Temporal fusion transformer-based strategy for efficient multi-cloud content replication

TFT for time series forecasting

An attention-based Deep Neural Network with excellent performance and interpretability is called TFT. Engineers from Google introduced the TFT in 2019. TFT is a novel transformer architecture designed to efficiently process time-series data in cloud computing environments. TFT offers the potential for both interpretable predictions and multi-horizon forecasting (Junankar, Sondhi & Nair, 2023). Different dimensions of temporal relationships are modeled using recurrent layers and interpretable self-attention layers. Appropriate features are chosen using specialized components, and extraneous features are suppressed using a succession of gating layers. Three different aspects are supported by TFT such as time-dependent data along with already identified inputs in the future. In addition, there are categorical/static variables, also referred to as time-invariant features, and time-dependent data that has only recently become discovered (Liao & Radhakrishnan, 2022). TFT is hence more adaptable than earlier types. Through the discovery of globally relevant variables, enduring stable temporal patterns, and important events for the prediction issue, TFT aims to improve understandability of time series forecasting (Anandaraj et al., 2021). This achieves Explainable AI’s goal of making the output of the model more reliable and usable. The model needs the following inputs for a given timestep t, window for lookback w, and a Wmax window step in advance to a maximum, where t $\in$ [t−w…. t + Wmax]: Identified potential inputs x in the time period [t+1… t + Wmax], observed preceding inputs x in the time period [t−w… t], and a collection of static variables s be present. The time range [t+1… t + Wmax] is too covered using dependent variable y. TFT is used in the proposed system to detect popular files. It combines multiple time-series features from cloud to detect popular files by recognizing patterns in the data that indicate high usage. By combining multiple sources of data, the TFT detect patterns that are not visible when analyzing only one source. For example, the TFT combines usage data from multiple cloud providers to detect which cloud-hosted files are popular across multiple providers. Additionally, the TFT can detect changes in usage patterns over time by analyzing time-series data. It is used to identify which files are becoming more popular over time. Finally, the TFT identify outliers in the data, which is used to identify files that are abnormally popular or unpopular. Multi-horizon forecasting capability of the TFT is one of the key novelties of the proposed method. Unlike conventional models which focus on short-term predictions, TFT enables simultaneous forecasting across multiple time intervals. This allows the proposed system to predict future data popularity trends more effectively and ensures that replication strategies are proactive instead of reactive. TFT reduces latency and optimizes resource allocation across dynamic cloud environments by using a broader temporal perspective. The utilization of temporal attention mechanisms within TFT improves its ability to recognize and prioritize the most significant features in the generated dataset. It contrasts with conventional replication methods which often rely on fixed rules or heuristic approaches. The attention mechanism dynamically adjusts to evolving patterns in data popularity and cloud resource availability. It is significantly improving prediction accuracy and replication decisions. Finally, the proposed framework’s adaptability and scalability further differentiate it from existing methods. This adaptability ensures efficient and reliable performance even in fluctuating multi-cloud environments, addressing limitations commonly associated with conventional replication strategies.

Problem formulation

The information storage unit in the cloud is a block to decrease access time. An original data is broken up into multiple blocks if it is too huge in size. The unit for data access, however, is typically a data file. The characteristics of proposed technique are as follows. (1) Mathematical representation formed in Sun et al. (2012) is used and further expanded and explained how the quantity of copies and system availability relate to one another. (2) The temporal locality is used to identify the popular data using TFT and the replication operation will start when a data file’s popularity reaches a dynamic threshold. (3) Replicas are also distributed evenly among data nodes. There are mainly four stages to adapt for attaining the maximum benefits of replication. In the first stage, it is not a fair way to identify several popular data because replicating every data files raises unnecessary burden of maintaining numerous replicas and raises the replication cost beyond the satisfactory limit. In second stage, producing extra copies of a data file wastes storage space and makes storage more difficult and so only a fair number of replicas are created. The demand for a data file at a given time, on the other hand, can decide the best possible number of replicas. The amount of data replication is proportional to the availability rate according to researchers. However, in case of system availability, more data replicates raise overhead charges. The next stage in the replication process is to determine where the new replicas are placed. Locating replicas at random will not improve the performance of system. As a result, copies should be located at right place at right time so that the system’s performance and availability are improved. The next important stage in the replication is to find how efficiently perform the replication process. Consistency is the capacity of multiple users to perform read and write simultaneously. The replication criterion’s primary difficulty is storing all data consistently.

This section explains the preferred architectural model for sharing data between cloud nodes and keeping replication in right place. It is being utilized in a number of research (Yu et al., 2022; Slimani, Hamrouni & Ben Charrada, 2020). Data replication access and placement through cloud nodes are described in the proposed model framework. As a result, this depends on previous studies to obtain the best access to the selected nodes at the lowest cost and the quickest route between DCs. By utilizing the statistical distribution across nodes in various ways, optimization of data replication placement using the heterogeneous system is done. Every DC has different stages, therefore the VM is different from the DCs, and so on. Figure S3, describes the formal model for cloud data center architecture as a cloud data service scheme usually consists of the scheduling agent, replica selector and agent, as well as data centers. The replication process is managed by the scheduling agent, which stores all information about the number of replicas and their locations across different data centers.

Let $\mathrm{C}=\{{\mathrm{c}}_1,{\mathrm{c}}_2,\dots ,{\mathrm{c}}_{\mathrm{n}}\}$ be n number of cloud users, $S\mathrm{T}=\{S{\mathrm{T}}_1,S{\mathrm{T}}_2,\dots ,S{\mathrm{T}}_{\mathrm{n}}\}$ be a set of tasks of the cloud user set C, and $S{\mathrm{T}}_{\mathrm{i}}=\{s{\mathrm{t}}_{\mathrm{i}1},s{\mathrm{t}}_{\mathrm{i}2},\dots ,s{\mathrm{t}}_{\mathrm{i}\mathrm{n}\mathrm{i}}\}$ be a subset of tasks of the i^th client c_i, where n_i is used to represent the amount of subtasks, and $s{\mathrm{t}}_{\mathrm{j}}$ is the j^th task given to the scheduling agent over a cloud interface. If ${\mathrm{c}}_0$ has two tasks, then $S{\mathrm{T}}_0=\{s{\mathrm{t}}_1,s{\mathrm{t}}_2,s{\mathrm{t}}_3\}$, and ${\mathrm{n}}_0$ = 3. A task $s{\mathrm{t}}_{\mathrm{j}}$ is defined by a four tuple such as $s{\mathrm{t}}_{\mathrm{j}}=(ti{d}_{\mathrm{j}},t{r}_{\mathrm{j}},t{d}_{\mathrm{j}},t{f}_{\mathrm{j}})$, where $ti{d}_{\mathrm{j}}$, $t{r}_{\mathrm{j}}$, $t{d}_{\mathrm{j}}$ and $t{f}_{\mathrm{j}}$ are the identification of task, rate of task generation, time limit time of task along with the number of needed files to perform the task $s{\mathrm{t}}_{\mathrm{j}}$, respectively (Awad, Abdelkader & Salam, 2021; Bai et al., 2013; Kamila et al., 2022). $DC=\{d{\mathrm{c}}_{\mathrm{m}}{d}_1,{\mathrm{c}}_{\mathrm{m}}{d}_2,\dots ,d{\mathrm{c}}_{\mathrm{m}}{d}_n\}$ are the representation of data center contain s_m data nodes on a physical machine PY.

Each node executes a virtual machine, and is defined by $d{\mathrm{c}}_{\mathrm{m}}{d}_{\mathrm{j}}$ that is a five tuple $d{\mathrm{c}}_{\mathrm{m}}{d}_{\mathrm{j}}=(d{\mathrm{c}}_{\mathrm{m}}{d}_{\mathrm{j}},d\mathrm{c}{r}_{\mathrm{j}},d\mathrm{c}t{s}_{\mathrm{j}},d\mathrm{c}{f}_{\mathrm{j}},d\mathrm{c}b{w}_{\mathrm{j}})$, where $d{\mathrm{c}}_{\mathrm{m}}d\mathrm{j}$, $d{\mathrm{c}}_{\mathrm{m}}{d}_{\mathrm{j}}$, $d{r}_{\mathrm{j}}$, $dt{\mathrm{s}}_{\mathrm{j}}$, $d{f}_{\mathrm{j}}$ and dcbwi are used to identify the data node, rate of arrival of request, average service providing time, probability of network failure and data node’s network bandwidth such as $d{\mathrm{c}}_{\mathrm{m}}{d}_{\mathrm{j}}$, respectively. To ensure the service performance of the each data center DC, the rate of task generation $t{r}_{\mathrm{j}}$ of cloud consumer set C, the rate of arrival of request $d\mathrm{c}{r}_{\mathrm{j}}$ as well as chance of failure $d\mathrm{c}{f}_{\mathrm{j}}$ of DC need to reach Eq. (1).

(1) $${\sum }_{i=0}^{NS}t{r}_i\le {\sum }_{j=0}^{m}dc{r}_{j}X\left(1-dc{f}_j\right)$$where $trj$ is the rate of generation of task j, is the rate of request arrival of task j on the node i, $dfk$ is the chance of failure of task j. Let $\mathrm{D}\mathrm{F}=\{\mathrm{d}{\mathrm{f}}_1,\mathrm{d}{\mathrm{f}}_2,\dots ,\mathrm{d}{\mathrm{f}}_{\mathrm{l}}\}$ are the available set of data files at data center. $\mathrm{B}=\{{\mathrm{B}}_1,{\mathrm{B}}_2,\dots ,{\mathrm{B}}_{\mathrm{n}}\}$ are collection of blocks in the data center and ${\mathrm{B}}_{\mathrm{j}}=\{{\mathrm{b}}_{\mathrm{j}1},{\mathrm{b}}_{\mathrm{j}2},\dots ,{\mathrm{b}}_{\mathrm{j}\mathrm{m}1}\}$ are the j^th subset of blocks belonging to the j^th data file df_j. It is stripped into m_j predetermined blocks in compliance with its length. Any block b_j is defined by a five tuple ${\mathrm{b}}_{\mathrm{j}}=(bi{d}_{\mathrm{j}},b{p}_{\mathrm{j}},b{s}_{\mathrm{j}},bn\mathrm{j},bt\mathrm{j})$ where $bi{d}_{\mathrm{j}},b{p}_{\mathrm{j}},b{s}_{\mathrm{j}},b{n}_{\mathrm{j}}\mathrm{a}\mathrm{n}\mathrm{d}b{t}_{\mathrm{j}}$ are the identification of block, number of requests, size of the block, the number of replicas needed and the last access time of the block b_j, respectively. While user c_k send a request to access a block $b_{\mathrm{j}}$ from a data node $d\mathrm{m}{d}_{\mathrm{j}}$ with guaranteed bandwidth performance, bandwidth $b{s}_{\mathrm{j}}/dt{\mathrm{s}}_{\mathrm{i}}$ need to be consigned to this session. The entire bandwidth utilized to hold diverse set of requests from cloud user set C need to be less than $d\mathrm{c}b{w}_{\mathrm{j}}$, as shown by Eq. (2).

(2) $${\sum }_{i=0}^{NS}{\displaystyle \frac{\mathrm{b}{\mathrm{s}}_{\mathrm{j}}}{\mathrm{d}\mathrm{t}{\mathrm{s}}_{\mathrm{i}}}\le \mathrm{d}\mathrm{c}\mathrm{b}{\mathrm{w}}_{\mathrm{j}}.}$$

NS represents the upper limit of network connections of data node $d{\mathrm{c}}_{\mathrm{m}}{d}_{\mathrm{j}}$ which provide services simultaneously, $b{s}_{\mathrm{j}}$ represents the block size of block $b\mathrm{l}$, $dt{\mathrm{s}}_{\mathrm{i}}$ represents the typical service time of data node $d{\mathrm{c}}_{\mathrm{m}}{d}_{\mathrm{j}}$, $d\mathrm{c}b{w}_{\mathrm{j}}$ represents the bandwidth of the network available for data node $d\mathrm{c}b{w}_{\mathrm{j}}$. Availability of block is defined as the capability of a data block to offer appropriate service below agreed restraints. The block availability of a block $b_{\mathrm{j}}$ is represented as $\mathrm{A}B\mathrm{j}$. $\mathrm{A}{\mathrm{B}}_{\mathrm{j}}$ is the possibility of block $b_{\mathrm{j}}$ in an available state. $(\mathrm{A}{\mathrm{B}}_{\mathrm{j}})$ is the possibility of block $bk$ in an unavailable status, and $P(\mathrm{A}{\mathrm{B}}_{\mathrm{j}})=1-P(\mathrm{A}{\mathrm{B}}_{\mathrm{j}})$. The number of replicas of block $b\mathrm{j}$ is $b{\mathrm{m}}_{\mathrm{j}}$. It is apparent that block $b\mathrm{j}$ is considered not available only if all the replicas of block $b\mathrm{j}$ are unavailable. Hence the unavailability as well as availability of block $b\mathrm{j}$ are calculated as per Eqs. (3) and (4).

(3) $$P(\mathrm{A}{\mathrm{B}}_{\mathrm{j}})=1-(1-\mathrm{P}(\mathrm{a}{\mathrm{b}}_{\mathrm{k}}){)}^{b\mathrm{m}\mathrm{j}}$$

(4) $$P(\mathrm{A}{\mathrm{B}}_{\mathrm{j}}^{\mathrm{\prime }})=1-\mathrm{P}(\mathrm{a}{\mathrm{b}}_{\mathrm{k}}{)}^{b\mathrm{m}\mathrm{j}}.$$

The capability of a data file to deliver appropriate service within predetermined restrictions is known as availability of file. The availability of file for a data file dj is represented as $A{\mathrm{F}}_{\mathrm{j}}$. ( $A{\mathrm{F}}_{\mathrm{j}}$) is the chance of data file d_j in the state of unavailable status, and $P(A{\mathrm{F}}_{\mathrm{j}})=1-P(A{\mathrm{F}}_{\mathrm{j}})$. If the data file dj is divided into mj predetermined blocks represented using $B\mathrm{j}=\{b\mathrm{j}1,b\mathrm{j}2;\dots ;\mathrm{j}\mathrm{m}1\}$, which are distributed on different data nodes. $M\mathrm{j}=\{b\mathrm{m}\mathrm{j}1,b\mathrm{m}\mathrm{j}2,\dots ,\mathrm{m}\mathrm{j}\mathrm{m}\mathrm{k}\}$ is the collection of the numbers of replicas of the blocks of $B\mathrm{j}$. The unavailability and availability of data file dj is given as:

(5) $$P(A{\mathrm{F}}_{\mathrm{j}})=1-(1-\mathrm{P}(\mathrm{b}{\mathrm{a}}_{\mathrm{j}}){)}^{\mathrm{b}\mathrm{m}\mathrm{j}}{)}^{\mathrm{m}\mathrm{j}}$$

The available possibility of every replica is represented as $\mathrm{P}(ba\mathrm{j})$ in data file dj if the data file dj is divided into mj blocks. Each block in data file dj has mj replicas available for it, and each and every blocks at the same location need to have the similar available possibility because each and every blocks need to be located in data nodes with similar configuration in the cloud data centers.

Algorithm and pseudo code

A strategic level algorithm (Algorithm 1) of the proposed system is given below with steps to be followed. This algorithm provides a structured approach to build an efficient content replication framework using the TFT model.

• 1)

  Initially set the value for availability and unavailability of each block replica of block b_l, P(ab_l) and P(uab_l)

• 2)

  While data file dj at all data centres DC do the following

  • a)

    Determine the degree of popularity dp_l of a block b_l of data file d_j using TFT.

  • b)

    Determine replication factor FR_j of data file d_j using degree of popularity dp_l

  • c)

    If the value of FR_j is less than threshold T, then enable the replication process for the data file f_j

• 3)

  End while

• 4)

  while each replication process for data file fj:

  • a)

    for every block bj in data file fj:

    • i)

      determine the new FRj by introducing replication at each and every data centre DCj

    • ii)

      implement the replication that yields the highest new FRj

  • b)

    end for

• 5)

  end while

• 6)

  identify the file fj with the minimum degree of popularity in the dataset:

  1. while true:

     1. eliminate the replica that results in a new FRj, without replication, exceeding the threshold T

  2. end while

• 7)

  end while

The process of determining the degree of popularity of a block bj is framed as a time series forecasting issues and addressed using TFT. dp_j represents upcoming access frequency, which is predicted using the number of access demands, n_ad(m), at a particular moment m. TFT uses an attention based deep neural network that combines excellent performance with interpretability. It is a time series prediction method which offers accurate predictions with low computational cost. The rates of measured request arrivals and service demands are chosen for short-term forecasting using TFT. The proposed strategy is inspired by the observation that files accessed frequently in recent times are probable to experience similar demand in the near future. Predictive statistics based on file access patterns are used to infer this (Bouhouch, Zbakh & Tadonki, 2023; Arasteh et al., 2023). The replication process is initiated when the accessibility of every existing replica surpasses a predefined threshold, and the replication factor is established using data blocks. A new replica with a higher replication factor is created on a chosen node. The number of additional replicas is determined using a heuristic approach designed to enhance file accessibility. This article adopts the problem formalization outlined in Sun et al. (2012). However, for forecasting future data file requests, a simplified time-series method is employed in the proposed system.

Determine the popularity of file

In the proposed system, TFT is employed to determine the popularity of individual files in the cloud system. It takes into account basic temporal aspects, the frequency with which files are accessed, and how recently they were accessed, and brings in temporal aspects and manners of how frequent the user is in accessing them over time. The other criteria considered are time associated with the file, number of different users, and the size of the file. These factors are combined to compute a normalized score that effectively represents the overall popularity of each file. The TFT uses its predictive capabilities to identify files that are likely to experience high demand in the near future. The system assures efficient allocation of resources and enhanced access performance by giving priority to these files. The replication process starts when a file’s popularity score rises above a dynamic threshold. Because of its flexibility, this threshold makes the system to react to shifting access trends. In order to increase accessibility and decrease latency for end users, more copies of the content are produced throughout the replication process. This ensures that frequently accessed files remain readily available, optimizing system performance and meeting user demands efficiently. By integrating TFT with adaptive replication strategies, the proposed system achieves a balance between computational efficiency and user satisfaction in a cloud. The formula to compute the degree of popularity of the file by using TFT is given below.

(6) $$\mathrm{T}\mathrm{F}\mathrm{T}\left(\mathrm{f}\mathrm{j}\right)=\left(1/\mathrm{T}\right)\ast \sum \mathrm{t}=1\mathrm{T}\left(\mathrm{f}\left(\mathrm{t}\right)\ast \beta \left(\mathrm{t}\right)\right)$$where f(t) represents frequency of data file by time t, T symbolizes total number of time steps, and β(t) describes adjustable weighting factor for time t. The adjustable weighting factor is determined by various methods, such as taking into account the popularity of the file in the past or the relative importance of the file at that time step. The TFT produces an overall popularity score for the file, which is used to determine the most popular file in cloud computing.

Replication factor from popularity degree

The replica factor (RF) is defined as the ratio of the total bytes of data files (fj) demanded by all tasks within the designated constraint to the popularity degree. It is utilized to decide whether the data file fi, represented as RFi in the code, should be replicated.

(7) $$\begin{array}{r}\mathrm{R}\mathrm{e}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}(\mathrm{R}\mathrm{F}\mathrm{j})=(\mathrm{P}\mathrm{o}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{l}\mathrm{e})/(\mathrm{R}\mathrm{e}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e})\end{array}$$

(8) $$\begin{array}{rl}& \mathrm{R}\mathrm{e}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}=\left(\mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{R}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{s}+\mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{s}\mathrm{t}\right)/\\ & \mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{s}\end{array}$$

Simulation setup and parameter

CloudSim is an open source toolkit used to simulate cloud environments (Ghobaei-Arani & Shahidinejad, 2021; Saharan et al., 2020). It provides a simulation environment for modeling the cloud computing infrastructure, services, and applications. It is designed to help researchers and industry practitioners to explore and analyze various cloud computing scenarios (Sun et al., 2012). CloudSim with added module for TFT is a powerful software suite that enables cloud computing systems to be more efficiently and effectively managed. It offers a broad collection of tools for managing and optimizing the performance of cloud computing systems. TFT works by merging multiple data sources into a single unified view, and then applying temporal fusion to analyze the data. Cloudsim with TFT for data replication allows users to study the performance of data replication strategies on cloud computing platforms. The tool allows users to specify the replication strategies and parameters to be used, as well as the performance metrics to be monitored (Maweu et al., 2021). Table S2 specifies the actual configuration depending on the type of data centers, number of systems, PE per system, MIPS and Bandwidth. The simulation results are compared with different replication strategies to identify the most effective ones. In the simulated environment, 42 data centres are established. The number of processing components (PCs) on each of the 670 virtual machines designated as service providers ranges from 2 to 6. Each of the fifty individual data files in the cloud storage environment has a size between (0.1, 15) GB. Each file is kept in a block, which is a fixed-size storage unit (bs = 0.1 GB). The same data file’s blocks are dispersed over various virtual machines. Every data file has one initial replica, which is distributed at random. In furtherance of simplicity, it is assumed that one single data file will serve as both the replication element and the base element for data storage (Rambabu & Govardhan, 2023). The 670 virtual computers receive 1,500 tasks; each requests some data files. It is distributed according to the Poisson distribution with the preceding set of task. Configuration settings for evaluating the proposed system are shown in the Table S3.

Performance evaluation

TFT provides a robust and scalable approach to content replication across multiple clouds by taking into account temporal dependencies and uncertain user demands (Fu, Zhou & Han, 2021). It provides better performance by dynamically adapting replication strategies based on changing user demands and network conditions. TFT provides a good balance between performance, scalability, and computational complexity for content replication across multiple clouds. However, the specific performance of the TFT may vary depending on the network topology, the specific parameters used in the model, and other factors. Additionally, the use of multiple clouds for content replication may also involve additional costs and complexities that need to be considered.

Dataset generation

TFT models are designed to handle time-series data, which is used to model various aspects of cloud file access patterns. Therefore, a dataset for training TFT models for cloud file access include both file access patterns and corresponding time-series data. Tabular Generative Adversarial Network is used for synthetic tabular data generation that includes time-series data that captures the key characteristics of cloud file access patterns (Slimani, Hamrouni & Ben Charrada, 2020). The snapshot of data is shown in Fig. S4. This CloudSim configuration is the infrastructure setup used for the cloud environment in the content replication strategy across the multi-cloud environment. Such configurations simulate the server configurations and network environment in which the TFT based strategy is tested and validated. The various types of data centers reflect differences in the computational as well as the networking capabilities of these centers as essential when replicating content across different cloud contexts. The synthetic dataset used for this experimentation includes 10,000 records generated using TGAN, with variability across multiple attributes such as file type, file size, access patterns, and user actions, reflecting inherent biases and imbalances observed in real-world cloud environments. It highlights the high correlation (0.93), low distortion (RMSE: 0.04, MAE: 0.03), and strong similarity (0.96) between the synthetic and real datasets. Moreover, privacy results confirm no duplication of real data points, ensuring ethical data synthesis. For validation, real-world datasets were indirectly referenced by ensuring the synthetic data statistically mimics real-world distributions.

Parameters for evaluation

System effective rate in bytes: The system effective rate (SER) in bytes ‘R’, is the ratio of the aggregate bytes requested by all tasks in a system to the total bytes potentially accessible (Li et al., 2021). The independence of file requests is ensured as any two requests will access distinct replicas. This is because a single data file access operation is limited to requesting only one file. One or several data files may be requested concurrently by users from set U.

Replica numbers: A sufficient number of data file replicas must be created in order to maintain a high system effective rate in bytes (Yu, Liu & Fan, 2021). The block availability is set to 0.7 initially in order to assess the convergence of the proposed method, and various values of the adjustable α weighting parameter are used to determine the required replicas number.

Response latency: The time between when a job is submitted and when the result is returned is the response latency for a data file. The average response latency of the system, is the indicative measure of response time in favor of every data request task completed by the client can be ascertained by Mazumdar et al. (2019).

Rate of successful execution of task: It is a measure of how often a particular task or process is completed successfully. It is typically expressed as a percentage of successful executions compared to the total number of attempts. This metric is used to evaluate the performance of a variety of tasks and processes, including software applications, customer service operations, and manufacturing processes. The successful execution rate is used to determine the overall efficiency of a system or process, as well as identify areas for improvement (Govardhan & Dugyani, 2024).

Result and analysis

The weighted relevance of the different input features in the TFT is shown in Fig. S5. These weights, highlight which features most influence the model’s predictions of data popularity patterns, are generated from the attention processes within TFT. Certain features such as the use of cloud content, network latency, historical replication, data size, and security policies are given more weight compared to others. This realization demonstrates how well the TFT finds and ranks the most important characteristics for precise predictions. Dynamically weighing attributes allows for flexibility in adjusting to different multi-cloud setups, which improves content replication decision-making. The mean squared error (MSE) values for the TFT model during training and validation are shown in Fig. S6. As a measure of prediction accuracy, MSE determines the typical squared difference among the predicted and actual values. The model which fits the observed data better is indicated using lower values of MSE. The figure’s findings show that the model successfully reduces error during learning, guaranteeing precise and reliable predictions for the replication method. By minimizing unnecessary resource usage and improving system efficiency, this increase in accuracy aids in the optimization of replication decisions. The number of training iterations carried out during the TFT optimization is shown by the 50 iterations in Fig. S6. In order to guarantee that the model converges and captures enough temporal patterns for accurate predictions, these iterations were chosen. After 50 iterations, the data showed steady, dependable performance that was neither overfit nor underfit. The MAE attained by the TFT model is displayed in Fig. S7. An intuitive measure of prediction error, MAE is calculated as the average of the absolute differences among actual and predicted values. The figure’s low MAE values show that the model continues to produce forecasts with a high degree of exactness. Since they minimize delay and avoid over or under provisioning of resources in multi-cloud scenarios, accurate predictions are crucial for optimizing content replication. For clarity and also to show the dynamics of the TFT’s early training, the figure is limited to 10 epochs. The most important learning takes place during these early epochs, providing information about convergence patterns and performance enhancements. Given that subsequent epochs exhibit very slight changes, extending the figure past 10 would introduce needless complication. However, the entire training process continued for the entire number of epochs specified in the proposed approach, and the discussion shows the outcomes of the entire training process in Fig. S7.

In the absence of employing the TDRS technique, the number of replicas for large-scale data files is set at 3, resulting in a total of four copies for each data file. As illustrated in Fig. S8, with an increasing number of tasks, the rate of successful execution of tasks experiences a significant decline, particularly when the task count surpasses 50%. The lower the availability of blocks, the lower the rate of successful execution becomes. The proposed algorithm maintains a high rate of successful execution in the cloud environment, consistently exceeding 90%. It can be inferred that the proposed algorithm enhances and sustains the successful execution rate at a reliable and elevated level. As illustrated in Fig. S9, with an increase in the number of replicas, the TD2RS algorithm ensures a consistently high level of system effective rate in bytes. When the average block availability exceeds 0.8 and the number of replicas is fixed at 4, the system effective rate in bytes remains near to 1, even when the average block availability drops below 0.2. To maintain the system effective rate in bytes near 1, the number of replicas must not exceed 20. This observation highlights that the TD2RS algorithm significantly enhances the system effective rate in bytes. As shown in Fig. S10, over time, there is a rapid increase in the number of replicas. Subsequently, this count of replicas stabilizes at a level determined by the adjustable parameter β(t). It is inferred that a higher value for the adjustable parameter necessitates a greater number of replicas to sustain the desired system effective rate in bytes. It is proved that the TD2RS algorithm has an excellent convergence rate. As shown in Fig. S11, when the amount of tasks increase, the response latency also raises significantly, particularly when the task load is greater than 70%. The fewer availability of block is, the longer the response latency will be. Figure S12 illustrates the TD2RS method has 95% replication efficiency compared to the other methods because of optimized resource utilization. It also has a higher task throughput, handling 90 tasks, which is significantly higher than that of FRS (60), CIR (70), and LRM (75) this reveals that the system can handle large tasks. Considering computational overhead, TD2RS takes the lowest measure (5 ms/task). Moreover, TD2RS does 95% of fault tolerance, and produce accuracy. Combined, these findings mean that TD2RS becomes the least error-prone and fastest-acting strategy for multi-cloud content replication, while showcasing overall superior performance in all the measures. A conclusion is drawn that TD2RS algorithm improves the response latency and retains the response latency at a steady state within a small time span. The performance of the model under different conditions is summarized in Table S4, where normal operation yields the highest performance metrics, while server failures and high load lead to significant degradation.