## 2 Related Work
### Single Workflow Allocation Model  
These allocation models consider only one workflow at a time for allocation having a specified number of vertices (tasks), represented by DAG [7] or Petri net [8], and can be further sub-divided by workflow as follows:  
* **List-based models:** There are some classic list-based workflow algorithms [9; 19; 25; 26; 27; 28; 29; 30; 31; 32; 33] such as SPHEFT [25], LMT [10], Modified Critical Path (MCP) [27], critical-path-on-a-processor (CPOP) [9], dynamic level scheduling (DLS) [19], heterogeneous earliest finish time (HEFT) [9], dynamic critical path (DCP) [28], predict earliest finish time (PEFT) [24], Energy and Reliability Aware Scheduling algorithm (SERAS) [30], list-based workflow allocation [31], list-based security-oriented deadline aware workflow allocation (SODA) [32], and multi-objective workflow allocation (MOWA) [33]. The fundamental idea of list-based allocation models is to prepare an ordered task list by sorting them as per their priorities. These can be static or dynamic and follow two steps, namely, task selection and task allocation, one after another for each task from the list. The HEFT algorithm's benefits include being very targetable, quick, and adaptable and having good performance. Task prioritization and processor selection are two processes that it uses to bound the number of processors in a heterogeneous distributed system [9]. In the first stage, tasks are arranged using upward/downward rank in descending/ascending order. The optimal resource is chosen in the second step to reduce the actual finish time. A crucial path is used by CPOP [9] provided in the DAG. The best processor is assigned to handle all tasks on the critical path, and the remaining tasks are distributed using HEFT. The LMT [10] process involves two stages. The tasks from the same level are executed in parallel. During the second phase, these are mapped to the most suitable resource in terms of completion time. In [24], the authors present a novel list-based workflow allocation named PEFT for heterogeneous computing to minimize the makespan without increasing the time complexity. PEFT [24] is an extended version of HEFT [9], and it is based on an optimistic cost table. PEFT's performance is better than HEFT's on the makespan. SERAS [30] considers dynamic voltage and frequency scaling (DVFS) to reduce the power consumption problem and proposes a novel smart strategy for workflow execution to minimize the completion time and maximize the reliability in the cloud environment. A DAG scheduling model [31] is developed for optimizing the QoS parameters at the CCE platform in cloud computing systems. In SPHEFT [25], SODA [32], and MOWA [33], the authors extend the HEFT [9] approach. SPHEFT [23] optimizes the guarantee ratio and satisfies the security requirement, whereas SODA [32] optimizes the risk probability by satisfying the security demand and deadline [9]. Further, the authorsproposed the MOWA [33] algorithm, which optimizes the simultaneous makespan and flowtime and compared it with HEFT [9]. The performance results of [25; 32; 33] show that they are better than HEFT. * **Clustering-based models:** Heuristics for clustering workflows are designed to reduce the amount of time needed to switch between related activities. List-based heuristics produce unnecessary idle gaps on machines, as in HEFT [9], SPHEFT [25], and SODA [32], because they do not consider communication sharing. Clustering approaches are successful for both homogenous and heterogeneous systems. These approaches are fast at sorting workflows; additionally, list-based approaches transverse the workflow using topological sorting, and for this reason, they can perform only local optimization, while clustering approaches consider global optimization to map tasks on clusters. Therefore, clustering approaches have been used. The two components of clustering-based techniques are task mapping to clusters and task ranking within the cluster [34; 35].