Hybrid Workload Enabled and Secure Healthcare Monitoring Sensing Framework in Distributed Fog-Cloud Network

: The Internet of Medical Things (IoMT) workﬂow applications have been rapidly growing in practice. These internet-based applications can run on the distributed healthcare sensing sys-tem, which combines mobile computing, edge computing and cloud computing. Ofﬂoading and scheduling are the required methods in the distributed network. However, a security issue exists and it is hard to run different types of tasks (e.g., security, delay-sensitive, and delay-tolerant tasks) of IoMT applications on heterogeneous computing nodes. This work proposes a new healthcare architecture for workﬂow applications based on heterogeneous computing nodes layers: an application layer, management layer, and resource layer. The goal is to minimize the makespan of all applications. Based on these layers, the work proposes a secure ofﬂoading-efﬁcient task scheduling (SEOS) algorithm framework, which includes the deadline division method, task sequencing rules, homomorphic security scheme, initial scheduling, and the variable neighbourhood searching method. The performance evaluation results show that the proposed plans outperform all existing baseline approaches for healthcare applications in terms of makespan.


Introduction
Nowadays, the usage of medical devices based on the Internet of Medical Things (IoMT) network to deal with healthcare issues has been growing progressively [1]. The IoMT is a network that is composed of medical sensors, wireless technology and distributed cloud computing technologies [2]. Therefore, the combination of IoMT and healthcare devices can improve the quality of human life and provide better care services and create a more cost-effective system [3]. Recently, many IoMT-based applications have been developed node level are widely ignored. Due to this, the failure ratio of tasks and deadline of applications are missed over a wide range. This paper proposes a novel scheduling system for mixing fne-grained and workfow IoMT tasks in distributed and virtual machinebased mobile edge cloud networks to cope with the issues mentioned earlier. This work considers both workfow and fne-grained tasks simultaneously, the proposed serverless functions and a virtual machine aware service environment in a distributed mobile edge cloud network. The function as a service (FaaS) is a cost-effcient model for fne-grained tasks which pay for the execution of tasks rather than provisioning for monthly or yearly for not using tasks. For the workfow tasks, the virtual machine-based solution has been proposed in the system. Each application is divided into three types of tasks: security tasks, delay-sensitive tasks, and delay-tolerant tasks. The proposed IoMT system consists of different paradigms such as mobile computing, fog computing, and cloud computing based on task types. The study's goal is to minimize both makespans of applications and the cost of the system during problem formulation. In summary, this paper makes the following contributions to solve the scheduling problem.
• Initially, the study devises the mathematical model of hybrid work of IoMT applications with many objectives. The hybrid workloads consist of fine-grained and workflows tasks, and the multi-objective functions are makespan, cost, and energy consumption. Each objective function has different weights to optimize the IoMT for each application; • The study devises three-phase level scheduling methods such as deadline-effcient, cost-effcient and energy-effcient ones in the IoMT system to optimize the overall system in the network; • To maintain the security requirements of fne-grained and workfow workloads, the fully homomorphism Encryption (FHE)-enabled security is suggested to ensure the security in IoMT for all applications; • To optimize all objectives together, the study devises the deep graph convolutional network-enabled weighting scheme to boost and optimize the study's overall nonlinear objective functions in different convolutional networks.
The sections are organized as follows. Section 2 presents existing studies related to the considered problem. Section 3 defines all steps of the problem formulation. Section 4 outlines the proposed methods and their solutions. Section 5 illustrates the performance evaluation of techniques on different workfow benchmarks. Section 6 presents the conclusion of the paper.

Related Work
For many years, Internet of Medical Things (IoMT) frameworks or systems have gained signifcant traction in various medical sectors. Many different sorts of healthcare workloads are taken into account in the IoMT to tackle various scheduling and offoading issues. Workfows, applications, services, and fne-grained and coarse-grained models are examples of workloads. The IoMT consists of different heterogeneous computing nodes where a connection between computers or computer programmes is known as an application programming interface (API). It is a form of software interface that provides a service to other programmes. An API specifcation is a document or standard that defnes how to create such a connection or interface. An API is implemented or exposed by a computer system that meets this standard. The term API can be used to refer to either the specifcation or the implementation. As a result, as indicated in Table 1, there are different multi-objective techniques for each workload, each with its own set of restrictions and security requirements. In the study of [1], the workfow application, deadline constraint, weighting method, and remote Cloud VMs along with the RSA security mechanism aware IoMT system are suggested. The objective is to offoad healthcare data with their deadlines on the cloud servers. The study of [2] suggested IoMT-based coarse-grained healthcare workloads, with resource constraints and the programming aware constraint method on latency optimal edge nodes. The study implemented a DES security mechanism for offoaded workloads in the system. The goal is to minimize end to end latency. The study of [3] suggested IoMT based on the independent healthcare workload, budget objective, goalprogramming multi-objective method, latency optimal cloudlet deployed virtual machines and CRC32 security mechanism. The aim is to minimize end to end latency. Refs. [4,5] suggested an IoMT system based on workfow that is fne-grained and quality of service (QoS) aware, as well as a min-max multi-objective method and distributed edge implemented virtual machines and DES and RSA security for healthcare applications. The goal is to minimize resource consumption and energy and delay the objectives of the study. The vector evaluated genetic algorithm (VEGA) allows dealing with multiple objectives. However, the min-max algorithm only achieved good results with the single constraints in nondominant solutions on the Pareto frontier.
The studies [6][7][8] devised dynamic and secure IoMT systems based on different primitives such as workflow applications, deadlines, Genetic Algorithm (GA) on virtual machines (VMs), which enable cloud data centers, and RSA-based networks. The purpose of these studies is to gain dynamic results for healthcare applications in distributed cloud data centers. The studies [9][10][11][12][13][14] proposed IoMT with a tuple of implementations, such as coarse-grained workload, and optimized the objectives' lateness and energy with particle swarm optimization schemes in distributed RSA-enabled fog virtual machines. Particle swarm optimization (PSO) is a computational method for solving problems by iteratively improving a potential solution against a set of quality criteria. The message digest (MD5) enabled the secure distributed cloudlets and fog node aware IoMT systems suggested by [15][16][17][18][19][20]. The workload considered to be coarse-grained is solved by a multi-objective approach and ant-colony is done so with a dynamic approach. The objective is to minimize service cost, latency and delay of applications in the IoMT system. The deadline, resource and lateness are considered during offloading and resource allocation in the system.
The applications, services, application programming interface (API) and model-based workload have been implemented in [21][22][23][24][25][26][27]. The virtual machines, container and serverless aware resources are offered during workload execution in the system. The min-max, Multi-objective Evolutionary Genetic Algorithm (MOGA) and NSGA-II-enabled multiobjective-based techniques suggested to solve the healthcare problems in distributed fog cloud nodes. The goal is to optimize different objectives with nondominance and dominance schemes with the Pareto frontier tool for different healthcare workloads. These studies considered the single constraint during decision in IoMT. The deep convolutional neuron network-enabled healthcare system is suggested in [28][29][30][31]. The goal is to handle multiple objectives such as energy, makespan, and cost of coarse-grained applications in the distributed IoT fog cloud network in the system. These studies suggested a dynamic heuristic based on reinforcement learning where the considered workload is only coarse-grained in the system for offoading and resource allocations.
To the best of our knowledge, a hybrid workload-enabled and secure healthcare monitoring sensing framework in a distributed fog cloud network has not been studied yet. The considered problem and system in the present study differ from existing works [1, 2,18,22,[28][29][30][31] in the following way. The proposed work considers the hybrid workloads such as workflow and the fine-grained model and the proposed mathematical model, whereas the study devises the functions and virtual machine aware fog cloud network which was not considered in the existing works. The main reason for this is that the research focuses on the cost-efficient scheduling and resource-optimal allocations of workload in the distributed fog cloud network. Therefore, in the considered problem, the study has three different conflicting objectives: makespan, lateness, and energy consumption with cost, deadline, and lateness constraints in the IoMT system. The existing multi-objective approaches cannot be applied to hybrid workloads in the IoMT because all existing objectives require a lot of decision time and resources to find optimal solutions for all objectives in IoMT. Therefore, the study considers the deep graph-based convolutional network-enabled algorithm framework to solve the supposed problem in the IoMT.

Proposed Architecture
The study proposes a new secure mobile edge cloud architecture to run IoMT workfow applications in a distributed environment. The proposed architecture consists of three main layers, the application layer, management layer and resource layer, as shown in Figure 1. The IoMT workfow applications layer consists of multiple applications where each application is composed of three different types of functions. The nodes, such as the blue node, show security tasks, the light node shows delay-sensitive tasks, and the red node displays delay-tolerant functions. The architecture initially takes the inputs of all applications into the management layer. The workfow tasks are annotated as the design time in different types, such as security tasks, delay-sensitive tasks, and delay-tolerant tasks. The execution time and energy consumption are anticipated in advance before scheduling tasks to any node by exploiting the energy profler and workload execution profler at the design time of applications. These mechanisms of application partitioning and the time estimation are already published in our previous work [7]. Therefore, this work only focuses on scheduling, not application partitioning and offoading in the current model. The IoMT agent is an administrator in the management layer that processes the requested IoMT workfow applications P = {a1, . . . , aP}. The IoMT agent consists of the following components: deadline division, task sequencing, homomorphic security scheme, initial scheduling and Variable neighborhood Searching (VNS). The deadline division divides the deadline d a of all IoMT applications into task deadlines based on their execution time on different computing nodes. All the tasks are sorted based on their requirements by the sequencing rules. The rules are earliest due date and cost of resources. We assigned the priority to each task in the following way: The homomorphic security method encrypts and decrypts security tasks locally on the devices. The Denial of Service (DoS) and surfng profling handles and identifes an attack in the network. This way, we can save resource and time before offoading and scheduling in the system. Initial scheduling maps all tasks based on sorting and security requirements onto heterogeneous mobile edge cloud computing effciently. After that, a VNS-based searching method improves the initial solution from candidate solutions.
The resource layer consists of mobile computing, edge computing and cloud computing. Resource-constrained mobile computing only executes security annotated tasks with private keys. Furthermore, delay-sensitive tasks are carried out using edge computing which locates the edge of the network with ultra-low latency. Finally, all delay-tolerant tasks are carried out using cloud computing. Table 2 describes the notation of the mathematical model of the considered problem. The heterogenous computing nodes (e.g., mobile edge cloud) j The jth computing node ζ j The processing speed of computing node j R The resource of computing nodes r The resource particular r N Total number of task T Set of all tasks t i The tth task of T This study considered two types of application workloads with different processes such as fne-grained tasks and workfow tasks.

Fine-Grained Tasks
The healthcare fne-grained tasks have their data, deadlines, and required CPU per execution during the process. Each fne-grained task is isolated; it needs a separate function to run its operation. The fne-grained task shown in Figure 2 has three types of tasks: secure tasks, delay-sensitive tasks, and delay-tolerant tasks. The study makes the Problem Formulation of Workfow Tasks in the following way. The paper investigates P number IoMT workfows applications, i.e., {a1, a2, . . . , aP}. The directed acyclic graph, i.e., a(V, E) illustrates constraint rules of applications, where i illustrates a particular task, and e(i, j) ∈ E represents the communication nodes among different tasks. There are certain rules in IoMT tasks: (i) a task i should fnish before starting task j. Furthermore, some tasks use original data and some of them have generated data. The notation w i is an original datum of a particular task, and w i,z generated data of precedence during execution. Each IoMT application a categorized tasks into three lists: (i) security list S = {s i = 1, . . . , S ∈ Va}, delay-sensitive tasks (ii) L = {l i = 1, . . . , L ∈ Va}, and delay-tolerant tasks DR = {dr i = 1, . . . , DR ∈ Va}.
The present paper discusses the scenario of real-life healthcare IoMT applications, as shown in Figure 3. In the system model, there are three types of task lists: (1) secure tasks, i.e., S = {s i = 1, . . . , S ∈ Va}, which must be encrypted and decrypted locally by IoMT devices; (2) delay-sensitive tasks, i.e., L = {l i = 1, . . . , L ∈ Va}, which must be performed on edge nodes because of their latency requirements; (3) delay-tolerant tasks, i.e., DR = {dr i = 1, . . . , DR ∈ Va}, which are offoaded to the public cloud for execution. There are three layers in the system: the edge layer, where all organizations such as hospitals, clinics, and any medical centre use different IoMT devices to run IoMT applications. These applications secure data locally on their own devices, and delaysensitive tasks are offoaded via an access point (e.g., wif) to the edge layer for execution. Furthermore, via the internet, all applications offoaded their tasks to the public cloud. The categorized tasks we already defned in detail above.  We denote the speed factor of all computing nodes in the following way, i.e., ζ j {ζ j 1, . . . , ζ j }, whereas the work shows the computing nodes resources in the following way, e.g., R = {r = 1, . . . , rR}. We determine the execution time of a particular task in the following way.
In Equation (1), the vector y i = 0 means the execution of a task in the local machine, e.g., y i = 1. It implies the performance of a task on the edge and y i = 2 executions of a task in the cloud.
IoMT workfow applications have relationship and communication time requirements due to transferring of data between them.
Equation (2) determines the communication time between constraint tasks in workfow while sharing their data for execution.
If two tasks i and j are being carried out in the local machine, there is no communication time between them, i.e., z i = 0. If two tasks i and j are running on an edge LAN network, then there is a fxed communication time between them, i.e., z i = 1. Finally, if two tasks i and j are being carried out on a cloud WAN network, then there is fxed communication time between them, i.e., z i = 2. The constraint (3) calculates the communication time between tasks i, j. We determine the fnish time of a general task in the following way.
Equation (4) calculates the fnish time of a task. We obtained the makespan of IoMT workfow applications as MW denotes the makespan of all IoMT workfow applications in Equation (5). The paper presents the problem mathematically as follows: min MW (6) which is subject to Equation (6) shows the objective function of each application.
Equation (7) denotes the deadlines for completion of tasks of all applications.
Constraint (8) shows all the requested workloads of applications that must not exceed the limits of resources during execution.
Constraints ((9), (10), and (11)) show that each task to be assigned to one node, and each node can execute one task at a time when it is successfully assigned to any particular node.

Problem Formulation of Fine-Grained Tasks
This study considers T number of fne-grained tasks, i.e., {t = 1, . . . , T}. Each task has a workload, e.g., W t and t d deadline. The number of fog cloud functions is represented by F = { f 1, f 2, . . . F}. Each function has a memory size of f m. The execution time of fne-grained tasks is determined in the following way. (12) calculates the execution time of a task on the function in node j Therefore, the execution cost of all tasks is determined in the following way.
The functions can run on only computing nodes such as j1 to M. Therefore, the cost of the function is to be determined by the memory size and execution time as determined in Equation (13).

Energy Consumption Computing Nodes
This study determines the energy consumption due to virtual machines and particular function nodes. Therefore, j w is the energy consumption per watt of node j to run virtual machines and functions. The power consumption of nodes is determined in the following way.
t=1 v=1 j=1 f =1 Equation (14) determines the energy consumption due to both the workfow and fne-grained tasks in the computing nodes.
The study examines multi-objective problems such as energy, makespan, and lateness of both workfow and fne-grained jobs based on the suggested mathematical formula. As a result, multi-objective optimization is a subsection of multiple criteria decision making that deals with mathematical optimization problems that necessitate simultaneous optimizations of many objective functions. The Pareto frontier is used to construct the multi-objective problem. The Pareto frontier is an optimal technique for solving the problem restrictions since the study has conficting aims in the suggested system with various resources. No one solution simultaneously optimizes each objective for a nontrivial multiobjective optimization problem. The objective functions are incompatible in this instance, and there are a (potentially infnite) number of Pareto optimal solutions. If there is no improvement in a single function value without deteriorating some of the other objective values, the key is nondominated, Pareto optimum, Pareto-effcient, or noninferior. All Pareto optimum solutions are deemed equally desirable without any additional subjective preference information. Many existing multi-objective optimization techniques from many problems suggested formulating and solving them. The goal could be to locate a representative group of Pareto optimal solutions, quantify the trade-offs in achieving several objectives, or identify a single solution that satisfes a human decision maker's subjective preferences (DM). min Equation (15) shows the objective functions of both workfow and fne-grained tasks.

Proposed Security-Effcient Optimal Solution (SEOS) Algorithm Framework
This work considers the IoMT workfow applications, where each application has three types of tasks: security tasks, delay-sensitive tasks, and delay-tolerant tasks. We analyze the heterogeneous computing nodes (e.g., mobile node, edge node and remote cloud node) that are distinct by their speeds and resources. The advised problem is secure offoading and scheduling for IoMT workfow applications in heterogeneous computing nodes. This section proposes the Security-Effcient Offoading and Scheduling (SEOS) algorithm framework, which consists of different components to solve the considered problem. Initially, we divide the applications into task deadlines. In the second part, we sort all tasks into topological order based on the proposed three sequence rules. The thirdparty offoading-based homomorphic encryption method encrypts and decrypts security tasks locally on the local devices. Due to precedence constraint requirements, the cyphertext data of tasks are offoaded to the edge cloud for delay-sensitive tasks. The edge node applies computation on cypher-text instead of converting it into plaintext. The fnal part is local searching-based task scheduling, where all tasks are scheduled in different computing nodes. We explain the SEOS framework steps in the following algorithm, Algorithm 1.

Deadline Division
The deadline division is a way to divide the application deadline into task deadlines; this way, we can achieve the quality of tasks based on their deadlines. For example, we split the applications into the following form.
Initially, we obtained the ratio of all applications based on Equation (16), which determines the division of the deadline of each application with the makespan of the application. This way, we assigned the deadline to each task based on the execution time and communication based on executions ((17)- (19)).
Algorithm 2 divides the deadline of all applications into task deadlines to obtain the optimal makespan of each application onto heterogeneous computing nodes.

Task Sequencing
In this section, we introduce task sequencing rules based on the following methods. Earliest Due Date (EDD) is exploited to order the tasks in a deadline manner. Each task is prioritized via Equations (20) and (21). Smallest Process First (SPF) is exploited when the smallest processing task is assigned the highest rank and scheduled before the longest process task. Smallest Slack Time First (SSTF) method shows the remaining time between fnish time and the actual deadline should be smaller when a task i is scheduled on the same paradigm. We assigned the priority to each task in the following way: We assume that the w i is equal to whether ordinal data or generated of the task i during priority assignment. Both Equations (20) and (21) defne the priority of all tasks from entry the task i to exit V by considering all predecessors and successors of the given application. Initially, we sort the topological priority of tasks in the following way.

•
All workfow tasks sort out by descending order by their deadlines; • All fne-grained tasks sort out by their deadlines.
We tried all sequences during initial task scheduling until submitted tasks are satisfed by the given requirements.

Security Aware Offoading Method
The Homomorphic Encryption [32] is a tool that allows computation on encrypted data of tasks. In this way, data of tasks remain private and confdential during offoading and scheduling at heterogenous mobile edge cloud networks. FHE encourages securitysensitive applications to work with sensitive data in untrusted environments. The geographically distributed computation and heterogeneous mobile edge cloud networking; secure communication is a good indication related to the applications.
When the data transfers to the cloud, we use standard encryption methods to secure the operations and the data storage. Our basic concept was to encrypt the data to the cloud provider before sending it back. However, at every transaction, the last one has to decrypt data. Therefore, the client will need to provide the server (cloud provider) with the private key to decrypt data before executing the required calculations, affecting the confdentiality and privacy of data stored in the cloud.
The secure homomorphic Algorithm 3 takes as input a list of security tasks S, which is annotated at the time of design. Algorithm 3 has the following steps. Firstly, it encrypts all security tasks of all applications locally and offoads them for assistance to external computing nodes. Secondly, the computing nodes apply the ciphertext instead of plaintext and then return them to the corresponding end-user devices. Finally, it will decrypt the results of encrypted tasks locally on the computers. foreach (i = 1 S) do DoS ← 1 Denial of Service Attack present; p ← large integer; q ← large integer; Decrypted all tasks; d c (i y ) = i y a mod n; End inner loop; else DoS=1; Waiting for offoading; 21 End Main; In this paper, we suggest implementing a system for performing operations on encrypted data without decrypting them, which will produce the same results after calculations as if we were directly operating on the raw data. Homomorphic encryption systems are exploited to execute encrypted data operations without understanding the private key (without decryption); the client is the sole owner of the secret key.
In the considered problem, the study considered the homomorphic encryption in the following condition. If Enc (a) and Enc (b) are used to estimate Enc (function (a, b)), where function can be: +, x, and outwardly practicing the private key. Moreover, additive homomorphic encryption considers raw data additions is the Pailler.
In contrast, Equation (23) is multiplicative homomorphic encryption. An algorithm is fully homomorphic if both properties are satisfed simultaneously.
For the multiplicative homomorphic encryption,let us assume that n = pq, where p and q integer primes. Then, we choose a and b keys such that ab = 1, i.e., (mod φ(n)). In contrast, b and n represent the public key, and p, q, and a denote the private key. We encrypt sensitive tasks in the following way.
Equations (24) and (25) show the encryption and decryption of a task. We suppose that s i and s j are plaintexts of task i and j; then, we denote as follows b b e c (s i ) e c (s j ) = s i s j mod n = (s i , s j ) b mod n = e c (s i , s j ).
We defne the FHE security scheme in Algorithm 3 as follows: • Let us assume the algorithm takes the s i and s j inputs as the security tasks, and they require encryption locally on the IoT devices; • p and q are long integers exploited during the encryption round. n is cross multiplication during block-switching performed from lines 2 to 6; • e is a small positive number employed for variation in the ordinal 64-bit block of encryption. At the same time, gdc and mod functions perform the fully homomorphic operation; • The algorithm performs encryption on security tasks from lines 7 to 15. The list was added after all were encrypted after applying the security mechanism. The offoader engine is a method used inside devices which offoads the ciphertext of tasks to the system for further computations. Once the calculation was practiced on ciphertext, and the result was sent back to the devices, and they all decrypted on devices with their private keys; • DoS is the profling that identifes denial of service in the system; if it is 1 it means there is a risk of attack else, otherwise it will remain zero.

Initial Task Scheduling
The initial scheduling is not the fnal scheduling of all tasks, and they can reschedule heterogeneous mobile edge cloud networks (e.g., heterogeneous computing nodes). The initial scheduling depends upon the deadline division component, task sequencing and security scheme. We propose the iterative scheduling algorithm, Algorithm 4, which shows the process of scheduling tasks under their requirements.
Algorithm 4 performs the scheduling in the following way: • Initially, the algorithm conducts deadline division, which shows the deadline of each task; • All tasks schedule based on given sequences by sequence rules methods; • All local tasks are encrypted and decrypted by the homomorphic security method and executed locally in the devices; • The delay-sensitive tasks are scheduled at the edge node; this is necessary for all nodes, and the requested workload must be less than their resources during processing;. • All delay-tolerant tasks are to be scheduled at the public cloud for execution; • The algorithm iteratively allocates all tasks to heterogeneous computing nodes and calculates the makespan of each IoMT workfow application at initial scheduling. Optimize objection based on Equation (6); calculate the objective function in the following way; Calculate execution time of delay-sensitive tasks based on Equation (4); Optimize objection based on Equation (6); Calculate execution time of local tasks based on Equation (4); Optimize objection based on Equation (6); Z ← dr i ← r; 23 End-Loop;

Searching Optimal Solution-Based VNS
The variable neighborhood Search (VNS) solves the initial scheduling when tasks are distributed and allocated to different computing networks. It traverses distant neighborhoods of the current obligatory solution, i.e., Z, and proceeds from beyond the new key if any improvement is made. Algorithm 5 is a global search iterative algorithm that improves the current solution with the new one via variable temperatures. If the temperature decreases, the makespan of applications reduces the initial schedule with the new key.
Algorithm 5 has the following steps to reach the optimal solution: • The algorithm takes the initial cost of each application with the initial solution C; • The temperature tmp is a variable whose initial value = 100; it reduces to near zero, as tmp minimizes the cost of each application minimizes; • The set of candidate solutions, i.e., N, and C 0 is a new solution with available costs compared with the initial solution C; The Boltzmann constant, i.e., rand(0, 1) ≤ e tmp is an acceptance method; it allows one to replace the original solution with a new one with the minimum exponential rate and temperature tmp. The rate of change in Δtmp temperature could be minimized or increased depending upon the situation; • If the solution reached the maximum level, no furthermore improvement is made, then the algorithm accepts C * as a fnal solution.

Energy-Effcient Scheduling
All the nodes are ordered according to the power consumption in the network. In the frst step, both fne-grained and workfow applications are scheduled based on their deadlines. In the second step, all the tasks are rescheduled based on their execution costs. Finally, in the third scheduling, all nodes are rescheduled according to their power consumption to minimize their power consumption without violence or service quality applications. Algorithm 6 reschedules all tasks based on computing nodes' energy. In contrast, it is no matter if either the energy of node j is consumed due to virtual machines or functions for executing the workfow and fne-grained workload. Algorithm 6 ensures the energy-effcient scheduling without violating the deadline and cost of applications in the system. Apply Dynamic Voltage Frequency Scaling method to re-arrange the node according to their power consumption; Calculate the power consumption of nodes based on Equation (14); Schedule all workloads based on Algorithms 4 and 5; End of Assignment until all workloads checked respect nodes energy consumption;

Multi-Objective Deep Graph Convolutional Network-Based Scheme
These days, for graph-structured aware applications, the usage of deep convolutional networks have become extremely popular. As a result, multi-objective decisions based on heterogeneous resources and parameters of applications can be made effciently. However, early neural networks could only be implemented with regular or Euclidean data, even though many data in the actual world have non-Euclidean graph structures. The nonregularity of data structures has driven recent advances in graph neural networks. As a result, graph neural networks have developed different variations in recent years, with Graph Convolutional Networks (GCNs) being one of them. GCNs are also one of the most fundamental graph neural networks variations.
The study devises the weighting multi-objective nondominant schemes based on the deep graph convolutional network. Algorithm 7 shows the process of the proposed method with different steps. The algorithm has three layers: the input layer, deep convolutional layer, and output layer. According to the given scenario in Figure 4, the algorithm performs the following operations. The input model takes by model as the graph ; The variable features x j for individual node j; Each deep convolutional network layer is the nonlinear function; Calculate the workloads and functions optimization based on Algorithms 4-6; Calculate the weight sum of all objectives should be optimal than existing weight in different convolutional layers; End of Inner Optimization; End of sum optimization ; 16 End of main; • In the frst step, the workload of all applications after initial scheduling will be considered an input; • All objectives have their weights concerning workloads and resources; • The resources are virtual machines and functions which are assigned based on their cost function; • The deep convolutional network chooses the best optimal weight of all objectives and sum them together. If the optimal weight is greater than the existing one, the multiobjective weight of all objectives is optimal, e.g., Z * ; • All types of tasks such as delay-sensitive, delay-tolerant and security ones and their quality of service must be satisfed as defned in Figure 4. • Every 10 min, the multi-objective tasks will call to optimize each objective function based on the available weights in the network; • If the algorithm fnds no further improvement, it will terminate the network with no further improvement in the system.

Performance Evaluation
This section shows the effciency and effectiveness of the proposed work via the simulation results. Somehow, the simulation results are the same as a real-practice experiment in practice. The performance evaluation part consists of many sub-parts such as parameter setting, system implementation, component calibrations and result discussion. The paper explains sub-parts in detail to ensure an easy understanding of the experiment.

Parameter Settings
This subsection shows the experimental setup of the program confguration, languages and computing nodes as shown in Table 3. All parameters are included in the implementation part, such as programs and algorithms, in the JAVA, Python and YAML languages. There are three computing nodes confgured for the proposed architecture. For instance, mobile node (e.g., HTC G17 and Samsung 1997), edge node (e.g., Intel 5 laptop, AndroidX86 runtime), and cloud node (e.g., AndroidX86 Amazon). We repeated all experiments 50 times with different parameters. Table 3 describes the simulation parameters of the experiment. Furthermore, we extended the computing nodes resource specifcation into a different table, Table 4. The main goal of this is to offer the computing capability and resource availability of each node in the system. There are three types of resources: a likewise mobile node, edge node and cloud node. All nodes are distinct by their speeds and resource specifcations. All resources of different computing nodes are fxed, and they cannot scale up and scale during runtime in the implemented system. Table 4. Heterogenous node resource specifcation.

Component Calibration
There are three main layers in the proposed architecture, as shown Figure 1. However, the application layer and system layer components are included in the calibration to evaluate the performances of the entire system. The features are secure offoading, task sequencing, and task scheduling. In addition, the Relative Percentage Deviation (RPD) was adopted to measure the performances of the components, as mentioned earlier, to run many types of IoMT workfow tasks in the system. The RPD measures in the following way: (27) shows the overall performances of all applications using distributed computing (e.g., mobile, edge and cloud nodes). The Z is the initial scheduling in the system; however, due to roaming features of applications, the initial solution of scheduling could be replaced with optimal scheduling Z * during the searching for space in the solution. As we mentioned above, all answers are achieved via candidate solutions during global searching with limited iterations during the process. The RPD% is the difference between the initial and best solutions during the entire process.

Iomt Workfow Tasks and Fine-Grained Tasks
The study implemented both types of workloads such as workfow and fne-grained in the simulation confguration fle. Figure 5 shows the interfaces of the system with the results of workfow dag tasks graph during execution in the system. All tasks are workfows; some have original data, and some share their data for processing. All tasks are constrained by their predecessors and successors in the system.

Workfow Tasks Generator
In this paper, we consider only three types of tasks. All workfow applications are real IoMT applications, which are open source and available at GitHub: https://github.com/ OpenIoMeT/Iomet-wiki accessed on 1 July 2021. Initially, we analyzed all applications in DAG graphics with different types of tasks. The initial application is annotating notations (e.g., all types of tasks annotated at the design time). After that, we converted the IoMT workfow into a DAG graph, where blue nodes are security tasks (e.g., local tasks), light yellow nodes are edge tasks, and red nodes are remote tasks, and they have their execution time and communication time (e.g., ms and kb) due to precedence constraints.

Discussion of Results
This subsection compares the results of IoMT workfow tasks with the proposed framework with its components and existing offoading and scheduling frameworks. The discussion of component results starts with the following subsections.

Secure Offoading Performance
After the deadline division for each task, the security aware offoading applies security to the list of security tasks locally at the devices. We implemented fully homomorphic encryption and decryption methods that convert plaintext of security tasks into ciphertext in the application layer. Then, the offoader engine offoads those tasks to the system to be carried out further. The other performance means the ciphertext data of tasks are the inputs of different tasks in the system. Therefore, it is necessary, and we measured the accounts of the offoading method into two environments. The frst environment is stable where there is no risk of hacking or Denial of Service (DOS) attacks; another environment is unstable where some chances of DoS exist in the network during offoading. In this case, we compared our proposed secure offoading schemes with the existing best security aware offoading schemes, i.e., baseline 1 and baseline 2. In baseline 1, an RSA-based encryption method is implemented, which offoads tasks with encrypted data to the server, and then the server decrypts tasks with the key and performs computations. After the calculation again, the server encrypted tasks and sent them back to the devices, and then devices interpreted all tasks in the original form. This entire process is risky, and we can trust the untrusted cloud, and it is not good practice to leave essential data on the server. Figure 6a,b show that the proposed component (e.g., secure offoading) of the SEOS framework outperforms in any environment compared to the existing secure offoading techniques concerning resources and performance. The main reason behind this is that all existing baseline approaches only consider the security and require resources; however, the proposed secure offoading method encrypted and decrypted all tasks based on their deadlines and availability of resources. Furthermore, before offoading to any nodes, we anticipated the available network which was either secure or not in the system. Our approach can stabilize and be unstable because we care about resource utilization, tasks' QoS and network stability before sending data to the surrogate edge or remote servers.  A denial of service (DoS) outbreak happens whenever verifiable applications can not access their edge nodes or remote nodes resources for further execution due to either a cyber attack or network attack in the system. These nodes may be concerned by any attack and not able to respond. A denial of service attack may harm both resources and time even though tasks are encrypted. With this consideration, the proposed secure offloading method, including encryption decryption and deadline, detects and anticipates any attack before offloading via network monitoring and surfing profiling at the local device. It may save our resources and time during offloading in all kinds of environments. Therefore, Figure 7a-d show that the component of SEOS outperforms in terms of resource utilization and the deadlines of tasks, and identifes DoS in advance, in contrast to all existing approaches which considered only encryption and decryption and resources without deadlines and availability of DoS attack.  Figure 8a,b show that the proposed task sequence rules adopt initial sorting and dynamic sorting to maintain the deadline of tasks for the runtime. Therefore, it is necessary to execute all tasks under their deadlines with a minimum loss of generosity.

Task Scheduling
Based on security-effcient offoading, sorting with different rules, task scheduling is the fnal phase where all tasks must be completed with precedence and deadline constraints. We set four fows of IoMT tasks with different numbers for scheduling. These tasks have different types, as we discussed above. The goal of the study is to minimize the makespan of all applications. We consider the four various applications with a different number of tasks. Each application has three different types of tasks and deadlines with constraint rules. Somehow, a few tasks are executed in parallel order, and few tasks are performed in the sequencing order; it depends upon the application order. We implemented Heterogeneous Earliest Finish Time (HEFT) and genetic algorithm (GA) as the baseline 1 framework, and Dynamic Heterogeneous Earliest Finish Time (DHEFT) and particle Swarm Optimization framework as baseline 2. These frameworks are widely investigated for traditional and mobile workfow applications in the literature. These frameworks offer different components to run mobile workfow applications in additional steps, such as task sequencing and scheduling. We ran all applications with other frameworks (e.g., SEOS, baseline 1 and baseline 2), the results of all applications with their objectives can be seen in Figure 9a-d. Each application has different requirements, such as security, latency, and resources to run its tasks. However, the SEOS outperforms all existing frameworks in terms of all makespans and the needs of all applications. The main reason for this is that all existing algorithm frameworks have some races in the encryption and decryption format. They consume many resources and time to run different types of tasks ( Figure 10): (i) Encryption of all tasks locally with the sharing key and offoading to the surrogate server for further execution. The server decrypts all tasks with a shared key and applies computation on plaintext instead of ciphertext. After the calculation, the server again encrypts tasks into ciphertext and send back their results. Furthermore, local devices decrypt the result into plaintext with the key. This way, the authentication, time and resources are challenging and uses at extending level. (ii) All existing studies partition the application into different types of tasks at the runtime based on various parameters (e.g., deadline, availability of resources, network contexts). However, due to the dynamic environment and load balancing situation in computing, these techniques beneft from lower running time and waste of resources. (iii) The loss of deadline and failure ratio of tasks in the system becoming very high. Therefore, the proposed SEOS partitioned the application at the design level to security, latency and resource requirements of all applications effciently and ran them in the heterogeneous computing node during execution.

Conclusions
This work proposed a new healthcare architecture based on workfow applications based on heterogeneous computing nodes, consisting of different layers: an application layer, management layer, and resource layer. The goal is to minimize the makespan of all applications. Based on these layers, the work proposed the secure offoading-effcient task scheduling (SEOS) algorithm framework, which includes the deadline division method, task sequencing rules, homomorphic security scheme, initial scheduling, and variable neighborhood searching method. The performance evaluation results show that the proposed plans outperform all existing baseline approaches for healthcare applications in terms of makespan. The discussion of the results showed that the proposed idea and SEOS framework outperformed all IoMT applications' existing methods in heterogeneous computing nodes. The discussion of results and comparison has been made via different components based on HSD and ANOVA famous techniques. However, there are few things to be improved in the future.
This work did not consider the mobility aware offoading and scheduling for IoMT workfow in a heterogeneous computing node environment. The runtime uncertainty in the network contexts, load balancing, failure of tasks situation will be future work of our study. We will design deep reinforcement learning architecture and framework, which will include policy, Q-deep learning, and different methods.