###### Abstract  
Edge computing enables devices with insufficient computing resources to offload their tasks to the edge for computing, to improve the service experience. Some existing work has noticed that the data size of offloaded tasks played a role in resource allocation shares but has not delved further into how the data size of an offloaded task affects resource allocation. Among offloaded tasks, those with larger data sizes often consume a larger share of system resources, potentially even monopolizing system resources if the data size is large enough. As a result, tasks with small or regular sizes lose the opportunity to be offloaded to the edge due to their limited data size. To address this issue, we introduce the concept of an emergency factor to penalize tasks with immense sizes for monopolizing system resources, while supporting tasks with small sizes to contend for system resources. The joint offloading decision and resource allocation problem is formulated as a mixed-integer nonlinear programming (MINLP) problem and further decomposed into an offloading decision subproblem and a resource allocation subproblem. Using the KKT conditions, we design a bisection search-based algorithm to find the optimal resource allocation scheme. Additionally, we propose a linear-search-based coordinate descent (CD) algorithm to identify the optimal offloading decision. Numerical results show that our proposed algorithm converges to the optimal scheme (for the minimal delay) when tasks are of regular size. Moreover, when tasks of immense, small and regular sizes coexist in the system, our scheme can exclude tasks of immense size from edge resource allocation, while still enabling tasks of small size to be offloaded. task offloading; edge computing; offloading decision; KKT; coordinate descent +
Footnote †: journal: 2023  
differentiated tasks into high-computation and high-communication tasks and proposed processing high-communication tasks at the edge or nearby peer devices, while offloading high-computation tasks to the cloud. Some prior work [10; 11; 16] formulated the closed-form solution for bandwidth and computing resource allocation in time-division multiple access (TDMA) MEC systems, indicating that the share of bandwidth allocated to the offloaded task was proportional to its data size. However, these studies have not thoroughly examined the impact of significant differences in data size on resource allocation, or how to address this issue if necessary. While some articles [10; 11] have attempted to differentiate the weights of mobile devices (tasks) to emphasize the differences in task requirements, to our knowledge, they, like other existing works, have overlooked the fact that tasks with small data sizes may be crowded out of resource allocation by tasks with immense sizes, thereby losing the opportunity to be offloaded. In this paper, we investigate the offloading decision and resource allocation mechanism among tasks with significant differences in data size, and we propose a scheme to prevent tasks with immense sizes from monopolizing system resources, while still allowing tasks with small sizes to contend for system resources. The main contributions of this paper are as follows:  
* To address the issue of tasks with immense sizes monopolizing system resources, we introduce the concept of an emergency factor to support tasks with small sizes in contending for system resources. The joint optimization of offloading decisions and edge resource allocation among tasks with significant differences in data size is formulated as a mixed-integer nonlinear programming problem. * We decompose the MINLP problem into two subproblems and propose a linear-search-based coordinate descent method and a bisection-search-based resource allocation algorithm to address the offloading decision and resource allocation subproblems, respectively.