Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 372 https://internationalpubls.com Nonlinear Analysis of EDF Scheduling Framework for Resource Distribution in Cloud Computing Neelima Priyanka Nutulapati1, Sukumar Babu Bandarupalli2, B Sunil Kumar Babu3, Subbulakshmi R4 1Professor, Department of CSE, Potti Sriramulu Chalavadi Mallikarjunarao College Engineering and Technology, Andhra Pradesh, India. dr.priyanka.nutulapati@gmail.com 2Research Scholar, Department of CSE, JNTU Kakinada, Andhra Pradesh, India. sukumar316@gmail.com 3Research Scholar, Department of ECE, Gandhi Institute of Engineering and Technology University, Gunupur, Odisha, India. sunil478kumar@gmail.com 4Assistant Professor, Department of CSE, Karpagam Institute of Technology, Coimbatore, Tamilnadu, India, subbulakshmi.cse@karpagamtech.ac.in Article History: Received: 17-07-2024 Revised: 30-08-2024 Accepted: 12-09-2024 Abstract: In modern times, the field of information technology is significantly shifting towards cloud computing. This innovative technology involves the permanent storage of resources on servers, which clients access via the internet. Typically, a cloud comprises a collection of resources known as virtual machines, capable of managing both computational tasks and storage needs. As the demand for cloud services continues to rise, the scheduling of these resources presents a considerable challenge. Scheduling refers to the workflow management necessary to complete tasks within the system. An efficient scheduler adapts its scheduling policy dynamically in response to changing conditions and task requirements. Cloud computing represents a recently developed technology where resources, whether physical or virtual machines, are permanently stored on servers and accessed by users through the internet. The cloud offers various service models, including Platform as a Service (PaaS), Software as a Service (SaaS), and Infrastructure as a Service (IaaS). In this context, IaaS refers to a set of resources, including virtual machines, that provide computational and storage services. Given the increasing adoption of cloud technology, resource scheduling has become a critical task. Hence, optimizing the scheduling of requests to ensure the best utilization of cloud resources is essential. This paper introduces a Nonlinear Analysis of EDF Scheduling Framework for resource allocation that considers deadlines and processing times when assigning resources to specific jobs. The performance metrics, including Average Turnaround Time, Average Waiting Time, and Average Deadline Violation, show a significant improvement when compared to traditional scheduling models such as First-Come, First-Served (FCFS), the Shortest Job First (SJF), and Simple Earliest Deadline First (EDF) models. Keywords: Resources, Scheduling, Virtual Machines, Deadlines, deadlock violations, FCFS, SJF, EDF, Average Waiting Time, Average Turnaround time, jobs, process, etc. 1. Introduction Cloud Computing represents an innovative technology where resources are permanently stored on servers, accessible to clients via the internet. This technology encompasses both physical and virtual machines, allowing users to leverage these resources through online connectivity. This access is made possible by the internet, a huge network of interconnected public and private networks that may be Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 373 https://internationalpubls.com accessed through a variety of devices. Cloud services offer dynamic solutions to end users by utilizing scalable and virtualized resources over the internet. Users typically engage with these services on a pay-per-use basis, ensuring that the services provided are reliable and designed to maximize the quality and utility of network storage and system resources. As a flexible service provider, the cloud operates on a consumption-based model. Many industry experts anticipate that cloud technology will continue to gain prominence within the IT sector. The cloud offers various service models, including Software- as-a-Service (SaaS), which allows users to access software through a single platform (e.g., salesforce.com); Platform-as-a-Service (PaaS), which provides a shared platform for software and data access (e.g., Azure Services, Amazon Web Services, Google App Engine); and Infrastructure-as-a- Service (IaaS), which focuses on security and backup support (e.g., Amazon EC2, VMware, IBM BlueMix). Cloud Computing finds applications across diverse fields such as scientific research, commercial enterprises, and education. Within the cloud ecosystem, job scheduling plays a crucial role in ensuring efficient workload distribution and resource management. The primary objective of scheduling algorithms in this environment is to optimize resource utilization effectively. In a cloud platform, processing user tasks necessitates the use of cloud resources[1]. Typically, in cloud computing, the resources needed for a job request are provided in the form of Virtual Machines (VMs). The scheduler in cloud computing is responsible for managing a specified number of job requests and allocating the necessary cloud resources (VMs) for each request. In this environment, a variety of resource types may be required to fulfil a job request. Scheduling involves the orderly sharing of available resources among the jobs. When a request is made, the corresponding resources are allocated as Virtual Machines (VMs). To address multiple requests, a sequence of various resources may be needed. The Scheduler organizes these resource types systematically to ensure optimal sharing among the job requests, facilitating effective resource utilization. Resources can include machine instances, data storage devices, applications, or environments. Proper allocation of these cloud resources to clients is a critical aspect of cloud computing. Therefore, an efficient scheduling model that is aware of deadlines is essential for managing the specified number of jobs. Figure 1: Cloud Computing Architecture Figure 2: Scheduling Process in Cloud In this paper, we present the design and development of a Nonlinear Analysis of EDF Scheduling model for resource allocation, focusing on performance metrics such as Average Turnaround Time, Average Waiting Time, and Average Deadline Violation. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 374 https://internationalpubls.com 2. Related Work Greedy Based Job Scheduling Algorithm [2]: This algorithm emphasizes Quality of Service (QoS), recognizing cloud computing as a service driven by business needs. Its primary objective is to minimize completion time, thereby offering a more efficient solution to scheduling challenges. By categorizing tasks according to QoS, the algorithm invokes the relevant functions. When evaluated against other algorithms utilizing the Berger model and existing CloudSim scheduling strategies, it demonstrated superior performance. Earliest Feasible Deadline First [4]: This algorithm seeks to enhance the efficiency of the Earliest Deadline First (EDF) approach by reducing its time complexity. The scheduling is primarily determined by deadlines, and the algorithm optimizes time complexity through process migration across different machines. A Scheduling Algorithm based on Priority for VM Allocation [5]: This algorithm aims to deliver greater benefits to service vendors and providers. In scenarios where resources are insufficient to meet all requests, it introduces a priority-based approach to identify the most suitable allocations. This method significantly enhances resource utilization compared to the First-Come, First-Served (FCFS) strategy. Improved Cost Based Algorithm [6]: This algorithm significantly enhances the efficiency of resource allocation for jobs compared to traditional cost-based scheduling methods. It organizes tasks based on the processing capabilities of the available resources. A Priority Based Job Scheduling Algorithm [7]: In this scheduling framework, each job is assigned a priority value, guiding the allocation of resources accordingly. The author addresses challenges related to complexity, consistency, and makespan, asserting that performance can be enhanced by minimizing makespan. Credit-Based Scheduling Algorithm [8]: In this algorithm, the author emphasizes two key scheduling parameters: user priority and task length. Credits are assigned based on these factors, leading to a job order that is determined by sorting tasks according to their credit values in descending order. Consequently, the scheduler prioritizes the job with the highest credit value for processing. This approach demonstrates improved efficiency compared to earlier scheduling methods. Efficient Round Robin CPU Scheduling Algorithm [9]: The author introduces a novel approach that integrates quantum time with the Shortest Job First (SJF) algorithm. Jobs are organized in ascending order and can be preempted based on the defined quantum time. The results indicate that the average waiting time and turnaround time achieved through this Efficient Round Robin (ERR) method surpass those of traditional CPU scheduling algorithms. ERR ensures fairness in scheduling and is particularly effective in time-sharing environments, as each process receives an equal time slice, minimizing prolonged waiting for CPU access. Priority-Based Earliest Deadline First Scheduling Algorithm [10]: This algorithm merges elements from both the Priority-Based Scheduling Algorithm and the Earliest Deadline First algorithm. Its primary focus is on optimizing memory utilization and resource allocation. By enhancing the completion times of preempted jobs, this algorithm significantly boosts scheduling efficiency. The Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 375 https://internationalpubls.com authors address the challenge of waiting times for preempted tasks by employing a waiting queue to manage these processes effectively[11]. 3. Proposed Work: Nonlinear Analysis of EDF Scheduling Framework for Resource Distribution in Cloud Computing Resource allocation in cloud computing typically involves assigning virtual machines to fulfil job requests. Given that users have specific requirements regarding response and waiting times, new EDF Scheduling model based on deadlines has been developed. In this model, the scheduler receives 'n' job requests from various users and allocates resources in the form of virtual machines to manage these requests[3][9]. The model recognizes that processing a job may necessitate 'm' different types of virtual machines in a sequential manner to meet the task's deadline while considering both response and waiting times. An analytical model has been created to evaluate average turnaround time, average waiting time, and deadline violations, comparing it with other scheduling strategies such as First Come First Serve (FCFS), Shortest Job First (SJF), and Earliest Deadline First scheduling models. The allocation of virtual machines (VMs) for each job request in the proposed model is illustrated in Figure 1. Let req11, req22, ..., reqn represent the set of job requests in cloud computing, where 'n' indicates the total number of requests and reqi signifies the ith job request. Each job request reqi requires ti1 units of time on a VM of type-1, ti2 units on a VM of type-2, and so forth, up to tim units of time on a VM of type-M to complete its task. Let dli denote the deadline for reqi to finish its task, with deadlines calculated using a new approach aimed at minimizing deadline violations. dli = (ti1+ti2+ … +ti4) /4 + (Median(ti1) * α1 + ti1 * α2 ) + (Median(ti2) * α3 + ti2 * α4 ) + …….. + (Median(tim) * α2m-1 + ti4 * α2m ) Where 0 < αi< 1 For example, when m=4 dli = (ti1+ti2+ti3+ti4) /4 + (Median(ti1) * α1 + ti1 * α2 ) + (Median(ti2) * α3 + ti2 * α4 ) + (Median(ti3) * α5 + ti3 * α6) + (Median(ti4) * α7 + ti4 * α8 ) Figure 3. Nonlinear Analysis of EDF Scheduling Framework Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 376 https://internationalpubls.com The performance metrics can be determined through specific calculations based on a given scheduling sequence. The waiting time for request reqi is calculated as the difference between its completion time (ci) and the total processing time of the request (ti1 + ti2 + … + tim). The waiting time for reqi encompasses the duration taken to initiate its processing on VM of type-1, the interval between the completion of tasks on VM of type-1 and the commencement of tasks on VM of type-2, the time between finishing work on VM type-2 and starting on VM type-3, and continues in this manner up to the time elapsed between the completion of tasks on VM of type-(M-1) and the initiation of tasks on VM of type-M. We define si as the starting time of reqi on VM of type-1 and ci as the completion time of reqi on VM of type-M. wi= ci – (ti1+ ti2+ …+ tim) The difference between the task request's deadline (dli) and its actual turnaround time (ci) is known as the deadline breach of the job request (dvti). i.e dvti = wi − dli where wi >dli All job requests will have their average waiting time (AWT) and average turnaround time (ATT) calculated as follows. AWT = (∑ wi ) / n n 𝑖=1 ATT =(∑ ci ) / n n 𝑖=1 Average Deadline Violation with respect to turn around time (ADVT) can be calculated as follows. ADVT = (∑ dvti) / n n 𝑖=1 Algorithm: Nonlinear Analysis of EDF Scheduling Algorithm Input : ‘n’ number of job requests with processing times ti1, ti2, ,ti3…, tim on ‘m’ types of Virtual Machines VM1, VM2, VM3 and VMm, p number of instances are available for each Machine d1i is deadline of ith job request Output : Optimal Scheduling sub sequences Seq1, Seq2, Seq3, ….Seqp 1. begin 2. i=0; 3. solution_vector = empty; 4. for k=1 to 2m do 5. αk = choice(0.1,0.9); 6. end for; 7. for each job request ri with minimum deadline and processing time based on β and γ among all unprocessed jobs do 8. add the job request ri to the solution_vector at index i; Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 377 https://internationalpubls.com 9. i=i+1; 10. end for; 11. for i=0 to n-1 do 12. j = i % p; 13. supplement the scheduling subsequence Seqj with the solution vector [i] 14. end for; 15. for i=1 to p do 16. calculate performance metrics for each scheduling sub sequence Seqi; 17. end for; 18. determine the overall scheduling sequence's aggregate performance metrics 19. end; The Nonlinear Analysis of EDF Scheduling Algorithm accepts ‘n’ job request and assign feasible values for αi (0 < αi< 1) and β and γ for better performance metrics. 4. Performance Evaluation of the Framework A specialized simulation environment has been created to evaluate the First Come First Serve (FCFS) Scheduling, Shortest Job First (SJF) Scheduling, and Earliest Deadline First Scheduling, utilizing ‘p’ Virtual Machine instances for each resource category. Job requests and their processing times are generated randomly using a Gaussian distribution. The process begins with the application of the FCFS scheduling algorithm, which organizes jobs based on their arrival order and divides the scheduling sequence into ‘p’ subsequence’s. Subsequently, the SJF Scheduling algorithm is implemented by arranging the jobs in ascending order of their total processing times (ti1 + ti2 + ti3 + … + tim) and further segmenting the scheduling sequence into sub-scheduling sequences. The Multi-Stage Scheduling algorithm is then applied without taking deadlines into account. Following this, the Simple Earliest Deadline First Scheduling algorithm is employed to produce an optimal scheduling sequence, which is also divided into ‘p’ scheduling sub sequences. Finally, the Nonlinear Analysis of Earliest Deadline First Scheduling algorithm is utilized to achieve an optimal scheduling sequence, again splitting it into ‘p’ scheduling sub sequences. This algorithm determines the optimal solution by assigning appropriate values to β and γ. Performance evaluation metrics are calculated at the conclusion of the process. In Table 1, we analyse n=32 jobs across m=4 types of Virtual Machines, with p=8 instances available. The parameters α1=0.2, α2=0.3, α3=0.4, α4=0.6, α5=0.2, α6=0.3, α7=0.2, and α8=0.3 are used to compute the deadlines for each job request (dli). Table 1: Scheduling Instance n=32, m=4 and p=8 ri ti1 ti2 ti3 ti4 dli 0 124 457 77 5 687 1 402 22 104 78 525 2 322 429 35 56 777 3 150 130 158 64 500 4 405 123 202 72 663 5 31 441 33 64 631 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 378 https://internationalpubls.com 6 172 352 160 94 719 7 204 80 75 61 440 8 248 410 181 87 818 9 448 344 142 74 843 10 90 330 0 64 551 11 160 140 180 34 510 12 330 52 18 23 434 13 237 454 236 94 883 14 71 444 41 2 625 15 204 296 18 66 595 16 322 241 30 18 594 17 328 41 272 19 561 18 277 386 210 33 799 19 297 117 177 38 566 20 376 71 115 14 523 21 54 102 201 1 413 22 162 335 71 63 633 23 54 90 178 19 400 24 180 473 195 26 808 25 232 72 210 39 511 26 267 176 178 27 595 27 496 312 148 58 837 28 20 112 171 2 387 29 51 481 66 22 671 30 36 148 238 34 481 31 376 276 122 48 720 Table 2: FCFS Scheduling for Instance n=32, m=4 and p=8 S_TYPE ri si ci wi dli dvti FCFS 0 0 663 0 687 0 FCFS 1 124 840 234 525 315 FCFS 2 526 1368 526 777 591 FCFS 3 848 1629 1127 500 1129 FCFS 4 0 802 0 663 139 FCFS 5 405 1066 497 631 435 FCFS 6 436 1575 797 719 856 FCFS 7 608 1636 1216 440 1196 FCFS 8 0 926 0 818 108 FCFS 9 248 1256 248 843 413 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 379 https://internationalpubls.com FCFS 10 696 1434 950 551 883 FCFS 11 786 1724 1210 510 1214 FCFS 12 0 423 0 434 0 FCFS 13 330 1351 330 883 468 FCFS 14 567 1508 950 625 883 FCFS 15 638 1845 1261 595 1250 FCFS 16 0 611 0 594 17 FCFS 17 322 982 322 561 421 FCFS 18 650 1556 650 799 757 FCFS 19 927 1738 1109 566 1172 FCFS 20 0 576 0 523 53 FCFS 21 376 764 406 413 351 FCFS 22 430 1061 430 633 428 FCFS 23 592 1214 873 400 814 FCFS 24 0 874 0 808 66 FCFS 25 180 1097 544 511 586 FCFS 26 412 1263 615 595 668 FCFS 27 679 1693 679 837 856 FCFS 28 0 305 0 387 0 FCFS 29 20 701 81 671 30 FCFS 30 71 1033 577 481 552 FCFS 31 107 1207 385 720 487 Table 3: SJF Scheduling for Instance n=32, m=4 and p=8 S_TYPE ri si ci wi dli dvti SJF 0 240 1075 412 687 388 SJF 1 90 696 90 525 171 SJF 2 583 1425 583 777 648 SJF 3 0 502 0 500 2 SJF 4 472 1274 472 663 611 SJF 5 204 822 253 631 191 SJF 6 492 1270 492 719 551 SJF 7 0 420 0 440 0 SJF 8 1034 1960 1034 818 1142 SJF 9 364 1553 545 843 710 SJF 10 0 484 0 551 0 SJF 11 20 534 20 510 24 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 380 https://internationalpubls.com SJF 12 0 423 0 434 0 SJF 13 877 1898 877 883 1015 SJF 14 54 643 85 625 18 SJF 15 36 620 36 595 25 SJF 16 150 761 150 594 167 SJF 17 706 1366 706 561 805 SJF 18 502 1530 624 799 731 SJF 19 286 915 286 566 349 SJF 20 330 906 330 523 383 SJF 21 0 358 0 413 0 SJF 22 125 1069 438 633 436 SJF 23 0 341 0 400 0 SJF 24 287 1629 755 808 821 SJF 25 54 607 54 511 96 SJF 26 235 1106 458 595 511 SJF 27 664 1678 664 837 841 SJF 28 0 305 0 387 0 SJF 29 180 889 269 671 218 SJF 30 0 456 0 481 0 SJF 31 231 1247 425 720 527 Table 4: Simple - EDF Scheduling for Instance n=32, m=4 and p=8 S_TYPE ri si ci wi dli dvti S-EDF 0 472 1252 589 687 565 S-EDF 1 54 660 54 525 135 S-EDF 2 501 1465 623 777 688 S-EDF 3 0 502 0 500 2 S-EDF 4 532 1334 532 663 671 S-EDF 5 456 1025 456 631 394 S-EDF 6 427 1209 431 719 490 S-EDF 7 0 420 0 440 0 S-EDF 8 937 1863 937 818 1045 S-EDF 9 596 1730 722 843 887 S-EDF 10 330 814 330 551 263 S-EDF 11 0 514 0 510 4 S-EDF 12 0 423 0 434 0 S-EDF 13 599 1739 718 883 856 S-EDF 14 430 988 430 625 363 S-EDF 15 252 836 252 595 241 S-EDF 16 150 761 150 594 167 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 381 https://internationalpubls.com S-EDF 17 204 864 204 561 303 S-EDF 18 487 1557 651 799 758 S-EDF 19 36 665 36 566 99 S-EDF 20 54 630 54 523 107 S-EDF 21 0 358 0 413 0 S-EDF 22 420 1219 588 633 586 S-EDF 23 0 341 0 400 0 S-EDF 24 582 1779 905 808 971 S-EDF 25 20 573 20 511 62 S-EDF 26 160 808 160 595 213 S-EDF 27 384 1449 435 837 612 S-EDF 28 0 305 0 387 0 S-EDF 29 333 1019 399 671 348 S-EDF 30 0 456 0 481 0 S-EDF 31 456 1278 456 720 558 Table 5: Nonlinear Analysis of EDF Scheduling for Instance n=32, m=4 and p=8 when β=0.1 and γ=0.9 S_TYPE ri si ci wi dli dvti N-EDF 0 240 1075 412 687 388 N-EDF 1 90 696 90 525 171 N-EDF 2 337 1359 517 777 582 N-EDF 3 0 502 0 500 2 N-EDF 4 472 1274 472 663 611 N-EDF 5 330 920 351 631 289 N-EDF 6 492 1270 492 719 551 N-EDF 7 0 420 0 440 0 N-EDF 8 689 1615 689 818 797 N-EDF 9 364 1553 545 843 710 N-EDF 10 0 484 0 551 0 N-EDF 11 20 534 20 510 24 N-EDF 12 0 423 0 434 0 N-EDF 13 877 1898 877 883 1015 N-EDF 14 54 643 85 625 18 N-EDF 15 36 620 36 595 25 N-EDF 16 150 761 150 594 167 N-EDF 17 361 1155 495 561 594 N-EDF 18 847 1753 847 799 954 N-EDF 19 180 809 180 566 243 N-EDF 20 204 780 204 523 257 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 382 https://internationalpubls.com N-EDF 21 0 358 0 413 0 N-EDF 22 125 1069 438 633 436 N-EDF 23 0 341 0 400 0 N-EDF 24 287 1629 755 808 821 N-EDF 25 54 607 54 511 96 N-EDF 26 580 1228 580 595 633 N-EDF 27 664 1678 664 837 841 N-EDF 28 0 305 0 387 0 N-EDF 29 286 927 307 671 256 N-EDF 30 0 456 0 481 0 N-EDF 31 477 1299 477 720 579 Table 6: Nonlinear - EDF Scheduling for Instance n=32, m=4 and p=8 when β=0.2 and γ=0.8 S_TYPE ri si ci wi dli dvti N-EDF 0 240 1075 412 687 388 N-EDF 1 90 696 90 525 171 N-EDF 2 337 1359 517 777 582 N-EDF 3 0 502 0 500 2 N-EDF 4 472 1274 472 663 611 N-EDF 5 330 920 351 631 289 N-EDF 6 492 1270 492 719 551 N-EDF 7 0 420 0 440 0 N-EDF 8 689 1615 689 818 797 N-EDF 9 364 1553 545 843 710 N-EDF 10 0 484 0 551 0 N-EDF 11 20 534 20 510 24 N-EDF 12 0 423 0 434 0 N-EDF 13 877 1898 877 883 1015 N-EDF 14 204 771 213 625 146 N-EDF 15 36 620 36 595 25 N-EDF 16 150 761 150 594 167 N-EDF 17 361 1155 495 561 594 N-EDF 18 542 1533 627 799 734 N-EDF 19 180 809 180 566 243 N-EDF 20 54 630 54 523 107 N-EDF 21 0 358 0 413 0 N-EDF 22 430 1061 430 633 428 N-EDF 23 0 341 0 400 0 N-EDF 24 592 1621 747 808 813 N-EDF 25 54 607 54 511 96 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 383 https://internationalpubls.com N-EDF 26 275 1109 461 595 514 N-EDF 27 664 1678 664 837 841 N-EDF 28 0 305 0 387 0 N-EDF 29 286 927 307 671 256 N-EDF 30 0 456 0 481 0 N-EDF 31 477 1299 477 720 579 The metrics for First Come First Serve (FCFS) scheduling pertaining to the specified problem instance are presented in Table 2. In a similar manner, Table 3 illustrates the scheduling metrics for Shortest Job First (SJF) scheduling, while Table 4 provides the scheduling metrics for the Simple Earliest Deadline First scheduling models. The metrics for Enhanced-EDF Scheduling are detailed in Table 5, where Beta is set to 0.1 and Gamma to 0.9 in the job selection order. Additionally, Table 6 displays the Enhanced-EDF Scheduling metrics with Beta at 0.2 and Gamma at 0.8 in the job selection order. Table 7: Comparison of Scheduling Metrics when n=32, m=4 and p=8 S_TYPE Average Turn Around Time (ATR) Average Waiting Time (AWT) Average Deadline Violation (ADVT) FCFS 1148 500.5 536 SJF 961 314.3 355.6 Simple-EDF 964 316.6 355.8 Nonlinear-EDF (β=0.1 and γ=0.9) 951 304.3 345.6 Nonlinear-EDF (β=0.2 and γ=0.8) 940 292.5 334 The comparative analysis of scheduling metrics, namely ATR, AWT, and ADVT, across four scheduling models is presented in Table 7. In the FCFS Scheduling model, the ATR is recorded at 1148, whereas it is 961 in the SJF Scheduling model, 964 in the Simple EDF Scheduling model, 951 in the Nonlinear-EDF with parameters (β=0.1 and γ=0.9), and 940 in the Enhanced-EDF with parameters (β=0.2 and γ=0.8). Regarding the AWT, the FCFS Scheduling model shows a value of 500.5, in contrast to 314.3 in the SJF Scheduling model, 316.6 in the Simple EDF Scheduling model, 304.3 in the Nonlinear-EDF with (β=0.1 and γ=0.9), and 292 in the Enhanced-EDF with (β=0.2 and γ=0.8). Similarly, the ADVT in the FCFS Scheduling model is 536, while it is 355.6 in the SJF Scheduling model, 355.8 in the Simple EDF Scheduling model, 345.6 in the Nonlinear-EDF with (β=0.1 and γ=0.9), and 334 in the Nonlinear-EDF with (β=0.2 and γ=0.8). The graphical depiction of these performance metrics is illustrated in Figure 4. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 1 (2025) 384 https://internationalpubls.com Figure 4: Comparison of Scheduling Metrics when n=32, m=4 and p=8 5. Conclusion The Nonlinear Analysis of EDF Scheduling Framework for Resource Distribution in Cloud Computing optimizes job scheduling for resource allocation by taking into the account both deadlines and processing times. Experimental results indicate that the proposed EDF Model outperforms traditional scheduling models such as FCFS, SJF, and Simple EDF in terms of key performance metrics, including Average Turnaround Time, Average Waiting Time (AWT), and Average Deadline Violation with respect to Turnaround Time (ADVT). References [1] Barrie Sosinsky, “Defining Cloud Computing” in Cloud Computing Bible, Indianapolis, Indiana: Wiley Publishing, Inc. 2011. [2] Li, Ji, LonghuaFeng, and Shenglong Fang. "A greedy-based job scheduling algorithm in cloud computing." Journal of Software 9.4 (2014): 921-925. 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