute clusters in geographically distributed data centers. 2. Integration of production-scale workload traces capturing realistic job arrivals, execution durations, resource demands, and hardware affinity constraints. 3. A safety-constrained Model Predictive Control algorithm that jointly schedules jobs and thermostat setpoints to achieve optimal performance under physical constraints. 4. Experimental evaluations across nominal operation and varying workload intensities. These experiments reveal how physical couplings materially influence scheduling policy performance. DataCenterGym enables principled evaluation of datacenter scheduling algorithms under realistic thermal and power constraints without requiring access to production infrastructure. I Related Works Geo-distributed scheduling: Geographic load balancing reduces operational cost by routing workloads across regions with heterogeneous electricity prices [23], with extensions for deadlines, data locality, and capacity constraints [28, 30, 19]. Most approaches treat power and thermal limits as fixed feasibility constraints rather than dynamic states coupled to workload decisions. Datacenter resource managers: Production systems such as Borg [26] and Mesos [9] prioritize scalability, fairness, and utilization, while thermal management is handled reactively through throttling or emergency cooling [18]. Consequently, schedulers are rarely evaluated for temporal thermal or energy effects. Thermal- and power-aware scheduling: Temperature-aware placement mitigates hotspots and cooling demand [18], and joint workload–cooling coordination reduces energy use [17]. Power-aware schedulers such as PMapper [27] enforce instantaneous limits but do not account for thermal inertia. Anticipatory control [12, 3], together with data-driven forecasting of building-level thermal dynamics [21, 22], motivates predictive models used in control-oriented scheduling. Carbon-aware scheduling: Schedulers exploit spatial and temporal variation in grid carbon intensity to reduce emissions [24, 7, 31, 6], but rely on coarse-grained power models that omit cooling and thermal constraints. Hierarchical demand-response mechanisms coordinate operators and tenants under power limits [29]. Learning-based scheduling: Reinforcement learning has been applied to cluster-scale scheduling [15] and extended to geo-distributed systems [19]. Policy performance depends critically on simulator fidelity; omitting thermal inertia, cooling response, or power limits risks poor generalization. Simulation platforms: CloudSim-style simulators support geo-distribution and energy modeling [5, 11, 2] but decouple scheduling from delayed physical feedback. SustainGym [13] and Clockwork [25] benchmark sustainability-aware optimization while abstracting job placement and thermal throttling. OpenDC [16] emphasizes scalability but omits closed-loop thermal and cooling interactions. Positioning: DataCenterGym provides a closed-loop, cyber–physical simulation of geo-distributed data centers that jointly models job scheduling, queueing, thermal dynamics, cooling control, and power constraints, enabling evaluation beyond capacity-only abstractions. I DataCenterGym Environment DataCenterGym models online job allocation as a controlled, discrete-time stochastic environment whose state transitions are driven by workload arrivals, job execution, thermal dynamics, cooling control, and power evolution. By varying workload characteristics, ambient conditions, and physical parameters, the environment spans diverse operating regimes while preserving a consistent decision structure. This section defines the state, action space, and system dynamics. Figure 1: Closed-loop interaction in DataCenterGym. The scheduler observes the system state, selects job assignment and cooling actions, and the environment advances via coupled workload execution, thermal dynamics, and power evolution. I-A Problem Formulation We consider an online scheduling problem over C compute clusters distributed across D geo-distributed datacenters. Time is discretized into intervals t=0,…,Tt=0,…,T with step size Δt t. Jobs arrive over time with heterogeneous resource demands, execution durations, priorities, and hardware affinities, and must be scheduled subject to compute capacity, thermal, and power constraints. I-A1 State Space The system state comprises cluster-level scheduling variables and datacenter-level environmental variables. At the cluster level, each cluster i∈1,…,Ci∈\1,…,C\ is characterized by: (i) available electrical power capacity pi,tp_i,t, (i) effective compute capacity ci,tc_i,t, and (i) queue length qi,tq_i,t. Cluster utilization ui,tu_i,t is defined as the total active resource demand assigned to cluster i ( Section I-B3) and is therefore not included as an independent state variable. At the datacenter level, each datacenter d∈1,…,Dd∈\1,…,D\ maintains: (i) an internal thermal state θd,t _d,t, representing a control-level temperature proxy, (i) ambient (outdoor) temperature θd,tambθ^amb_d,t, and (i) electricity price ψd,t _d,t. These variables are shared across all clusters hosted within the same datacenter. The scheduler observes the aggregated system state ot=[pi,t,ci,t,qi,t]i=1C⊕[θd,t,θd,tamb,ψd,t]d=1D,o_t= [p_i,t,\;c_i,t,\;q_i,t ]_i=1^C\; \; [ _d,t,\;θ^amb_d,t,\; _d,t ]_d=1^D, (1) yielding an observation dimension of 3C+3D3C+3D. I-A2 Action Space The action at time t is given by at=(atjob,atcool)a_t=(a^job_t,a^cool_t), consisting of job assignment and cooling control decisions. For each arriving job j∈tj _t, the scheduler selects an assignment atj∈1,…,Ca^j_t∈\1,…,C\, where atj=ia^j_t=i assigns the job to cluster i, and atj=0a^j_t=0 defers the job to a future time step. Cooling actions specify datacenter-level temperature setpoints atcool=[θ1,ttarget,…,θD,ttarget]∈[θmin,θmax]D,a^cool_t= [θ^target_1,t,…,θ^target_D,t ]∈[ _ , _ ]^D, (2) which are tracked by local PID controllers that determine the resulting cooling power Φd,tcool ^cool_d,t. In our evaluation, dynamic cooling setpoints are optimized only by MPC-based controllers. Heuristic baselines operate with fixed, datacenter-specific setpoints and do not actively control cooling. I-B System Dynamics This subsection describes the physical processes governing state transitions, including workload arrivals, job execution, thermal evolution, cooling control, throttling, ambient conditions, power consumption, and electricity pricing. I-B1 Time Model and System Indexing Each cluster i is characterized by a heat generation coefficient αi _i (W per unit of compute), a compute power coefficient ϕi _i (W per unit of compute), and a maximum compute capacity cimaxc _i. Clusters within the same datacenter share thermal and electrical infrastructure; thermal dynamics and cooling control are modeled at the datacenter level. I-B2 Workload Model At each time step, the environment generates a batch of jobs λt=(rj,dj,vj,τj)j∈t _t=\(r_j,d_j,v_j, _j)\_j _t, where rjr_j denotes required resources, djd_j is execution duration, vjv_j is priority, and τj∈CPU,GPU _j∈\CPU,GPU\ specifies hardware affinity. Jobs not scheduled immediately remain queued. Workload arrivals are instantiated from the Alibaba cluster trace dataset [1], providing realistic arrival patterns, execution durations, resource demands, and hardware constraints observed in production systems. I-B3 Job Execution Model Jobs execute over multiple time steps, with remaining duration evolving as dj,t+1rem=dj,trem−1d^rem_j,t+1=d^rem_j,t-1, until completion. Cluster utilization is given by ui,t=∑j∈i,trju_i,t= _j _i,tr_j, where i,tA_i,t denotes the set of active jobs assigned to cluster i, subject to the capacity constraint ui,t≤ci,tu_i,t≤ c_i,t. Completed jobs with dj,t+1rem=0d^rem_j,t+1=0 are removed. The queue length qi,tq_i,t tracks the number of waiting (unscheduled) jobs associated with cluster i. I-B4 Thermal Dynamics Datacenter temperature evolves according to a lumped thermal RC model [22]: θd,t+1=θd,t+ΔtCd∑i∈dαiui,t⏟Compute Heat−ΔtCdRd(θd,t−Td,tamb)⏟Passive Dissipation−ΔtCdΦd,tcool⏟Active Cooling. _d,t+1= _d,t+ tC_d _i _d _iu_i,t_Compute Heat\!-\! tC_dR_d( _d,t-T^amb_d,t)_Passive Dissipation\!-\! tC_d ^cool_d,t_Active Cooling. (3) where dC_d denotes the set of clusters hosted in datacenter d, and RdR_d and CdC_d are thermal resistance (°C/W) and capacitance (J/°C), respectively. This formulation captures thermal inertia linking present scheduling decisions to future thermal constraints. I-B5 PID Cooling Control Cooling power is determined by a PID controller: Φd,tcool=min(Φdmax⏟Cooling Limit,Kpet⏟Proportional+Ki∑τ=0teτΔt⏟Integral+Kdet−et−1Δt⏟Derivative), ^cool_d,t= \! ( _d_Cooling Limit,\; K_pe_t_Proportional\!+\! K_i\! _τ=0^te_τ t_Integral\!+\! K_d e_t-e_t-1 t_Derivative ), (4) where et=max(0,θd,t−Td,ttarget)e_t= (0, _d,t-T^target_d,t) is the temperature tracking error, and KpK_p, KiK_i, and KdK_d are controller gains. I-B6 Thermal Throttling via Soft Constraints Sustained high temperatures trigger throttling that degrades effective compute capacity. For each datacenter d, we define thresholds θdsoft _d^soft (throttling onset) and θdmax _d (hard limit). Effective cluster capacity is ci,teff=cimaxg(θd,t),c^eff_i,t=c _i\,g( _d,t), (5) where ci,teff=cimaxmax(gmin,min(1, 1−(1−gmin)θd,t−θdsoftθdmax−θdsoft)).c^eff_i,t=c _i\, \! (g_ ,\; \! (1,\;1-(1-g_ ) _d,t- _d^soft _d - _d^soft ) ). (6) I-B7 Ambient Temperature Ambient temperature follows a diurnal process: θd,tamb=θbase,d+Adsin(2πtθ)+ϵt,ϵt∼(0,σ2),θ^amb_d,t= _base,d+A_d \! ( 2π tθ )+ _t, _t (0,σ^2), (7) capturing climate-dependent outdoor variability. When available, real temperature traces can be loaded in place of this model. I-B8 Power Dynamics Available electrical power capacity evolves as pi,t+1=pi,t⏟Available Power−ϕiui,t⏟Compute Power−κiΦd(i),tcool⏟Cooling Power+wi,t⏟Grid Inflow.p_i,t+1= p_i,t_Available Power\!-\! _iu_i,t_Compute Power\!-\! _i ^cool_d(i),t_Cooling Power\!+\! w_i,t_Grid Inflow. (8) where κi _i denotes the cluster-level cooling power coupling coefficient, d(i)d(i) is the datacenter hosting cluster i, and wi,tw_i,t represents grid power inflow. The environment enforces pi,t≥0p_i,t≥ 0 via admission control. I-B9 Electricity Pricing Electricity prices vary by location and time. Each datacenter faces time-varying prices, with ψd,t=ψdpeak _d,t= _d^peak for t∈peakt _peak and ψd,t=ψdoff-peak _d,t= _d^off-peak otherwise. Total operational cost is Costt=∑d=1D(ψd,t∑i∈dϕiui,t⏟Compute Cost+ψd,tΦd,tcool⏟Cooling Cost)Δt.Cost_t= _d=1^D ( _d,t\! _i _d _iu_i,t_Compute Cost\!+\! _d,t ^cool_d,t_Cooling Cost ) t. (9) I-B10 Cluster Dynamics and Job Progression Cluster state evolves through utilization updates, power consumption, and job completion. Completed jobs are removed from execution, and queue lengths are updated accordingly. IV Scheduling Policies for Evaluation We evaluate a representative set of scheduling policies spanning random, heuristic, and model-based control approaches to quantify trade-offs among throughput, queueing latency, thermal safety, and energy efficiency. All policies operate within the same DataCenterGym interface and are subject to identical feasibility and safety constraints. At each decision epoch t, the scheduler observes the system observation oto_t and selects a job allocation action at∈(ot)a_t (o_t). Notation Jobs are indexed by j, clusters by i, data centers by d, and time by t. Job j requires rjr_j units of compute of type τ(j)∈CPU,GPUτ(j)∈\CPU,GPU\. Cluster i has effective compute capacity ci,tc_i,t and utilization ui,tu_i,t, where ci,t=cimaxg(θd(i),t)c_i,t=c_i g( _d(i),t) accounts for thermal throttling. dC_d denotes the set of clusters hosted in data center d, and dτ⊆dC_d^τ _d the subset supporting hardware type τ. The set ℱ(j,ot)F(j,o_t) denotes clusters feasible for job j under observation oto_t, accounting for capacity, hardware affinity, and safety constraints. Thermal and power parameters θd,t _d,t denotes data center temperature, θd,ttargetθ^target_d,t the cooling setpoint, αi _i the heat-generation coefficient, and ϕi _i the compute power coefficient. The function g(θ)∈[0,1]g(θ)∈[0,1] denotes the monotone thermal throttling function defined in Section I. IV-A Random Baseline The random baseline assigns each arriving job uniformly at random among feasible clusters: ℙ(atj=i∣ot)=1|ℱ(j,ot)|,i∈ℱ(j,ot),0,otherwise.P(a^j_t=i o_t)= cases 1|F(j,o_t)|,&i (j,o_t),\\ 0,&otherwise. cases (10) This policy ignores physical system state and provides a lower-bound baseline. IV-B Greedy Capacity-Based Policy The greedy policy assigns each job to the feasible cluster with the lowest normalized utilization: i⋆=argmini∈ℱ(j,ot)ui,tci,ts.t.ci,t−ui,t≥rj.i = _i (j,o_t) u_i,tc_i,t .t. c_i,t-u_i,t≥ r_j. (11) This promotes load balancing and throughput but does not account for thermal dynamics or energy impact. IV-C Thermal-Aware Heuristic The thermal-aware heuristic routes jobs to avoid instantaneous thermal hotspots. For assigning job j to cluster i, the estimated post-assignment data center temperature proxy is θ~d(i),t(j)=θd(i),t+αirj. θ_d(i),t(j)= _d(i),t+ _ir_j. (12) Jobs are assigned to the feasible cluster minimizing θ~d(i),t(j) θ_d(i),t(j). This reduces immediate thermal stress but remains myopic to thermal inertia and future workload evolution. IV-D Power and Cooling-Aware Heuristic The power–cooling heuristic minimizes instantaneous energy impact. The marginal incremental power draw of assigning job j to cluster i is approximated by ΔPi,t(j)=ϕirj+ωΦ^d(i),tcool(j), P_i,t(j)= _ir_j+ω\, ^cool_d(i),t(j), (13) where ω>0ω>0 weights cooling relative to compute power and Φ^d,tcool(j) ^cool_d,t(j) estimates incremental cooling power: Φ^d,tcool(j)≈γ(θd,t−θd,ttarget⏟Thermal gap+Rdαirj⏟Heat load). ^cool_d,t(j)≈γ ( _d,t-θ^target_d,t_Thermal gap+ R_d _ir_j_Heat load ). (14) with gain γ>0γ>0. Jobs are assigned to the feasible cluster minimizing ΔPi,t(j) P_i,t(j). This policy captures instantaneous efficiency but does not plan over time. IV-E Safety-Constrained Model Predictive Control (SC-MPC) Model Predictive Control (MPC) solves a finite-horizon constrained optimization problem and replans at each step using new observations. Safety-constrained MPC (SC-MPC) [8] extends this framework by explicitly enforcing safety-critical limits via hard constraints and penalized soft constraint violations. Formally, following the notation of [8], consider discrete-time dynamics x(k+1)=f(x(k),u(k);η(k))x(k+1)=f(x(k),u(k);η(k)) with exogenous inputs η(k)η(k). At time k, SC-MPC solves min, _U, ξ ℓf(xN|k)+∑i=0N−1ℓ(xi|k,ui|k,ξi|k) _f(x_N|k)+ _i=0^N-1 (x_i|k,u_i|k, _i|k) (15) s.t. x0|k=x(k), x_0|k=x(k), (16) xi+1|k=f(xi|k,ui|k;η^i|k), x_i+1|k=f(x_i|k,u_i|k; η_i|k), (17) ui|k∈hard, u_i|k _hard, (18) xi|k∈hard, x_i|k _hard, (19) xi|k∈soft(ξi|k),ξi|k≥0. x_i|k _soft( _i|k), _i|k≥ 0. (20) where hard constraints enforce non-negotiable safety limits and soft constraints allow controlled violations through slack variables. Instantiation in DataCenterGym We set x(k)≡okx(k)≡ o_k and u(k)≡aku(k)≡ a_k. Predicted states evolve as o^k+i+1=f(o^k+i,ak+i;η^k+i), o_k+i+1=f( o_k+i,a_k+i; η_k+i), (21) where nominal exogenous inputs η η (ambient temperature and electricity price) effect the system evolution. Hard constraints enforce thermal and capacity safety: θ^d,k+i θ_d,k+i ≤θdmax, ≤ _d , (22) 0≤u^i,k+i 0≤ u_i,k+i ≤cimaxg(θ^d(i),k+i), ≤ c_i g( θ_d(i),k+i), (23) θd,k+itarget θ^target_d,k+i ∈[θmin,θmax]. ∈[ _ , _ ]. (24) IV-F Hierarchical Joint Scheduling and Thermal Control MPC We formulate data center operation as a joint scheduling and thermal control problem with a hybrid (discrete–continuous) action space. To achieve tractable optimization at scale, we adopt a Hierarchical MPC (H-MPC) architecture that decomposes control into (i) a data center-level supervisory MPC over horizon H1H_1 and (i) per-datacenter cluster-level scheduling MPCs over horizon H2H_2. Different horizons reflect slow thermal dynamics versus fast workload dynamics, with H2≤H1H_2≤ H_1 ensuring consistency with long-term thermal planning while remaining computationally tractable. IV-F1 Composite Action Space At each decision epoch t, the controller outputs a composite action at=(atsched,attherm)a_t= (a^sched_t,\;a^therm_t ), where atsched∈scheda^sched_t _sched and attherm=θd,ttargetd=1D∈[θmin,θmax]Da^therm_t=\θ^target_d,t\_d=1^D∈[ _ , _ ]^D. IV-F2 Stage 1 – Data Center-Level Supervisory MPC This stage optimizes admission decisions and thermal setpoints over horizon H1H_1 using aggregate workload variables. Let ρτ,k∈[0,1] _τ,k∈[0,1] denote the admission fraction for job type τ, and let nτ,kn_τ,k be the number of arrivals. The optimization problem tries to minimize total Energy, Queue Length, Thermal Difference from Target setpoints and admission (with soft thermal constraints) by minρτ,k,θd,ktarget,ξd,k∑k=0H1−1(λEEk⏟Energy+λQQk⏟Queue/Backlog+λT‖θd,k−θref‖2⏟Temperature Deviation) _\ _τ,k,\,θ^target_d,k,\, _d,k\ _k=0^H_1-1 ( _EE_k_Energy+ _QQ_k_Queue/Backlog+ _T\| _d,k-θ^ref\|^2_Temperature Deviation ) +∑k=0H1−1(λR∑τnτ,k(1−ρτ,k)⏟Rejection / Low-admission Penalty+λξ∑dξd,k⏟Slack Penalty) + _k=0^H_1-1 ( _R _τn_τ,k(1- _τ,k)_Rejection / Low-admission Penalty+ _ξ _d _d,k_Slack Penalty ) (25) subject to box constraints ρτ,k∈[0,1] _τ,k∈[0,1], θd,ktarget∈[θmin,θmax]θ^target_d,k∈[ _ , _ ], and soft thermal limits θd,k≤θdmax+ξd,k _d,k≤ _d + _d,k with ξd,k≥0 _d,k≥ 0, we enforce admission feasibility: ρτ,knτ,k⏟Admitted≤∑i∈dτ⌊ci,k−ui,kr¯τ⌋⏟Max Feasible in DC d,∀d,τ,k. _τ,kn_τ,k_Admitted≤ _i _d^τ c_i,k-u_i,k r^τ _Max Feasible in DC $d$,\ ∀ d,τ,k. (26) IV-F3 Stage 2 – Cluster-Level Scheduling MPC Given fixed setpoints and admission quotas from Stage 1, Stage 2 allocates jobs to individual clusters over horizon H2H_2. Let xτ,i(k)x^(k)_τ,i denote the number of type-τ jobs assigned to cluster i at time k. We minimize (queueing, energy, rejection) by minxτ,i(k) _\x^(k)_τ,i\ ∑k=0H2−1(λQ∑iqi,k⏟Queue/Backlog+λEEk⏟Energy)+λrej∑k,τrτ,k⏟Job Rejection _k=0^H_2-1 ( _Q _iq_i,k_Queue/Backlog+ _EE_k_Energy )+ _rej _k,τr_τ,k_Job Rejection (27) subject to ∑i∈dτxτ,i(k)⏟Routed Jobs=aτ,d(k)⏟Quota,xτ,i(k)r¯τ⏟Demand≤ci,k−ui,k⏟Headroom,xτ,i(k)∈ℝ+. _i _d^τx^(k)_τ,i_Routed Jobs\!=\! a^(k)_τ,d_Quota, x^(k)_τ,i r^τ_Demand\!≤\! c_i,k-u_i,k_Headroom, x^(k)_τ,i _+. IV-F4 Computational Complexity A centralized SC-MPC formulation introduces binary job–cluster assignment variables over horizon H = max(H1,H2) (H_1,H_2), leading to exponential worst-case complexity O(2CJH)O(2^CJH), where C denotes the number of clusters and J the number of jobs per time step. Relaxing these integrality constraints yields a polynomial-time optimization with complexity O((CJH)3)O((CJH)^3), which remains computationally prohibitive at scale. In contrast, H-MPC exploits hierarchical and geo-distributed structure by decomposing control into a low-dimensional data center–level supervisory MPC and D parallel per–data center scheduling subproblems, yielding a per-epoch complexity O(D3H3)+D⋅O((CJH/D2)3)O(D^3H^3)+D· O\! ((CJH/D^2)^3 ), which is strictly smaller than O((CJH)3)O((CJH)^3) for any D>1D>1 and enables scalable optimization in large systems. V Experimental Setup TABLE I: Experimental configuration (20 clusters across 4 datacenters). PID gains: KpK_p=4000–7000, KiK_i=80–150, KdK_d=800–1500. Throttling: θsoft _soft=32∘C, θmax _ =35∘C. Nominal regime: 200 jobs/step, 40/60 CPU/GPU. DC Clusters Capacity (CU) θamb _amb $/kWh R/CR/C Cooling Seattle 3CPU/2GPU 252K (157C,150G) 10± 5 0.08/0.06 0.003/700M 0.68MW, gming_ =0.2 α: CPU[0.3–0.7], CPU[4.0–5.0] T1,tT_1,t=23∘C Phoenix 2CPU/CPU 235K (65CPU,170G) 38± 12 0.22/0.14 0.004/600M 1.22MW, gming_ =0.7 α: CPU[0.6–0.8], CPU[6.5–8.0] T2,tT_2,t=25∘C Chicago 3CPU/2GPU 204K (144CPU,60GPU) 16± 10 0.13/0.09 0.005/550M 0.30MW, gming_ =0.4 α: CPU[0.4–0.6], GPU[3.5–4.5] T3,tT_3,t=24∘C Dallas 2CPU/3GPU 370K (90CPU,280GPU) 30± 11 0.19/0.11 0.002/520M 1.97MW, gming_ =0.3 α: CPU[0.5–0.7], GPU[6.0–9.0] T4,tT_4,t=24∘C We evaluate scheduling policies using Monte Carlo simulation on a geo-distributed datacenter topology with heterogeneous hardware. Unless otherwise stated, all experiments operate in the nominal regime targeting 60–70% utilization. V-A Simulation Environment All experiments use the DataCenterGym environment defined in Section I, including thermal dynamics, throttling behavior, and energy accounting. Here we summarize only the parameters relevant to the experimental configuration. Thermal Dynamics and Throttling Parameters: Datacenters follow the lumped RC thermal model and throttling mechanism described in Section I. The temperature state θ is modeled as a single scalar per datacenter, serving as a control-level thermal proxy rather than a physical CPU junction temperature. Accordingly, soft and hard thermal limits are defined at θsoft=32∘ _soft=32 C and θmax=35∘ _ =35 C, respectively, to induce throttling behavior within this abstracted model rather than to reflect realistic hardware operating thresholds (typically ∼ 80∘C), which are outside the scope of the lumped building-level RC approximation. Minimum throttling factors gming_ vary across datacenters in the range [0.2, 0.7][0.2,\,0.7]. Cooling setpoints are datacenter-specific and fixed in the range 23–25∘C unless explicitly optimized by the controller. Energy and cost parameters: Energy consumption is computed from compute and cooling power as defined in Section I, using a 5-minute timestep (Δt=300 t=300s). Time-of-use electricity prices vary by location between $0.06 and $0.22 per kWh. Job execution model: Jobs follow the capacity-constrained execution model described in Section I, with FIFO scheduling and backfilling. Energy efficiency is reported as total energy divided by completed jobs. Job Completion Tracking: Each job with resource demand r (CU), duration d (timesteps), and affinity τ∈CPU,GPUτ∈\CPU,GPU\ executes when capacity ≥r≥ r, decrementing d each timestep until completion. Capacity-constrained processing with backfilling: jobs process in FIFO order up to available capacity; if a job doesn’t fit, smaller jobs behind it can still execute. Completed jobs (NcompletedN_completed) enable energy efficiency calculation: E/J=Etotal/NcompletedE/J=E_total/N_completed. V-B System Configuration Experiments use across 20 heterogeneous clusters (C) and 4 geographically distributed data centers (D). Hardware characteristics, thermal parameters, and capacity distributions are summarized in Table I. Parameters were obtained via a structured offline calibration process combining physical feasibility constraints, documented operating ranges, and iterative closed-loop simulation. Automated tuning workflows and sensitivity analysis were used to efficiently explore the high-dimensional configuration space and identify stable, realistic operating points. All parameters were validated under closed-loop control, and no additional configuration assumptions are introduced beyond those reported in the table. V-C Workload Trace Workloads are derived from the Alibaba 2018 cluster trace [1], which contains 12.2M jobs over eight days. A contiguous 24-hour slice is extracted and mapped to 5-minute timesteps (288 per episode) to avoid startup artifacts. To target nominal utilization, arrivals are capped at 200 jobs per timestep. Alibaba CPU and memory demands are normalized to compute units (CU) and scaled to cluster capacities. Because GPU annotations are absent in the trace, a 40% CPU / 60% GPU affinity split is synthesized based on reported production GPU adoption rates [4]. (a) H-MPC (b) PowerCool (c) Greedy Figure 2: Thermal response under increasing workload. H-MPC actively tracks temperature setpoints, maintaining tightly bounded distributions and preserving thermal headroom. PowerCool moderates but does not prevent thermal escalation. Greedy drives the system into the throttling-active regime beyond λ≈1.6×λ≈ 1.6×. System Temperature indicates temperature around the Cluster which employ the throttling mechanism. V-D Evaluation Protocol Episodes: Each policy is evaluated over 24-hour episodes (288 timesteps). The system reaches thermal equilibrium within the first hour; therefore, no warm-up period is discarded. Statistical Methodology: Results are obtained via Monte Carlo evaluation with five independent random seeds. For each seed, workload arrivals and ambient temperature trajectories are held fixed across policies. Deterministic policies use seeded tie-breaking. Metrics are reported as mean ± standard deviation. Evaluation Metrics: Table I summarizes the performance metrics spanning QoS, thermal safety, and energy efficiency. TABLE I: Evaluation metrics Dimension Metric Definition QoS Utilization (UmeanU_mean) Mean CPU/GPU utilization (%) Queue Length (QmeanQ_mean) Mean queued jobs per cluster Thermal Temperature (θmean,θmax _mean, _max) Mean / max datacenter temperature (°C) Throttle Time (%) % timesteps with θd,t>θsoft _d,t> _soft Energy Total Energy EtotalE_total (kWh) Energy per Job Etotal/NcompletedE_total/N_completed (kWh) Cost $USD per 24-hour episode VI Experimental Evaluation We present two representative research questions that DataCenterGym can be used to study. Unless stated otherwise, all experiments assume the four-datacenter configuration described in Section V and employ the candidate scheduling policies introduced in Section IV. RQ1: How do scheduling policies compare in the nominal operating regime? RQ2: How does system behavior change as job arrival rates increase? VI-A RQ1: Nominal Operating Regime The nominal operating regime establishes a stable reference environment for calibrating system parameters. All policies are evaluated under identical workloads and dynamics. Non-MPC baselines employ fixed cooling setpoints, whereas MPC-based controllers jointly optimize cooling setpoints as part of the control action. However, in RQ1, safety-constrained MPC (SC-MPC) scheduling is computationally intractable (Sec. IV-F4), and the job scheduler does not scale with increasing decision step sizes. Consequently, we restrict SC-MPC to optimizing cooling setpoints θd,ttargetθ^target_d,t only, while delegating job placement to a fixed myopic heuristic. TABLE I: Policy comparison in the nominal operating regime (200 jobs/step, bundle_p088) Metric Random Greedy Thermal Power-Cool SC-MPC H-MPC Quality of Service CPU Util (%) 67.3 69.3 69.4 67.3 69.3 62.6 GPU Util (%) 73.9 71.8 71.9 75.9 71.8 70.9 CPU Queue 491 338 336 349 338 324⋆ GPU Queue 568 502 502 525 502 449⋆ Thermal Safety θmean _mean 23.4 23.5 23.5 23.4 22.6⋆ 23.2 θmax _max 26.4 27.2 27.5 27.1 25.3⋆ 26.3 Throttle (%) 0 0 0 0 0 0 Energy Efficiency kWh/Job 2.54 2.53 2.50 2.26 2.55 2.20⋆ Cost ($) 16,408 18,242 17,840 15,109 18,313 14,424⋆ Table I contrasts baseline heuristics, SC-MPC, and the proposed hierarchical MPC (H-MPC) under identical workloads in the nominal operating regime. As all policies operate far from thermal and capacity limits, observed differences primarily reflect control structure rather than stress-induced behavior. • Queue regulation via target utilization control: H-MPC achieves the lowest CPU and GPU queue backlogs while explicitly regulating aggregate load to a target utilization range of 60–70% (averaging ∼ 65%). Datacenter-level admission and thermal planning preserve capacity slack, reducing congestion before cluster-level scheduling. • Utilization is a control outcome: Greedy and SC-MPC push utilization toward saturation, which does not yield lower queueing delay. H-MPC instead trades marginal throughput for stable queue dynamics; utilization emerges from coordinated admission and cooling decisions rather than being directly optimized. • Thermal headroom without conservatism: All policies remain thermally safe with no throttling. SC-MPC maintains lower temperatures via conservative cooling, increasing energy cost, while H-MPC dynamically adjusts thermal setpoints to operate closer to safe limits. • Energy efficiency through coordination: H-MPC achieves the lowest total cost and kWh/job among all policies. Unlike Power-Cool, which relies on load concentration, H-MPC attains these gains through coordinated admission and cooling control. Overall Insight: In the nominal regime, H-MPC operates in a distinct control mode that jointly shapes workload intensity and thermal conditions upstream, yielding lower queues and competitive energy efficiency without relying on saturation. VI-B RQ2: Workload Intensity Sensitivity RQ2 examines how the system transitions from nominal to capacity-constrained operation as workload increases, and whether predictive control alters this transition. We test with different arrival rates λ∈0.5,…,3.0λ∈\0.5,…,3.0\ under Greedy, PowerCool, and H-MPC. Greedy exposes the plant’s intrinsic saturation behavior. PowerCool adds a reactive energy bias. H-MPC optimizes a coupled objective over throughput, thermal deviation, and cooling effort, actively tracking temperature setpoints while coordinating admission and scheduling. This enables anticipatory mitigation of thermal pressure before hard limits are approached. Figure 3: System saturation under increasing load. Each curve traces operating points as arrival rate λ increases. Greedy (gold) reveals the plant’s intrinsic saturation behavior, with a sharp knee marking the onset of congestion-dominated operation. PowerCool follows the same geometry. H-MPC (black diamonds) biases operation toward the nominal regime (shaded band), tracking the 60–70% target without aggressively chasing saturation. • Intrinsic saturation geometry: Greedy reveals a sharp utilization–congestion transition, with a knee near λ≈1.6×λ≈ 1.6×. PowerCool follows the similar plant frontier and is slightly inwards than Greedy which implies larger queue length as it attempts to reduce. • Nominal-regime tracking: H-MPC remains near the target operating band across the sweep, delaying entry into the congestion-dominated region. • Anticipatory thermal control: H-MPC suppresses temperature excursions before throttling is triggered, preserving headroom under load. PowerCool remains reactive; Greedy drives the system into thermal stress. Overall Insight: Workload scaling exposes an intrinsic utilization–congestion transition: heuristic policies ride the plant frontier toward saturation and thermal stress. H-MPC instead couples workload admission with predictive thermal control, biasing operation toward the nominal regime and preserving thermal headroom as load increases—effectively expanding the system’s safe operating envelope. VII Limitations and Future Work DataCenterGym makes simplifying assumptions to prioritize interpretability and experimental control, each of which motivates future extensions. • Thermal abstraction: While we employ a lumped RC-circuit thermal model in this work, this abstraction cannot capture fine-grained spatial and temporal thermal dynamics. Modeling realistic building behavior ultimately requires multi-zone thermal representations, which we leave to future work. • Network abstraction: Inter-datacenter latency, bandwidth, and data locality are not modeled. • Queueing model: Queues are aggregated without job dependencies or resource fragmentation; richer service and dependency-aware scheduling is a natural extension. • Learning-based control: We assume known dynamics and rely on model-based MPC; integrating learning-based or learning-augmented control to address model mismatch and non-stationarity is an important direction. • Energy supply: Power availability is treated exogenously; future work will integrate grid and renewable supply constraints . • Experimental scope: More stress testing (e.g., sharp job-arrival surges, sustained overload, and heavy-tailed service times) is left for future work. 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