A geographically distributed data center random optimization scheduling method considering spatiotemporal workload flexibility

Abstract

A random optimization scheduling method of geographically distributed data centers considering spatiotemporal workload flexibility comprises the following steps: 1) constructing a multi-physical coupling model of a geographically distributed data center system; 2) constructing a two-stage random optimization model based on the multi-physical coupling model of the geographically distributed data center system; 3) combining the Latin hypercube sampling method and the fast forward scenario reduction algorithm to generate a reduced scenario set; and 4) inputting the reduced scenario set into the two-stage random optimization model and using a solver to obtain an optimal scheduling strategy. The present application proposes a random optimization scheduling framework of geographically distributed data centers considering spatiotemporal workload flexibility. The model explicitly captures the migration of geographical workload and the transfer of temporal workload, so that the system can fully utilize the spatial and temporal flexibility under uncertainty.

Description

Technical Field

[0001] This invention relates to the field of power system energy dispatching technology, and specifically to a stochastic optimization scheduling method for geographically distributed data centers that considers the flexibility of spatiotemporal workloads. Background Technology

[0002] The rapid expansion of cloud computing, artificial intelligence, and large-scale digital services has significantly increased global demand for computing infrastructure. As a pillar of the modern digital economy, data centers (DCs) provide massive computing and storage capabilities for various online applications. However, the rapid growth of DC infrastructure has also led to substantial electricity consumption. Recent research indicates that DCs' share of global electricity demand is continuously expanding, and this share is expected to continue to grow as emerging technologies such as artificial intelligence and big data analytics further increase computing demands. The high energy consumption of DCs not only results in considerable operating costs but also raises serious concerns about environmental sustainability and carbon emissions. Therefore, in the context of sustainable development of digital infrastructure, improving the energy efficiency of DCs and achieving low-carbon operation has become an increasingly important research topic.

[0003] Current research on data distribution networks (DCs) is increasingly focusing on geographic load balancing. This involves distributing workloads across multiple locations and leveraging regional heterogeneity in electricity prices, climate conditions, and cooling efficiency for optimization. Based on this approach, various optimization frameworks have been proposed to minimize electricity costs, carbon emissions, or total energy consumption by coordinating workload allocation. Simultaneously, renewable energy sensing and carbon-sensing dispatch strategies are also evolving to better match DC operation with intermittent renewable energy supply, thereby enhancing the environmental sustainability of cloud computing platforms.

[0004] However, significant gaps remain in existing research. First, many existing studies are based on deterministic scheduling models, which are susceptible to prediction errors and may lead to suboptimal or fragile decisions in uncertain scenarios. Second, although stochastic and robust optimization methods have been introduced to capture uncertainties in workload demand, electricity prices, and renewable energy generation, research integrating them into the scheduling problem of geographically distributed DCs remains limited. Third, most previous work only considered a single dimension of flexibility (either workload transfer in the time dimension or workload migration in the spatial dimension), failing to coordinate the two within a unified framework. Therefore, the full value of spatiotemporal flexibility in geographically distributed DCs systems has not been fully explored. These limitations highlight the need for a more comprehensive optimization framework—one that can coordinate the scheduling of spatiotemporal workloads while explicitly addressing various uncertainties. Summary of the Invention

[0005] The purpose of this invention is to provide a stochastic optimization scheduling method for geographically distributed data centers that considers the flexibility of spatiotemporal workloads, comprising the following steps:

[0006] 1) Construct a multi-physical coupling model for a geographically distributed data center system.

[0007] 2) Based on the multi-physical coupling model of the geographic distributed data center system, a two-stage stochastic optimization model is constructed.

[0008] 3) Combine the Latin hypercube sampling method and the fast forward scene reduction algorithm to generate a reduced scene set.

[0009] 4) Input the reduced scenario set into the two-stage stochastic optimization model and use a solver to obtain the optimal scheduling strategy.

[0010] Furthermore, the geographically distributed data center system includes a global scheduler and several data centers.

[0011] The data center is used to generate workloads.

[0012] The workloads include inflexible workloads, time-transferable workloads, and space-transferable workloads.

[0013] The inflexible workloads are those generated and processed in real-time within the local data center.

[0014] The time-transferable workload is a workload generated in the local data center and executed with a delay within a specified time window in the local data center.

[0015] The space-migratable workloads are workloads generated in the local data center and migrated to other data centers for execution.

[0016] The global scheduler schedules workloads to local or other data centers based on workload characteristics and data center operation status.

[0017] The data center is used to execute workloads scheduled by the global scheduler.

[0018] Furthermore, the steps for constructing the multi-physical coupling model of the geographically distributed data center system include:

[0019] 101) Establish the overall workload model after workload migration, as shown below:

[0020] (1)

[0021] In the formula, t represents time, and i and j both represent data center indexes. Represents a collection of data centers. Indicates a time slot. This represents the maximum latency tolerance window. This represents the total workload processed in the i-th data center at time t. This represents the workload generated by the i-th data center at time t but executed in time slot τ. This represents the workload that migrates from the i-th data center to the j-th data center at time t.

[0022] Wherein, the amount of inflexible workload processed by the i-th data center at time t. As shown below:

[0023] (2)

[0024] In the formula, This represents the amount of inflexible workload generated by the i-th data center at time t.

[0025] Time-transferable workload model As shown below:

[0026] (3)

[0027] In the formula, This represents the amount of time-transferable workload generated by the i-th data center at time t.

[0028] Spatially Portable Workload Model As shown below:

[0029] (4)

[0030] In the formula, This represents the amount of spatially portable workload generated by the i-th data center at time t.

[0031] 102) Establish a cooling dynamic model based on equivalent thermal parameters, as shown below:

[0032] (5)

[0033] (6)

[0034] (7)

[0035] In the formula, Let represent the power requirement of the i-th data center at time t. , , These represent the power consumption of IT equipment, cooling system, and other equipment in the i-th data center at time t, respectively. This represents the number of servers in the i-th data center. This indicates the server's idle power consumption. This indicates the maximum power consumption under full load. This represents the average CPU utilization of the servers in the i-th data center at time t. This represents the number of servers that are powered on in the i-th data center at time t. This indicates the service rate of the data center.

[0036] The other equipment includes lighting and power distribution facilities.

[0037] 103) Establish a migration delay model between DCs, as shown below:

[0038] (8)

[0039] (9)

[0040] (10)

[0041] (11)

[0042] In the formula, This represents the total migration delay between DCs. These represent propagation delay, transmission delay, and processing delay, respectively. This represents the physical distance between the i-th data center and the j-th data center. This indicates the speed at which signals propagate in an optical fiber. This indicates the amount of data being migrated for the workload. This represents the bandwidth of the network link between the i-th data center and the j-th data center. This indicates the task completion rate.

[0043] Furthermore, the power consumption of the cooling system of the i-th data center at time t. As shown below:

[0044] (12)

[0045] In the formula, t represents time, and i represents the data center index. This represents the total thermal power of the i-th data center at time t. , Let represent the indoor air temperature of the i-th data center at times t and t-1, respectively. It represents the thermal resistance between indoor air and the external environment. This indicates the indoor air heat capacity. Let represent the outdoor air temperature of the i-th data center at time t. This indicates the thermal coefficient of IT equipment. This represents the power consumption of the IT equipment in the i-th data center at time t. This indicates the energy efficiency ratio of the cooling system.

[0046] Furthermore, the goal of the two-stage stochastic optimization model is to minimize the total power cost of all data centers throughout the entire scheduling cycle.

[0047] The total power cost for all data centers during the entire scheduling period is shown below:

[0048] (13)

[0049] In the formula, t represents time, and i represents the data center index. Represents a collection of data centers. Indicates the scheduling period. This represents the total power cost of all data centers throughout the entire scheduling cycle. Let represent the electricity price of the i-th data center at time t. Let represent the power requirement of the i-th data center at time t. Indicates the duration of a time period.

[0050] Furthermore, the constraints of the two-stage stochastic optimization model include DC operation constraints and end-to-end delay constraints.

[0051] The DC operation constraints are as follows:

[0052] (14)

[0053] (15)

[0054] (16)

[0055] (17)

[0056] In the formula, t represents time, and i represents the data center index. This represents the number of IT devices in the i-th data center at time t. This represents the number of active servers in the i-th data center. This represents the average CPU utilization of the servers in the i-th data center at time t. This indicates the maximum CPU utilization of the server. , Let represent the indoor air temperature of the i-th data center at times t and t-1, respectively. , These represent the upper and lower limits of indoor air temperature in the data center, respectively. This indicates the maximum permissible variation in indoor temperature.

[0057] The end-to-end delay constraint is as follows:

[0058] (18)

[0059] (19)

[0060] In the formula, j represents the data center index. This represents the workload that migrates from the i-th data center to the j-th data center at time t. This represents the bandwidth of the network link between the i-th data center and the j-th data center. Indicates the duration of a time period. This represents the total migration delay between DCs. This represents the system's maximum tolerable end-to-end delay.

[0061] Furthermore, the steps for generating the reduced scene set are as follows:

[0062] 301) Divide the probability distribution of the workload into several equally probable intervals, and randomly draw samples from each interval to construct the original scene set.

[0063] The probability weight of each scene in the original scene set satisfies the following condition:

[0064] (20)

[0065] (twenty one)

[0066] In the formula, , Both refer to a scenario. This represents the original scene set. Indicates the scene set in the original scene The probability weights. , Each is a set of scenes in the original scene. , The probability of.

[0067] 302) Construct a reduced scenario set and initialize the reduced scenario set as an empty set.

[0068] 303) Select the scene with the smallest total Euclidean distance from the other scenes in the original scene set, remove the selected scene from the original scene set and send it to the reduced scene set, and use the probability weight of the selected scene in the original scene set as the probability in the reduced scene set, and recalculate the probability weight of the selected scene in the reduced scene set.

[0069] The scene selected from the original scene set that has the smallest total Euclidean distance from the remaining scenes is shown below:

[0070] (twenty two)

[0071] (twenty three)

[0072] In the formula, This represents the scene selected from the original scene set that has the smallest total Euclidean distance from the other scenes. Indicates a scenario. Representing a scene and scene The Euclidean distance between them. t represents time, and i represents the data center index. Represents a collection of data centers. Indicates the scheduling period. , They represent the scenes respectively. Scene The total workload arrivals of the i-th data center at time t.

[0073] 304) Update the probability weights of the remaining scenes in the original scene set.

[0074] 305) Return to step 303) until the number of scenes in the reduced scene set reaches the preset number of scenes.

[0075] Furthermore, after inputting the reduced scenario set into the two-stage stochastic optimization model, the objective function of the two-stage stochastic optimization model is solved as follows:

[0076] (twenty four)

[0077] In the formula, Indicates a scenario. This represents a simplified set of scenarios. This indicates a reduced scenario set. The probability weights. Representing a scene Total power cost for all data centers.

[0078] Furthermore, the optimal scheduling strategy includes the local processing volume, migration reception volume, latency processing volume, transmission migration volume, number of active servers, average utilization, cooling power, and the expected total electricity cost and total energy consumption of the geographically distributed data center system for each data center in each time slot.

[0079] Furthermore, the solver includes a mixed integer programming solver.

[0080] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the above-described stochastic optimization scheduling method for a geographically distributed data center that considers spatiotemporal workload flexibility.

[0081] The technical advantages of this invention are undeniable. This invention proposes a stochastic optimization scheduling framework for geographically distributed data centers that considers the flexibility of spatiotemporal workloads. This model explicitly captures geographical workload migration and temporal workload transfer, enabling the system to fully utilize spatial and temporal flexibility in the context of uncertainty.

[0082] This invention constructs a comprehensive scheduling framework for geographically distributed data centers by jointly modeling three types of workloads: inflexible, time-shiftable, and spatially portable. The proposed framework clearly distinguishes between inflexible, time-shiftable, and spatially portable workloads, thereby enabling the coordinated utilization of this spatiotemporal workload flexibility.

[0083] This invention establishes a coupled operation model that integrates workload scheduling, server utilization, cooling power consumption, and inter-data center network constraints. Based on this model, an optimization model is constructed with the goal of minimizing operating costs, thereby minimizing the total cost of the geographically distributed data center system while satisfying service quality and thermal operation constraints.

[0084] This invention proposes a two-stage stochastic optimization method to address workload uncertainty. Latin hypercube sampling (LHS) and scenario reduction are employed to generate representative workload scenarios, enabling the proposed method to achieve robustness and computationally tractable scheduling under stochastic demand conditions. Attached Figure Description

[0085] Figure 1 This is a flowchart of the present invention;

[0086] Figure 2 This is a schematic diagram of the overall architecture of a geographically distributed data center (DCs) system.

[0087] Figure 3 A schematic diagram illustrating the relative energy-saving ratios under different workload flexibility mechanisms;

[0088] Figure 4 This diagram illustrates the hourly workload redistribution of the three DCs before and after the application of the scheduling strategy. Figure 4 (a) is a schematic diagram of the hourly workload redistribution of the first DCs before and after the application of the scheduling strategy; Figure 4 (b) is a schematic diagram of the hourly workload redistribution of the second DCs before and after the application of the scheduling strategy; Figure 4(c) is a schematic diagram of the hourly workload redistribution of the third DCs before and after the application of the scheduling strategy;

[0089] Figure 5 A schematic diagram of hourly active server scheduling plans for three DCs under different load uncertainty levels; Figure 5 (a) is a schematic diagram of the hourly active server scheduling plan for the first DCs under different load uncertainty levels; Figure 5 (b) is a schematic diagram of the hourly active server scheduling plan for the second DCs under different load uncertainty levels; Figure 5 (c) is a schematic diagram of the hourly active server scheduling plan for the third DCs under different load uncertainty levels. Detailed Implementation

[0090] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0091] Example 1:

[0092] See Figures 1 to 5 A stochastic optimization scheduling method for geographically distributed data centers that considers the flexibility of spatiotemporal workloads includes the following steps:

[0093] 1) Construct a multi-physical coupling model for a geographically distributed data center system.

[0094] 2) Based on the multi-physical coupling model of the geographic distributed data center system, a two-stage stochastic optimization model is constructed.

[0095] 3) Combine the Latin hypercube sampling method and the fast forward scene reduction algorithm to generate a reduced scene set.

[0096] 4) Input the reduced scenario set into the two-stage stochastic optimization model and use a solver to obtain the optimal scheduling strategy.

[0097] Example 2:

[0098] A stochastic optimization scheduling method for a geographic distributed data center that considers the flexibility of spatiotemporal workloads is described in Embodiment 1. Further, the geographic distributed data center system includes a global scheduler and several data centers.

[0099] The data center is used to generate workloads.

[0100] The workloads include inflexible workloads, time-transferable workloads, and space-transferable workloads.

[0101] The inflexible workloads are those generated and processed in real-time within the local data center.

[0102] The time-transferable workload is a workload generated in the local data center and executed with a delay within a specified time window in the local data center.

[0103] The space-migratable workloads are workloads generated in the local data center and migrated to other data centers for execution.

[0104] The global scheduler schedules workloads to local or other data centers based on workload characteristics and data center operation status.

[0105] The data center is used to execute workloads scheduled by the global scheduler.

[0106] Example 3:

[0107] A stochastic optimization scheduling method for a geographic distributed data center that considers the flexibility of spatiotemporal workloads, the main technical contents of which are described in any one of Embodiments 1 and 2, further comprising the steps of constructing a multi-physical coupling model of the geographic distributed data center system including:

[0108] 101) Establish the overall workload model after workload migration, as shown below:

[0109] (1)

[0110] In the formula, t represents time, and i and j both represent data center indexes. Represents a collection of data centers. Indicates a time slot. This represents the maximum latency tolerance window. This represents the total workload processed in the i-th data center at time t. This represents the workload generated by the i-th data center at time t but executed in time slot τ. This represents the workload that migrates from the i-th data center to the j-th data center at time t.

[0111] Wherein, the amount of inflexible workload processed by the i-th data center at time t. As shown below:

[0112] (2)

[0113] In the formula, This represents the amount of inflexible workload generated by the i-th data center at time t.

[0114] Time-transferable workload model As shown below:

[0115] (3)

[0116] In the formula, This represents the amount of time-transferable workload generated by the i-th data center at time t.

[0117] Spatially Portable Workload Model As shown below:

[0118] (4)

[0119] In the formula, This represents the amount of spatially portable workload generated by the i-th data center at time t.

[0120] 102) Establish a cooling dynamic model based on equivalent thermal parameters, as shown below:

[0121] (5)

[0122] (6)

[0123] (7)

[0124] In the formula, Let represent the power requirement of the i-th data center at time t. , , These represent the power consumption of IT equipment, cooling system, and other equipment in the i-th data center at time t, respectively. This represents the number of servers in the i-th data center. This indicates the server's idle power consumption. This indicates the maximum power consumption under full load. This represents the average CPU utilization of the servers in the i-th data center at time t. This represents the number of servers that are powered on in the i-th data center at time t. This indicates the service rate of the data center.

[0125] The other equipment includes lighting and power distribution facilities.

[0126] 103) Establish a migration delay model between DCs, as shown below:

[0127] (8)

[0128] (9)

[0129] (10)

[0130] (11)

[0131] In the formula, This represents the total migration delay between DCs. These represent propagation delay, transmission delay, and processing delay, respectively. This represents the physical distance between the i-th data center and the j-th data center. This indicates the speed at which signals propagate in an optical fiber. This indicates the amount of data being migrated for the workload. This represents the bandwidth of the network link between the i-th data center and the j-th data center. This indicates the task completion rate.

[0132] Example 4:

[0133] A stochastic optimization scheduling method for geographically distributed data centers that considers the flexibility of spatiotemporal workloads is proposed. The main technical contents are described in any one of Examples 1 to 3. Further, the power consumption of the cooling system of the i-th data center at time t is... As shown below:

[0134] (12)

[0135] In the formula, t represents time, and i represents the data center index. This represents the total thermal power of the i-th data center at time t. , Let represent the indoor air temperature of the i-th data center at times t and t-1, respectively. It represents the thermal resistance between indoor air and the external environment. This indicates the indoor air heat capacity. Let represent the outdoor air temperature of the i-th data center at time t. This indicates the thermal coefficient of IT equipment. This represents the power consumption of the IT equipment in the i-th data center at time t. This indicates the energy efficiency ratio of the cooling system.

[0136] Example 5:

[0137] A stochastic optimization scheduling method for geographic distributed data centers that considers the flexibility of spatiotemporal workloads is provided. The main technical contents are described in any one of Examples 1 to 4. Furthermore, the goal of the two-stage stochastic optimization model is to minimize the total power cost of all data centers throughout the entire scheduling cycle.

[0138] The total power cost for all data centers during the entire scheduling period is shown below:

[0139] (13)

[0140] In the formula, t represents time, and i represents the data center index. Represents a collection of data centers. Indicates the scheduling period. This represents the total power cost of all data centers throughout the entire scheduling cycle. Let represent the electricity price of the i-th data center at time t. Let represent the power requirement of the i-th data center at time t. Indicates the duration of a time period.

[0141] Example 6:

[0142] A stochastic optimization scheduling method for geographic distributed data centers that considers the flexibility of spatiotemporal workloads is provided. The main technical contents are described in any one of Examples 1 to 5. Furthermore, the constraints of the two-stage stochastic optimization model include DC operation constraints and end-to-end delay constraints.

[0143] The DC operation constraints are as follows:

[0144] (14)

[0145] (15)

[0146] (16)

[0147] (17)

[0148] In the formula, t represents time, and i represents the data center index. This represents the number of IT devices in the i-th data center at time t. This represents the number of active servers in the i-th data center. This represents the average CPU utilization of the servers in the i-th data center at time t. This indicates the maximum CPU utilization of the server. , Let represent the indoor air temperature of the i-th data center at times t and t-1, respectively. , These represent the upper and lower limits of indoor air temperature in the data center, respectively. This indicates the maximum permissible variation in indoor temperature.

[0149] The end-to-end delay constraint is as follows:

[0150] (18)

[0151] (19)

[0152] In the formula, j represents the data center index. This represents the workload that migrates from the i-th data center to the j-th data center at time t. This represents the bandwidth of the network link between the i-th data center and the j-th data center. Indicates the duration of a time period. This represents the total migration delay between DCs. This represents the system's maximum tolerable end-to-end delay.

[0153] Example 7:

[0154] A stochastic optimization scheduling method for a geographically distributed data center that considers the flexibility of spatiotemporal workloads, the main technical contents of which are described in any one of Embodiments 1 to 6, and further, the step of generating the reduced scenario set is as follows:

[0155] 301) Divide the probability distribution of the workload into several equally probable intervals, and randomly draw samples from each interval to construct the original scene set.

[0156] The probability weight of each scene in the original scene set satisfies the following condition:

[0157] (20)

[0158] (twenty one)

[0159] In the formula, , Both refer to a scenario. This represents the original scene set. Indicates the scene set in the original scene The probability weights. , Each is a set of scenes in the original scene. , The probability of.

[0160] 302) Construct a reduced scenario set and initialize the reduced scenario set as an empty set.

[0161] 303) Select the scene with the smallest total Euclidean distance from the other scenes in the original scene set, remove the selected scene from the original scene set and send it to the reduced scene set, and use the probability weight of the selected scene in the original scene set as the probability in the reduced scene set, and recalculate the probability weight of the selected scene in the reduced scene set.

[0162] The scene selected from the original scene set that has the smallest total Euclidean distance from the remaining scenes is shown below:

[0163] (twenty two)

[0164] (twenty three)

[0165] In the formula, This represents the scene selected from the original scene set that has the smallest total Euclidean distance from the other scenes. Indicates a scenario. Representing a scene and scene The Euclidean distance between them. t represents time, and i represents the data center index. Represents a collection of data centers. Indicates the scheduling period. , They represent the scenes respectively. Scene The total workload arrivals of the i-th data center at time t.

[0166] 304) Update the probability weights of the remaining scenes in the original scene set.

[0167] 305) Return to step 303) until the number of scenes in the reduced scene set reaches the preset number of scenes.

[0168] Example 8:

[0169] A stochastic optimization scheduling method for a geographic distributed data center that considers the flexibility of spatiotemporal workloads is provided. The main technical content is described in any one of Examples 1 to 7. Further, after inputting the reduced scenario set into the two-stage stochastic optimization model, the objective function of the two-stage stochastic optimization model is solved as follows:

[0170] (twenty four)

[0171] In the formula, Indicates a scenario. This represents a simplified set of scenarios. This indicates a reduced scenario set. The probability weights. Representing a scene Total power cost for all data centers.

[0172] Example 9:

[0173] A stochastic optimization scheduling method for geographic distributed data centers that considers the flexibility of spatiotemporal workloads is provided. The main technical contents are described in any one of Embodiments 1 to 8. Further, the optimal scheduling strategy includes the local processing volume, migration reception volume, latency processing volume, transmission migration volume, number of active servers, average utilization rate, cooling power, and expected total electricity cost and total energy consumption of the geographic distributed data center system for each data center in each time slot.

[0174] Example 10:

[0175] A stochastic optimization scheduling method for a geographic distributed data center that considers the flexibility of spatiotemporal workloads is provided. The main technical contents are described in any one of Embodiments 1 to 9. Furthermore, the solver includes a mixed integer programming solver.

[0176] Example 11:

[0177] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the stochastic optimization scheduling method for a geographically distributed data center that takes into account spatiotemporal workload flexibility, as described in any one of Embodiments 1 to 2.

[0178] Example 12:

[0179] See Figures 1 to 5 A stochastic optimization scheduling method for geographically distributed data centers that considers the flexibility of spatiotemporal workloads, the main technical contents of which include:

[0180] The steps are as follows:

[0181] S1: Constructing the System Model. Construct a multi-physical coupling model of a geographically distributed data center, clearly distinguishing between three types of workloads: those that are inflexible to schedule, those that are time-shiftable, and those that are spatially mobile; establish a functional relationship between server power and CPU utilization, introduce a dynamic cooling model based on equivalent thermal parameters, and quantify bandwidth limitations and end-to-end latency constraints, providing a precise system description foundation for subsequent scheduling.

[0182] S2: Establish a two-stage stochastic optimization model. Define the decision variables for the first-stage pre-scheduling and the second-stage rescheduling. With the optimization objective of minimizing the expected value of the total system electricity cost, construct a mixed-integer stochastic programming model. The model integrates multiple constraints such as workload conservation, server processing capacity, indoor temperature upper and lower limits and rate of change, network bandwidth and end-to-end latency.

[0183] S3: Uncertainty Handling and Scene Generation. Latin hypercube sampling is used to generate large-scale workload scenes, fully covering the uncertainty space. Then, a fast forward scene reduction algorithm is used to select a small number of representative scenes and assign them corresponding probability weights, thereby significantly reducing computational complexity while maintaining modeling accuracy.

[0184] S4: Two-stage optimization solution. First, based on the first-stage information shared by all representative scenarios, the server start-up and shutdown scheme and basic load allocation are solved; then, the second-stage rescheduling is performed independently for each scenario to achieve time shifting and space migration of the workload; with the goal of minimizing the probability-weighted expected cost, the optimal scheduling strategy is obtained with the help of a mixed-integer programming solver.

[0185] S5: Output scheduling scheme. Output the local processing volume, migration reception volume, latency processing volume, transmission migration volume, number of active servers, average utilization, cooling power of each data center in each time slot, as well as the expected total electricity cost and total energy consumption of the entire system, forming a complete operation scheme that can be directly used for day-ahead scheduling.

[0186] The characteristics of step S1 are as follows:

[0187] Step S1.1: Define the system architecture.

[0188] Considering a geographically distributed data center (DC) system comprised of multiple geographically dispersed facilities interconnected via wide-area communication links, user requests are generated in different regions and first arrive at their corresponding source DCs. Based on workload characteristics and operating conditions, system operators can process workloads locally, postpone some latency-tolerant demands to later periods, or migrate eligible tasks to other DCs. Different DCs differ in terms of electricity prices, thermal environment, and processing capacity. Therefore, the core of the scheduling problem is to coordinate and optimize the spatiotemporal distribution of workloads while meeting local server capacity limitations, indoor temperature requirements, and communication constraints between DCs.

[0189] like Figure 2 As shown, the operating cost of each DC depends not only on the workload processed locally, but also on the number of active servers, the power consumption of the corresponding IT equipment, cooling requirements, and the latency impact of workload migration. These components are interdependent, thus requiring joint modeling.

[0190] Step S1.2: Establish three types of workload models.

[0191] In geographically distributed data centers (DCs), user-generated workloads exhibit varying degrees of flexibility in time and space. To characterize the heterogeneous nature of computing tasks, the total workload within the system is categorized into three types: inflexible workloads, time-transferable workloads, and spatially transferable workloads. This classification allows the scheduler to leverage spatiotemporal flexibility to improve energy efficiency while meeting quality-of-service (QoS) requirements.

[0192] Inflexible workloads, corresponding to latency-sensitive tasks, must be processed immediately at the data centers (DCs) that generated the task and cannot be transferred across time or location. Typical applications include real-time online services and interactive applications. These tasks, requiring local processing, can be represented as:

[0193] (1)

[0194] in, and These represent the inflexible workload generated and processed by DCi at time t.

[0195] Time-transferable workloads refer to latency-tolerant tasks that can be delayed within a specified time window. Typical scenarios include batch processing jobs, data analysis, and offline computing tasks. The time scheduling constraints are shown in Equation (2), ensuring that all time-transferable tasks are completed within the allowed delay window.

[0196] (2)

[0197] in, This represents the workload generated at time t but executed in time slot τ. This represents the amount of time-transferable workload generated at time t, and D represents the maximum latency tolerance window.

[0198] Spatially portable workloads refer to tasks that can be scheduled and processed across different data centers (DCs) through load balancing. These tasks typically have moderate latency requirements, and their operational efficiency can be improved through load balancing among geographically distributed DCs. The corresponding spatial load allocation constraints can be expressed as:

[0199] (3)

[0200] in, This represents the workload that migrates from DCi to DCj at time t. This represents the amount of spatially portable workload generated by DCi, and N represents the set of geographically distributed DCs.

[0201] After load migration, the total workload processed by DCi at time t can be expressed as:

[0202] (4)

[0203] Equation (4) simultaneously characterizes the temporal and spatial flexibility of the workload in the geographic distributed DCs system, laying the foundation for the optimization model proposed in step S3.

[0204] Step S1.3: Introduce a cooling dynamic model based on equivalent thermal parameters.

[0205] The majority of a DC's energy consumption comes from the operation of IT equipment and the cooling system. The power consumption of IT equipment depends primarily on the workload. To ensure the equipment operates at a suitable temperature, the cooling system power needs to be adjusted in real time. The cooling system provides cooling capacity, removes heat generated by IT equipment and heat transferred from outside, and maintains the internal ambient temperature of the DC. Therefore, this patent divides the energy consumption of DCs into three parts: IT equipment, cooling system, and other equipment.

[0206] (5)

[0207] in, Let i be the power demand of DC at time t; , and These represent the power consumption of IT equipment, cooling system, and other equipment in DC i, respectively.

[0208] Server power consumption is typically related to its CPU utilization. Empirical studies show that even when idle, servers consume a significant proportion of their peak power. Therefore, server power consumption can be modeled as a linear function of CPU utilization. Let... Let DCi represent the average CPU utilization of the server at time t. Then, the IT power consumption of DCi can be expressed as:

[0209] (6)

[0210] (7)

[0211] in, This represents the number of active servers in DCi. Indicates the server's idle power consumption. This indicates the maximum power consumption under full load.

[0212] In reality, cooling load power consumption mainly consists of two parts: one is the internal heat load generated by IT equipment handling workloads; the other is the external disturbance caused by heat transfer under the influence of outdoor weather conditions. The relationship between computing power, cooling power, and indoor / outdoor temperature can be derived using the ETP model.

[0213] (8)

[0214] (9)

[0215] in, and These are indoor and outdoor air temperatures, respectively. Total DC thermal power; Thermal coefficient of IT equipment; The energy efficiency ratio of the cooling system; Indoor air heat capacity; Let be the thermal resistance between indoor air and the external environment. The analytical recursive form of equation (8) can be expressed as:

[0216] (10)

[0217] Combining equations (8) to (10), the power consumption expression for the cooling system based on the ETP model can be derived:

[0218] (11)

[0219] As can be seen from equation (11), the cooling system provides cooling power and removes the heat generated by the IT equipment as well as the heat transferred from the outside.

[0220] Step S1.3: Quantify bandwidth limitations and end-to-end delay constraints, and establish a network model between DCs.

[0221] In geographically distributed data centers (DCs), workload migration between DCs inevitably incurs network communication latency. When a task migrates from one DC to another, the end-to-end latency mainly consists of three parts: propagation latency, transmission latency, and processing latency. These latency factors collectively affect the response speed and quality of service for latency-sensitive applications. Therefore, the total end-to-end latency of a migration task can be expressed as:

[0222] (12)

[0223] in, These represent propagation delay, transmission delay, and processing delay, respectively.

[0224] Propagation delay refers to the time required for a data packet to travel from a source DC to a destination DC via an optical fiber link. It primarily depends on the physical distance between the two DCs and the speed of signal propagation in the fiber. The propagation delay between DC i and DC j can be expressed as:

[0225] (13)

[0226] in, DCi represents the physical distance between DCi and DCj, and v represents the speed of signal propagation in the optical fiber, which is usually close to the speed of light.

[0227] Transmission delay refers to the time required to transmit task data over a network link between data centers (DCs), and is primarily determined by the amount of data in the migration task and the available bandwidth of the link. Transmission delay can be calculated as follows:

[0228] (14)

[0229] Where S represents the amount of data for the migration workload. This indicates the available bandwidth of the network link between DCi and j.

[0230] The processing delay corresponds to the queuing and execution time of a task after it arrives at the destination DC. This paper uses an M / M / 1 queuing system to model the task processing process. This model is suitable for service systems with random arrivals and exponential service times. Let λ be the task arrival rate and μ be the service rate of the DC, then the expected processing delay can be expressed as:

[0231] (15)

[0232] This formula can effectively characterize the queuing delay caused by the workload congestion of target DCs.

[0233] The characteristics of step S2 are as follows:

[0234] Step S2.1: Define decision variables and modeling objectives.

[0235] Consider a geographically distributed data center (DC) system consisting of a set of geographically dispersed data centers (DCs), denoted as N. The scheduling period T is discretized into several hourly segments. In each hourly segment, the DCs are categorized into inflexible workloads, time-transferable workloads, and spatially migrated workloads as defined in step S1. By utilizing time transfers and migrations between DCs, the scheduler can reallocate flexible workloads to improve the overall operational economy of the system.

[0236] set up Let be the electricity price of DC i at time t, and Δt be the duration of the time period. The goal of the optimization model is to determine the workload scheduling, server configuration, and resource adjustment strategies to minimize the total electricity cost of all DCs throughout the entire scheduling period, while satisfying workload service constraints and operational constraints. Accordingly, the total electricity cost of the geographically distributed DCs system throughout the entire scheduling period can be expressed as:

[0237] (16)

[0238] Step S2.2: Establish a workload scheduling constraint model.

[0239] The workload scheduling constraints directly follow the workload model of equations (1)–(4), mainly including inflexible workload processing constraints, time-transferable workload conservation constraints, delay window constraints, and spatial migration balance constraints.

[0240] Step S2.3: Establish a DC operation constraint model.

[0241] Operational constraints are used to ensure that workloads allocated to each data center can be safely handled within their server capacity and thermal constraints. These constraints can be described as follows:

[0242] (17)

[0243] (18)

[0244] in, The total number of servers for DCi; The maximum CPU utilization allowed for reliable server operation.

[0245] The cooling system needs to remove internal heat generated by IT equipment as well as heat transferred from the outdoor environment. Based on the ETP thermal model, the cooling power is determined by the thermal balance of the DCs and the coefficient of performance of the cooling system. The internal ambient temperature of the DCs needs to be maintained within an allowable range, which can be expressed as:

[0246] (19)

[0247] (20)

[0248] In the formula, and These are the lower and upper limits of indoor temperature for DCs, respectively. This represents the maximum permissible variation in indoor temperature.

[0249] Step S2.3: Establish an end-to-end delay constraint model.

[0250] While spatial workload migration can improve scheduling flexibility, it is limited by actual network conditions. Specifically, the total workload migrated on links between data centers must not exceed the available transmission capacity. Let... Given the available bandwidth between DCi and j, the migration decision must satisfy:

[0251] (twenty one)

[0252] Propagation delay is determined by the geographical distance between DCs, transmission delay depends on the workload data volume and link bandwidth, and processing delay is modeled based on the queuing behavior of the target DCs, as described in step S2. To ensure service quality, the following upper limit constraints on latency must be met:

[0253] (twenty two)

[0254] Where Tmax represents the maximum tolerable end-to-end delay of the system.

[0255] The above constraints can prevent excessive workload migration, prevent violations of bandwidth and latency requirements, and thus ensure the quality of service of geographically distributed DCs systems.

[0256] The characteristics of step S3 are as follows:

[0257] Step S3.1: Use Latin hypercube sampling to construct the original uncertain variable scenario.

[0258] To characterize the uncertainty of workload arrival, this paper adopts a scenario-based approach to describe the uncertain variables. Latin Hypercube Sampling (LHS) is used to generate representative workload scenarios. LHS is a hierarchical sampling method that offers higher sampling efficiency compared to traditional Monte Carlo methods. This method first divides the probability distribution of the uncertain workload into several equally probable intervals, and then randomly draws samples from each interval to ensure sufficient coverage of the entire uncertainty space. The original scenario set Ω can be obtained through LHS:

[0259] (twenty three)

[0260] in, The total number of scenarios generated is given by the given scenario ω, which represents one possible implementation of the workload arriving within the scheduling period. Each scenario corresponds to a probability. And satisfy:

[0261] (twenty four)

[0262] The above scenario provides a discrete approximation of workload uncertainty for stochastic optimization models.

[0263] Step S3.2: Use the fast-forward scene reduction algorithm to simplify the scene.

[0264] While LHS (Local Hierarchical Structure) can effectively characterize workload uncertainty, the number of generated scenes is typically large, significantly increasing the computational burden on the optimization model. To improve computational efficiency, this patent employs a Fast Forward (FF) scene reduction algorithm to obtain a smaller set of typical scenes. The FF algorithm selects the most representative subset of scenes by minimizing the probabilistic distance between the reduced scene set and the original scene set.

[0265] The iterative steps of the FF algorithm are as follows:

[0266] Initialize the reduced scenario set to an empty set.

[0267] Choose the scene that is closest to the other scenes.

[0268] Update the probability weights of the selected scene.

[0269] Repeat the above steps until the target number of scenes is reached.

[0270] After scene reduction, the reduced scene set Ω′ can be represented as:

[0271] (25)

[0272] in, To retain the number of scenes, satisfying .

[0273] The characteristics of step S4 are as follows:

[0274] Step S4.1: Define the overall framework for stochastic optimization.

[0275] In practical DC systems, the arrival of workloads is uncertain due to dynamic changes in user demand. To characterize this uncertainty, this patent employs the following... Figure 1 The two-stage stochastic optimization framework is illustrated. The first stage determines scheduling decisions based on predicted workload information, establishing an initial workload allocation scheme across data centers and time points, including server start / stop status and basic resource configuration. After the actual workload is implemented, the second stage performs retracement adjustments, ensuring all operational constraints are met and minimizing additional energy costs through workload reallocation and task migration.

[0276] Step S4.2: Solve the stochastic optimization model.

[0277] After completing scene generation and reduction, the stochastic optimization model is solved using the reduced scene set. The objective function can be expressed as:

[0278] (26)

[0279] in, The total cost of the geographic distributed data centers (DCs) system under scenario ω can be obtained by solving the resource optimization problem in the second stage, given the first-stage decision and the actual workload scenario.

[0280] Combining the objective function and the aforementioned constraints, the proposed model can be transformed into a two-stage stochastic mixed-integer optimization problem for cost-optimal scheduling of geographically distributed DCs. This model collaboratively optimizes temporal workload transfer, spatial workload migration, server configuration, and cooling operation, while simultaneously satisfying workload conservation, utilization constraints, thermal constraints, bandwidth constraints, and end-to-end latency requirements. The optimization objective is to minimize the expected total power cost of the interconnected DCs system within the scheduling period. Therefore, the proposed optimization framework provides a complete theoretical foundation for cost-effective and reliable DCs scheduling under uncertain workload conditions.

[0281] The characteristics of step S5 are as follows:

[0282] Output the local processing volume, migration reception volume, latency processing volume, transmission migration volume, number of active servers, average utilization, cooling power of each data center in each time slot, as well as the expected total electricity cost and total energy consumption of the entire system, forming a complete operation plan that can be directly used for day-ahead scheduling.

[0283] Example 13:

[0284] See Figures 1 to 5 A stochastic optimization scheduling method for geographically distributed data centers that considers the flexibility of spatiotemporal workloads, the main technical contents of which include:

[0285] 1. Basic data and parameter settings

[0286] To verify the effectiveness of the proposed two-stage stochastic scheduling framework, this embodiment designs a series of simulation experiments and comparative analyses to evaluate the performance of the proposed method in managing the operation of geographically distributed data centers (DCs) under workload uncertainty conditions, leveraging spatiotemporal workload flexibility. All optimization problems are modeled using YALMIP and solved using the Gurobi solver.

[0287] Numerical experiments were conducted based on a geographically distributed data centers (DCs) system consisting of three interconnected facilities. The proposed framework uniformly simulates server scheduling, cooling operation, and workload migration between DCs under uncertain workload scenarios, explicitly considering the thermal dynamics of each DC and the bandwidth and latency constraints of workload migration. To characterize the uncertainty, multiple workload scenarios were generated based on the baseline demand curve, and after reduction, a typical scenario set for stochastic optimization was obtained. To ensure the validity of the experimental results, the simulation used real operating data from an actual DC in China. Table 1 shows the main simulation parameters.

[0288] Table 1 Parameters of Distributed DC System

[0289]

[0290] 2. Calculation Results

[0291] (1) Ablation study on workload flexibility

[0292] To reveal the respective contributions of temporal workload transfer and spatial workload migration, this embodiment sets up four scenarios for ablation studies:

[0293] C1: The workload is processed locally only, without spatial migration or time transfer.

[0294] C2: The workload is processed locally only, allowing time-based migration but not spatial migration.

[0295] C3: Workloads can be migrated between DCs, allowing spatial migration but not temporal migration.

[0296] C4: Under deterministic requirements, both workload spatial migration and time transfer are allowed.

[0297] Table 2 presents the results of the ablation study, comparing the system performance of different combinations of time-shift and spatial migration. Compared to the baseline scenario C1 without flexibility, enabling only time-shift (C2) reduces total energy consumption from 104.24 MWh to 100.48 MWh, saving approximately 3.6% energy. This improvement is mainly due to the time-shifting of latency-tolerant tasks, reducing the number of active servers from 1443 to 1370 and increasing the average server utilization from 65.73% to 69.15%. In contrast, enabling only spatial migration (C3) slightly increases total energy consumption to 105.51 MWh, primarily due to the additional overhead from workload transfer between DCs. However, spatial migration improves load balancing between DCs and increases average utilization.

[0298] Table 2 Comparison of performance of different ablation experiments

[0299]

[0300] Optimal performance (C4) is achieved when both time-shift and spatial migration are enabled, reducing total energy consumption to 100.34 MWh, approximately 3.7% more energy-efficient than C1. The number of active servers is further reduced to 1366, with the average utilization rate increasing to 69.41%, the highest among all scenarios. The results demonstrate that leveraging spatiotemporal workload flexibility collaboratively enables more efficient spatiotemporal workload coordination, improving the overall energy efficiency and resource utilization of geographically distributed data centers (DCs).

[0301] To further elucidate the energy-saving mechanism of different workload flexibility strategies, Figure 3 The relative reduction rates of IT energy consumption, cooling energy consumption, and total energy consumption compared to scenarios without flexibility were compared. It is evident that time-shifting, by smoothing out peak server demand and optimizing load distribution during different time periods, can significantly reduce IT energy consumption; the energy-saving effect of spatial migration alone is relatively limited. In contrast, the combined temporal and spatial flexibility strategy achieves the highest energy-saving rate across all energy consumption components, indicating that temporal and spatial flexibility can effectively complement each other. Furthermore, the trend in cooling energy consumption is consistent with that of IT energy consumption, confirming that workload flexibility not only reduces computing energy consumption but also indirectly alleviates the cooling load on DCs.

[0302] Figure 4The paper demonstrates the hourly workload redistribution of three geographically distributed data centers (DCs) before and after applying the proposed scheduling strategy. Compared to the original load curves, the optimized load distribution shows significant changes: the workload processed by DC1 increases across multiple time periods, with an average increase of approximately 8%–10%, indicating that more flexible tasks are migrated to DC1 due to better operating conditions; the workload of DC2 shows a moderate time-shift adjustment, with an average increase of approximately 3%–5%, participating in system load balancing during some periods; the workload of DC3 decreases significantly, with an average decrease of approximately 12%–15%, as some of its tasks are transferred to other DCs with lower operating costs. Overall, the proposed scheduling framework effectively utilizes spatial migration and time shifting to achieve a more balanced workload distribution and improve the resource utilization of geographically distributed DCs.

[0303] (2) The impact of workload uncertainty on scheduling performance

[0304] To further investigate the role of stochastic uncertainty modeling, this embodiment analyzes the impact of different levels of workload uncertainty on the scheduling decisions and system performance of the proposed framework. Unlike deterministic analysis that relies solely on a single predicted value, the proposed two-stage stochastic model formulates a shared decision applicable to all reduction scenarios in the first stage, and then adaptively adjusts it based on the actual realization of uncertainty in the second stage. This structure enables the scheduler to explicitly consider potential workload fluctuations, maintaining feasible and reliable operation under various demand scenarios.

[0305] This embodiment uses the workload fluctuation range as the core uncertainty parameter, setting four uncertainty levels: ±5%, ±10%, ±15%, and ±20%. The aim is to reveal the response patterns of the proposed stochastic framework to increasing workload uncertainty in terms of energy consumption, operating costs, server configuration, and resource utilization.

[0306] As shown in Table 3, the proposed framework exhibits a smooth and moderate response to gradually increasing workload uncertainty. When the fluctuation range increases from ±5% to ±20%, the total energy consumption only increases from 100.12 MWh to 100.80 MWh, and the total operating cost only increases from... $ increased to The results show that although higher uncertainty requires additional resources to offset adverse scenarios, the overall increase in system cost and energy consumption remains at a low level, indicating that the proposed stochastic scheduling model can effectively smooth out workload fluctuations and will not cause a significant decrease in overall operating efficiency.

[0307] Table 3 compares the performance of the proposed stochastic scheduling framework under different workload uncertainty levels.

[0308]

[0309] Server performance metrics exhibited more predictable changes: as uncertainty increased, the average number of active servers rose from 1360 to 1376, while the average server utilization rate slightly decreased from 69.70% to 68.86%. This trend reflects the core mechanism of the two-stage stochastic model: to ensure that operational constraints are met under various potential load scenarios, the scheduler proactively reserves slightly more online servers as a capacity buffer, sacrificing a small amount of average utilization in exchange for higher adaptability and robustness under high-demand scenarios.

[0310] This indicates that uncertainty modeling not only changes the numerical value of the optimization objective but also fundamentally adjusts the system's operating strategy. Under higher uncertainty, the scheduler becomes more conservative in capacity allocation, avoiding overly compact resource integration. Therefore, the value of stochastic optimization lies not only in optimizing expected performance but also in generating scheduling schemes that remain stable and executable even when actual load deviates from predictions.

[0311] Figure 5 The hourly active server scheduling plans of the three data centers (DCs) under different load uncertainty levels were compared. It is evident that the server activation curves under different uncertainty levels generally follow a similar daily cycle, indicating that the proposed stochastic framework preserves the overall temporal scheduling structure. Meanwhile, significant differences exist during several peak and transitional periods, with the number of active servers dynamically adjusted to adapt to different actual loads. This suggests that workload uncertainty primarily affects the fine-grained capacity reservation of each DC, rather than the overall scheduling trend. Furthermore, the timing and magnitude of adjustments for DC1, DC2, and DC3 differ, indicating that the system addresses load uncertainty through differentiated local responses across the three DCs.

[0312] Overall, the results confirm that explicit stochastic handling of workload uncertainty is crucial for achieving reliable scheduling of geographically distributed data centers (DCs). As uncertainty increases, the proposed framework addresses this by moderately expanding server configuration and accepting a slight decrease in utilization, while keeping the increase in total energy consumption and operating costs low. This demonstrates that the proposed model achieves a good balance between energy efficiency and operational robustness, and is of significant importance for practical DC systems facing uncertain and time-varying demands.

Claims

1. A stochastic optimization scheduling method for geographically distributed data centers that considers the flexibility of spatiotemporal workloads, characterized in that, Includes the following steps: 1) Construct a multi-physical coupling model for a geographically distributed data center system; 2) Based on the multi-physical coupling model of the geographic distributed data center system, a two-stage stochastic optimization model is constructed; 3) Combine the Latin hypercube sampling method and the fast forward scene reduction algorithm to generate a reduced scene set; 4) Input the reduced scenario set into the two-stage stochastic optimization model and use a solver to obtain the optimal scheduling strategy.

2. The stochastic optimization scheduling method for a geographically distributed data center considering the flexibility of spatiotemporal workloads according to claim 1, characterized in that, The geographically distributed data center system includes a global scheduler and several data centers; The data center is used to generate workloads; The workloads include inflexible workloads, time-transferable workloads, and space-transferable workloads. The inflexible workloads are workloads generated and processed in real time in the local data center. The time-transferable workload is a workload generated in the local data center and executed with a delay within a specified time window in the local data center. The space-portable workloads are workloads generated in the local data center and migrated to other data centers for execution. The global scheduler schedules workloads to local or other data centers based on workload characteristics and data center operation status. The data center is used to execute workloads scheduled by the global scheduler.

3. The stochastic optimization scheduling method for a geographically distributed data center considering the flexibility of spatiotemporal workloads according to claim 2, characterized in that, The steps for constructing a multi-physical coupling model of a geographically distributed data center system include: 101) Establish the overall workload model after workload migration, as shown below: （1） In the formula, t represents time, and i and j both represent data center indexes. Represents a collection of data centers. Indicates a time slot; Indicates the maximum latency tolerance window; This represents the total workload processed in the i-th data center at time t; This represents the workload generated by the i-th data center at time t but executed in time slot τ; This represents the workload that migrates from the i-th data center to the j-th data center at time t; Wherein, the amount of inflexible workload processed by the i-th data center at time t. As shown below: （2） In the formula, This represents the amount of inflexible workload generated by the i-th data center at time t; Time-transferable workload model As shown below: （3） In the formula, This represents the amount of time-transferable workload generated by the i-th data center at time t; Spatially Portable Workload Model As shown below: （4） In the formula, This represents the amount of spatially portable workload generated by the i-th data center at time t; 102) Establish a cooling dynamic model based on equivalent thermal parameters, as shown below: （5） （6） （7） In the formula, This represents the power requirement of the i-th data center at time t; , , These represent the power consumption of IT equipment, cooling system, and other equipment in the i-th data center at time t, respectively. This represents the number of servers in the i-th data center; Indicates the server's idle power consumption; This indicates the maximum power consumption under full load. This represents the average CPU utilization of the servers in the i-th data center at time t. This represents the number of servers powered on in the i-th data center at time t; This indicates the service rate of the data center; The other equipment includes lighting and power distribution facilities; 103) Establish a migration delay model between DCs, as shown below: （8） （9） （10） （11） In the formula, Indicates the total migration delay between DCs; These represent propagation delay, transmission delay, and processing delay, respectively. This represents the physical distance between the i-th data center and the j-th data center; Indicates the speed at which signals propagate in an optical fiber; This indicates the amount of data used to migrate workloads; This represents the bandwidth of the network link between the i-th data center and the j-th data center; This indicates the task completion rate.

4. The stochastic optimization scheduling method for a geographically distributed data center considering the flexibility of spatiotemporal workloads according to claim 3, characterized in that, The power consumption of the cooling system of the i-th data center at time t As shown below: （12） In the formula, t represents time, and i represents the data center index. This represents the total thermal power of the i-th data center at time t; , Let represent the indoor air temperature of the i-th data center at times t and t-1, respectively; Indicates the thermal resistance between indoor air and the external environment; Indicates indoor air heat capacity; This represents the outdoor air temperature of the i-th data center at time t; Indicates the thermal coefficient of IT equipment; This represents the power consumption of the IT equipment in the i-th data center at time t; This indicates the energy efficiency ratio of the cooling system.

5. The stochastic optimization scheduling method for a geographically distributed data center considering the flexibility of spatiotemporal workloads according to claim 2, characterized in that, The objective of the two-stage stochastic optimization model is to minimize the total power cost of all data centers throughout the entire scheduling cycle. The total power cost for all data centers during the entire scheduling period is shown below: （13） In the formula, t represents time, and i represents the data center index. Represents a collection of data centers. Indicates the scheduling period; This represents the total power cost of all data centers throughout the entire scheduling cycle; Let represent the electricity price of the i-th data center at time t; This represents the power requirement of the i-th data center at time t; Indicates the duration of a time period.

6. The stochastic optimization scheduling method for a geographically distributed data center considering the flexibility of spatiotemporal workloads according to claim 2, characterized in that, The constraints of the two-stage stochastic optimization model include DC operation constraints and end-to-end delay constraints. The DC operation constraints are as follows: （14） （15） （16） （17） In the formula, t represents time, and i represents the data center index. This represents the number of IT devices in the i-th data center at time t; This represents the number of active servers in the i-th data center; This represents the average CPU utilization of the servers in the i-th data center at time t. This indicates the maximum CPU utilization of the server. , Let represent the indoor air temperature of the i-th data center at times t and t-1, respectively; , These represent the upper and lower limits of the indoor air temperature in the data center, respectively. This indicates the maximum permissible variation in indoor temperature. The end-to-end delay constraint is as follows: （18） （19） In the formula, j represents the data center index. This represents the workload that migrates from the i-th data center to the j-th data center at time t; This represents the bandwidth of the network link between the i-th data center and the j-th data center; Indicates the duration of a time period; Indicates the total migration delay between DCs; This represents the system's maximum tolerable end-to-end delay.

7. The stochastic optimization scheduling method for a geographically distributed data center considering the flexibility of spatiotemporal workloads according to claim 2, characterized in that, The steps for generating the reduced scene set are as follows: 301) Divide the probability distribution of the workload into several equally probable intervals, and randomly draw samples from each interval to construct the original scene set; The probability weight of each scene in the original scene set satisfies the following condition: （20） （21） In the formula, , Both represent scenarios; Represents the original scene set; Indicates the scene set in the original scene probability weights; , Each is a set of scenes in the original scene. , The probability of; 302) Construct a reduced scenario set and initialize it as an empty set; 303) Select the scene with the smallest total Euclidean distance from the other scenes in the original scene set, remove the selected scene from the original scene set and send it to the reduced scene set, and use the probability weight of the selected scene in the original scene set as the probability in the reduced scene set, and recalculate the probability weight of the selected scene in the reduced scene set. The scene selected from the original scene set that has the smallest total Euclidean distance from the remaining scenes is shown below: （22） （23） In the formula, This represents the scene selected from the original scene set that has the smallest total Euclidean distance from the remaining scenes. Indicates a scene; Representing a scene and scene The Euclidean distance between them; t represents time, and i represents the data center index. Represents a collection of data centers. Indicates the scheduling period; , They represent the scenes respectively. Scene The total workload arrivals of the i-th data center at time t; 304) Update the probability weights of the remaining scenes in the original scene set; 305) Return to step 303) until the number of scenes in the reduced scene set reaches the preset number of scenes.

8. A stochastic optimization scheduling method for a geographically distributed data center considering the flexibility of spatiotemporal workloads according to claim 2, characterized in that, After inputting the reduced scenario set into the two-stage stochastic optimization model, the objective function of the two-stage stochastic optimization model is solved as follows: （24） In the formula, Indicates a scene; Represents a set of reduced scenarios; This indicates a reduced scenario set. probability weights; Representing a scene Total power cost for all data centers.

9. A stochastic optimization scheduling method for geographically distributed data centers considering spatiotemporal workload flexibility according to claim 2, characterized in that, The optimal scheduling strategy includes the local processing volume, migration reception volume, latency processing volume, transmission migration volume, number of active servers, average utilization, cooling power, and the expected total electricity cost and total energy consumption of the geographically distributed data center system for each data center in each time slot.

10. A stochastic optimization scheduling method for a geographically distributed data center considering the flexibility of spatiotemporal workloads as described in claim 1, characterized in that, The solver includes a mixed integer programming solver.

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