## 2 Related Work
### Single Workflow Allocation Model
This integrates processes in the same cluster and assigns them to the same machines to obtain an overall minimal communication cost-sharing among tasks while sacrificing DAG parallelism. Therefore, it has been found that increasing parallelism and reducing communication delay are trade-offs [36]. Some of the standard clustering-based scheduling techniques are the linear cluster method [37], dominant sequence clustering [38], resource-aware clustering (RAC) [39], and CMWSL [40]. For machines with various capacities, the goal of RAC [39] is to achieve relative load balance and efficiency enhancement. To do this, RAC provides a dynamic scoring algorithm for each task, which is followed by task clustering and task distribution based on the processing power of the processors. With four phases, the cluster-based task scheduling method CMWSL [40] reduces the scheduling time for more heterogeneous machines. * **Duplication-based models**: These models repeat some portions of the parent tasks onto the processor to reduce transmission time. Duplication-based workflow allocation models generally assume that the resources are the same and that the computational time increases dramatically for the heterogeneous computing environment. The duplication-based heuristic is generally used together with list or cluster-based workflow scheduling to minimize the migration time among workflow tasks [41; 42]. A novel method that combines list scheduling with task duplication was proposed to achieve great performance with minimal complexity [9; 43; 44] by assigning the computational resources to more than one resource to minimize the waiting time of the precedence-constrained tasks. The duplication of tasks on the same machine minimizes the migration time between them. Some partial [42; 45; 46] and full [36; 37; 41; 43; 44; 47] duplication-based workflow algorithms are CPFD [36], TCSD [37], BTDH [41], PLW [42], TDS [45], DFRN [46], LCTD [47], CEFT [44], and DBEFT [44]. * **Meta-heuristic based models:** Meta-heuristic workflow allocation models provide an efficient method to move rapidly towards a very good solution. Some of the metaheuristic-based solution models in workflow scheduling are GA [48; 49; 50; 51; 52], PSO [53; 54], ACO [55; 56], ABC [57], AFS [58], BFO [59], Firefly [60; 61], BAT [62; 63], GSA [64], etc. One of the most extensively researched meta-heuristics in workflow scheduling is the genetic algorithm (GA), which creates new schedules using the genetic operators: selection, crossover, and mutation [48; 49; 50; 51; 52]. Particle swarm optimization is a swarm approach that has evolved from the social behavior of birds flocking. In [53], the authors have proposed a new directional and non-local-convergent PSO algorithm to optimize the makespan and cost dramatically in a cloud-edge computing environment, while the authors of [54] present the smart PSO-based secured workflowallocation in the cloud environment to find the optimal allocation with the lowest cost and makespan. In [55; 56], the authors present ant colony optimization-based workflow allocation with multi-objectives to optimize the resource cost, energy consumption, utilization, and makespan in the cloud data center. Similarly, [PERSON] and [PERSON] proposed a novel methodology for workflow allocation in a cloud environment using Artificial Fish Swarm (AFS) Algorithm IaaS Cloud Partial Critical Path and Hyper Elliptic Curve Cryptography to optimize the execution time with the lowest cost. In [60], the authors present a novel firefly-based multi-objective workflow allocation algorithm to optimize the makespan and resource utilization in cloud environments, whereas the authors of [61] present a cost-effective workflow allocation algorithm using firefly to optimize the cost and makespan in the same environment. In [62; 63], the authors present budget and energy-aware workflow allocation in the cloud environment to optimize resource cost and energy consumption using the BAT algorithm.