Task Offloading and Resource Allocation for Deterministic Service Provisioning in the IoT-Edge-Cloud Continuum

1 Submitted to Future Generation Computer Systems Journal (Elsevier)

Task Offloading and Resource Allocation for Deterministic Service Provisioning in the IoT–Edge– Cloud Continuum K. Aghababaiyan*, B. Coll-Perales*, and J. Gozalvez* *

Networked Systems Laboratory, Universidad Miguel Hernández de Elche, 03202 Elche, Spain

Abstract—Future networks will seamlessly integrate computing and communication resources within a unified ecosystem of IoT devices, edge nodes, and cloud servers, forming an IoT-edgecloud continuum. Within such an ecosystem, tasks can be dynamically offloaded to leverage resources across the continuum and efficiently scale with demand. Task offloading has traditionally focused on minimizing task execution latency or energy consumption. In contrast, we propose a deterministic task offloading and resource allocation scheme for the joint management of communication and computing resources to support services with deterministic service-level requirements. The proposed scheme aims to maximize the number of tasks completed on time, rather than minimizing the latency of individual tasks. To do so, it exploits variable task latency requirements to distribute the workload across the continuum. It can also prioritize high-priority tasks under resource scarcity. Numerical evaluations demonstrate that a deterministic task offloading strategy scales more effectively and can better guarantee timely task completion by balancing resource utilization across the continuum.

Keywords—Continuum, edge-cloud, deterministic, task offloading, resource allocation, IoT. I. INTRODUCTION The Internet of Things (IoT) is driving transformative changes across various domains, including connected and automated mobility and smart manufacturing. The work of K. Aghababaiyan is supported in part by the European Union under the 2024 MSCA Postdoctoral Fellowship program (project no. 101207598). This work has been also partially funded by the European Commission Horizon Europe SNS JU 6G-SHINE (GA 101095738) project, and by MCIN/AEI/10.13039/501100011033 THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

Connected vehicles rely on their own sensors, communication systems, and processing units to exchange real-time data for safer and more efficient driving tasks [1]. In the industrial IoT (IIoT) domain, collaborative robots (cobots) and autonomous guided vehicles dynamically interact with their environment for a more efficient execution of manufacturing and logistics tasks [2]. Critical services require efficient data processing for timely decision-making, which can place significant processing demands on computing resources as the complexity and number of tasks grow and requires careful latency management to meet deadlines of time-sensitive operations. In this context, the IoT-edge-cloud continuum has emerged as a key enabler to address increasing computational and latency challenges. The IoT-edge-cloud continuum seamlessly integrates computing, connectivity, intelligence, and services within a unified ecosystem of IoT devices, edge nodes, and cloud servers, and offers the possibility to dynamically plan and offload tasks’ execution across resources distributed in the continuum [3]. To this aim, it is necessary to jointly manage communication and computing resources across the continuum. To date, a strong focus has been on joint management schemes that minimize the task execution time. However, in critical verticals such as connected and automated mobility and smart manufacturing, it is usually more important to satisfy stringent deterministic service constraints - particularly in terms of bounded deadline compliance [4] than minimizing latency. Failure to meet these constraints may result in unsafe situations, operational disruptions, or system instability. The capacity to meet these constraints is (PID2020-115576RB-I00, PID2023-150308OB-I00), UMH and Generalitat Valenciana (CIAICO/2024/167). (Corresponding author: Keyvan Aghababaiyan). Email address: {kaghababaiyan, bcoll, j.gozalvez}@umh.es

2 Submitted to Future Generation Computer Systems Journal (Elsevier)

strongly conditioned by the resources available in the continuum, the context conditions, and the service requirements. Connected vehicles typically feature considerable onboard processing capabilities but operate in highly dynamic environments with fluctuating connectivity conditions and diverse service requirements. In addition, software-defined vehicles need to support functionalities updated and expanded over time with the same computing resources. Smart factories usually operate within (semi-) static and controlled network infrastructures but deploy a large variety of devices and require collaborative efforts between devices for manufacturing task execution. In this context, achieving the appropriate balance between local processing and task offloading is essential. While offloading to edge or cloud servers can expand available computing capacity, it may introduce additional latency. On the other hand, relying solely on local execution may be limited by the local processing capabilities. The key challenge lies in designing task offloading strategies that holistically manage resources across the continuum in a manner that prevents communication and computing bottlenecks, preserves balanced resource utilization, and guarantees deterministic service levels [5]. Most existing latency-based task offloading schemes [6]-[9] focus on minimizing individual task latency, which risks overloading resources if too many tasks are assigned to the nodes that individually can minimize latency, causing the system to operate in a locally optimal but globally inefficient manner. This paper advances the state of the art with a deterministic task offloading and resource allocation strategy designed to satisfy deterministic service-level requirements while effectively scaling by balancing workloads across the continuum. The proposed scheme focuses on completing tasks within bounded deadlines rather than minimizing individual task latency. By exploiting the available task latency budget, it balances workload distribution across the IoT–edge–cloud continuum, which helps prevent computing and communication congestions in specific computing units and communication links. The scheme has the ability to prioritize the timely execution of critical tasks under resource scarcity. Its potential and adaptability to heterogeneous IoT operational settings are demonstrated in representative connected mobility and smart manufacturing scenarios characterized by different processing capabilities and diverse task requirements. Numerical evaluations show that the proposed deterministic strategy can scale better and successfully complete a higher number of tasks on time than state-of-the-art schemes focused on minimizing individual task latency thanks to a more balanced THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

workload distribution across the continuum. The remainder of this article is organized as follows. Section II reviews the state-of-the-art in task offloading and resource allocation. Section III describes the system model adopted for task offloading and resource allocation across the IoT-edge-cloud continuum. Section IV presents the proposed deterministic task offloading and resource allocation scheme. Section V outlines the simulation setup, evaluation parameters and scenarios as well as the benchmark schemes. Section VI analyzes the evaluation results, and Section VII summarizes the key findings. II. STATE OF THE ART A key aspect in managing the IoT-edge-cloud continuum is determining the optimal distribution of task processing across resources in the continuum. This should be done noting that not all IoT nodes are resource-constrained; for instance, devices such as Connected and Automated Vehicles (CAVs) often feature powerful local processors. In recent years, growing attention has been devoted to developing task offloading and resource allocation schemes across different computing nodes of the continuum - ranging from local-edge cooperation to cloud-based and fully integrated IoT-edge-cloud continuum - with the goal of minimizing latency and improving the efficiency of distributed computing. The work in [10] focuses on latency-aware task execution in mobile edge computing, where computation occurs locally or at nearby edge servers. It optimizes resource allocation and offloading decisions to reduce latency, though it remains confined to the edge and local IoT nodes. Studies [6] and [7] expand this model by employing the computing capacity of interconnected IoT nodes, specifically vehicles, as distributed resources. In [6], parked and moving vehicles cooperate with an edge server to process offloaded tasks and minimize total priority-weighted processing latency through coordinated offloading among vehicles, and between vehicles and the edge. The study reported in [7] introduces greater flexibility by enabling vehicles to decide whether to execute tasks locally, offload them to a roadside unit, or share them directly with other vehicles. These studies emphasize the role of vehicles as mobile IoT devices that augment edge resources, contributing to latency reduction. [8] introduces an inverse offloading framework, where tasks are transferred from the edge back to vehicles. This scheme alleviates the computational burden on the edge server while maintaining low latency by effectively exploiting underused vehicular computing capacity. [11] focuses on cloud-centered task migration, and designs

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strategies that move computation from onboard vehicle systems to cloud servers to support cooperative processing. The study examines how centralized execution and 5G connectivity can meet increasing computational demands while maintaining latency below the required deadline constraints. [9] and [12] advance the concept toward multi-layer collaboration, forming a full IoT–edge–cloud continuum with the goal of minimizing latency. In [9], computation is organized across the full continuum, distinguishing between latency-sensitive and non–time-sensitive tasks, with the objective of minimizing latency for latencysensitive tasks. [12] integrates idle IoT and vehicular devices as intermediate computing nodes that cooperate with edge and cloud resources to minimize latency. Studies [13]-[15] focus on load balancing and spatial load distribution across resources in the continuum. In [13] and [14], the authors introduce schemes that identify overloaded edge nodes and reassign tasks or users to underutilized ones, thereby maintaining responsiveness and preventing congestion. [15] proposes a location-aware allocation scheme that redistributes computational tasks from congested regions to less utilized areas, improving overall system stability and latency consistency. Collectively, these studies highlight the potential of the IoT–edge–cloud continuum, and the importance of task offloading schemes to effectively exploit the continuum. To date, contributions have mostly focused on minimizing individual task execution latency. However, this focus increases the risk of overloading certain computing units and communication resources, while many vertical services require deterministic service levels and not necessarily minimizing the latency of each task. This paper addresses this gap with a deterministic task offloading and resource allocation strategy that prioritizes the timely completion of tasks within predefined deadlines and a balanced distribution of workloads across the continuum for better scaling. An initial version of this work was presented in [16]. This manuscript provides a robust extension to that past study by introducing a load distribution mechanism and a priority-based version of the proposed scheme. In addition, we conduct a thorough analysis on the impact of distinct operational environments—such as connected vehicular mobility and smart industrial manufacturing scenarios—demonstrating the performance, robustness, and adaptation of the proposed strategy under diverse network and device characteristics. III. SYSTEM MODEL We consider an IoT-edge-cloud continuum system THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

composed of heterogeneous IoT devices connected to edge computing nodes and a cloud server through a wide-area wireless network. The system model is designed to capture a broad range of operational environments where tasks generated by IoT devices can be processed locally or offloaded to edge or cloud, subject to communication and computing constraints and task-specific latency requirements. To reflect the diversity of real-world deployments, the model encompasses two representative emerging IoT–edge– cloud continuum scenarios: connected mobility and smart manufacturing. These scenarios exhibit fundamentally different characteristics in terms of device heterogeneity, local processing capabilities, task generation patterns, and reliance on network-assisted computation. The connected mobility scenario includes 𝐽𝑣1 lowpower wearable devices (e.g. smartwatches), 𝐽𝑣2 general-purpose mobile devices (e.g. smartphones), and 𝐽𝑣3 vehicles equipped with powerful onboard computing platforms where 𝐽𝑣 =𝐽𝑣1 +𝐽𝑣2 +𝐽𝑣3 . Tasks are generated by these three types of devices with proportions 𝛼𝑣1 , 𝛼𝑣2 , 𝛼𝑣3 , where 𝛼𝑣1 + 𝛼𝑣2 + 𝛼𝑣3 = 1. The smart manufacturing scenario considers a mix of 𝐽𝐼1 mobile IoT devices, 𝐽𝐼2 assembly robots, 𝐽𝐼3 advanced factory robots, and 𝐽𝐼4 autonomous guided vehicles with more constrained local processing capabilities than vehicles in the connected mobility scenario. 𝐽𝐼 = 𝐽𝐼1 + 𝐽𝐼2 +𝐽𝐼3 + 𝐽𝐼4 is the total number of IoT industrial devices. Tasks are generated by different types of devices with proportions 𝛼𝐼1 , 𝛼𝐼2 , 𝛼𝐼3 , 𝛼𝐼4 , where 𝛼𝐼1 + 𝛼𝐼2 + 𝛼𝐼3 + 𝛼𝐼4 = 1. Tasks 𝑓𝑖 , 𝑖𝜖 {1, … , 𝐼 } generated by the devices in both scenarios can be represented by the tuple {𝑐𝑖 , 𝑠𝑖 , 𝑠 ′ 𝑖 , 𝐺𝑖 , 𝐷𝑖 }. 𝑐𝑖 is the task 𝑓i ’s computational demand and 𝑠𝑖 is its associated size. When a task is delegated to the edge units or cloud server, the processed result must be transmitted back to the original unit. The size of processed results of 𝑓i is defined as 𝑠 ′ 𝑖 = 𝜌 ∙ 𝑠𝑖 , where 𝜌 < 1. 𝐺𝑖 is 𝑓i ’s generation time, and 𝐷𝑖 its deadline by which all processing must be completed. If the task is offloaded to the edge or cloud, the deadline accounts for the time required to transmit the task to the designated processing unit, the processing time, and the time needed to send the processed result back. Local IoT (𝑗𝜖𝐽; either 𝐽𝑣 or 𝐽𝐼 ), edge (𝑞𝜖𝑄) and cloud (C) computing units are modeled considering their processing power 𝜒𝑚 and maximum processing capacity 𝛸𝑚 over a time period T with Χ 𝑚 = 𝜒𝑚 . 𝑇, 𝑚 𝜖 𝑀; 𝑀 = (𝐽, 𝑄, 𝐶). The computing time for a task 𝑓𝑖 processed by computing unit 𝑚 is:

4 Submitted to Future Generation Computer Systems Journal (Elsevier)

𝑡𝑝𝑖 =

𝑐𝑖 . 𝜒𝑚

(1)

We consider that the wireless link to connect the IoT devices to the wide-area network is based on a Frequency Division Duplexing (FDD)-based Orthogonal Frequency Division Multiple Access (OFDMA) radio access interface. The amount of information that can be transmitted by a resource block 𝜅 𝜖 𝛫 can be expressed as follows: (2) 𝑅𝜅 = 𝑇𝑘 . 𝐵𝑊𝜅 × log 2 (1 + 𝛾𝜅 )(1 − 𝑒𝜅 ), where 𝑇𝑘 is the duration of the resource, 𝐵𝑊𝜅 is the resource’s bandwidth, 𝛾𝜅 is the Signal-to-Interferenceplus-Noise Ratio (SINR), and 𝑒𝜅 is the bit error rate, which is a function of the modulation and coding scheme (MCS) used. 𝛫 is the total number of orthogonal resource blocks, which are divided into 𝛫 𝑈𝐿 and 𝛫 𝐷𝐿 resources for the uplink and downlink bands. We assign each communication resource 𝜅 an MCS determined by its SINR 𝛾𝜅 . Channel fading is modeled with a Rayleigh distribution. Considering 𝛫𝑖𝑈𝐿 as the total number of resource blocks used in the uplink for the offloading of the tasks 𝑓𝑖 , the uplink channel data capacity can be estimated as: (3) 𝑅𝑈𝐿 = ∑ 𝑅 . 𝑖

𝜅𝜖𝛫𝑖𝑈𝐿

𝜅

Similarly, the downlink channel data capacity 𝑅𝑖𝐷𝐿 is computed as the sum of the capacities of the 𝛫𝑖𝐷𝐿 resource blocks allocated in the downlink. It should be noted that 𝑠𝑖 ≤ 𝑅𝑖𝑈𝐿 and 𝑠′𝑖 ≤ 𝑅𝑖𝐷𝐿 must hold to ensure that the uplink and downlink communication links can successfully transfer the task 𝑓𝑖 and its processing result, respectively. If task 𝑓𝑖 with size 𝑠𝑖 needs to be offloaded, its uplink transmission time is computed as: 𝑠𝑖 (4) 𝑖 𝑡𝑈𝐿 = 𝑈𝐿 , 𝑅𝑖 and the downlink transmission time for the processed result of this task can be expressed as: 𝑠′𝑖 (5) 𝑖 𝑡𝐷𝐿 = 𝐷𝐿 . 𝑅𝑖 When a task is offloaded to the edge or cloud, the time 𝑇𝑖 necessary to execute a task 𝑓𝑖 includes the processing time at the corresponding unit (𝑡𝑝𝑖 ), the time to upload the task from the IoT device to the computing unit 𝑖 (𝑡𝑈𝐿 ), and the time to download the processed result 𝑖 back to the IoT device (𝑡𝐷𝐿 ): 𝑖 𝑖 𝑖 (6) 𝑇𝑖 = 𝑡𝑝 + 𝑡𝑈𝐿 + 𝑡𝐷𝐿 . If the task is locally executed at the IoT device then 𝑇𝑖 = 𝑡𝑝𝑖 . A task is satisfactorily served if the total THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

execution time 𝑇𝑖 is less than or equal to the task’s deadline 𝐷𝑖 . IV. DETERMINISTIC TASK OFFLOADING AND RESOURCE ALLOCATION This section presents the proposed Deterministic task offloading and resource allocation scheme, operating over the IoT–edge–cloud continuum system described in Section III. The proposed scheme manages the heterogenous communication and computing resources available across the continuum to satisfy tasks' bounded latency deadlines, rather than minimizing individual task execution time. To this aim, we define the penalty cost HD as (7) 𝛨 = ∑ Λ (𝜏 ) , 𝐷

𝑖

𝑖𝜖𝐼

and Λ(𝜏𝑖 ) is a penalty function defined as: 0, 0 ≤ 𝜏𝑖 ≤ 1, Λ ( 𝜏𝑖 ) = { Π, 𝜏𝑖 > 1, with 𝜏𝑖 =

𝑇𝑖 𝐷𝑖

(8)

. This penalty function assigns a high cost

Π to tasks 𝑓i , 𝑖𝜖 {1, … , 𝐼 } whose execution time 𝑇𝑖 exceeds their deadline 𝐷𝑖 , while tasks completed within their deadlines incur no penalty. We initially formulate the task offloading and resource allocation problem as an optimization problem where the objective is minimizing the overall penalty cost 𝛨𝐷 : (9)

𝑀𝑖𝑛 𝛨𝐷 𝑠. 𝑡.

𝐶1 : 𝑎𝑖,𝑗 𝜖 {0, 1}, ∀𝑗𝜖𝐽, ∀𝑖𝜖𝐼,

𝐶2 : 𝑎𝑖,𝑞 𝜖{0, 1}, ∀𝑞𝜖𝑄, ∀𝑖𝜖𝐼, 𝐶3 : 𝑎𝑖,𝐶 𝜖{0, 1}, ∀𝑖𝜖𝐼, 𝐶4 : ∑

𝑗𝜖𝐽

𝑎𝑖,𝑗 + ∑

𝑞𝜖𝑄

𝑎𝑖,𝑞 + 𝑎𝑖,𝑐

≤ 1, ∀𝑖𝜖𝐼, 𝐶5 : ∑ 𝑐𝑖 𝑎𝑖,𝑚 ≤ 𝛸𝑚 ,

∀𝑚𝜖𝑀,

𝑖𝜖𝐼 𝑈𝐿 𝐷𝐿 { 𝐶6 : 𝑏𝑖,𝜅 , 𝑏𝑖,𝜅 𝜖 0, 1}, ∀𝑖𝜖𝐼, ∀𝜅𝜖Κ, 𝑈𝐿 𝐶7 : ∑ 𝑏𝑖,𝜅 = 1 , ∀𝜅𝜖Κ 𝑈𝐿 , 𝑖𝜖𝐼 𝐷𝐿 𝐶8 : ∑ 𝑏𝑖,𝜅 = 1 , ∀𝜅𝜖Κ 𝐷𝐿 , 𝑖𝜖𝐼

𝐶9 : 𝑠𝑖 ≤ ∑

𝜅𝜖𝛫𝑖𝑈𝐿

𝐶10 : 𝑠′𝑖 ≤ ∑

𝑅𝜅 , ∀𝑖𝜖I,

𝜅𝜖𝛫𝑖𝐷𝐿

𝑅𝜅 , ∀𝑖𝜖I,

𝑈𝐿 𝐶11 : 𝑏𝑖,𝜅 = 0, 𝑖𝑓 𝑡(𝜅) < 𝐺𝑖 ,

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𝐶12 : ∑𝑗𝜖𝐽 𝑎𝑖,𝑗 + ∑𝑞𝜖𝑄 𝑎𝑖,𝑞 + 𝑎𝑖,𝑐 = 0, i𝑓 𝑡 < 𝐺𝑖 + 𝑖 𝑡𝑈𝐿 , 𝐷𝐿 𝑖 𝐶13 : 𝑏𝑖,𝜅 = 0, 𝑖𝑓 𝑡(𝜅) < 𝐺𝑖 + 𝑡𝑝𝑖 + 𝑡𝑈𝐿 . Constraints 𝐶1 -𝐶4 use binary variables 𝑎𝑖,𝑗 , 𝑎𝑖,𝑞 and 𝑎𝑖,𝑐 to enforce that each task is allocated to a single computing unit, either in the IoT (𝐶1 ), edge (𝐶2 ), or cloud (𝐶3 ) domain. Constraint 𝐶5 ensures that the selected computing unit is not overloaded by the computation demand of the allocated task. Constraint 𝐶6 defines the allocation of communication resources to tasks in the uplink and downlink directions. Binary 𝑈𝐿 𝐷𝐿 variables 𝑏𝑖,𝜅 and 𝑏𝑖,𝜅 indicate whether communication resource 𝜅𝜖𝛫 is assigned to task 𝑓𝑖 - for offloading to the edge or cloud - for transmitting the processed result back to the IoT device, respectively. In line with OFDMA operation, constraints 𝐶7 and 𝐶8 ensure that each communication resource block is allocated to at most one task. Constraints 𝐶9 and 𝐶10 guarantee that the aggregated capacity of the allocated communication resources is sufficient to transmit the task in the uplink and its processed result in the downlink, respectively. Constraints 𝐶11 − 𝐶13 enforcethe temporal ordering of operations: uplink transmission can only occur after task generation, task processing after the uplink ,transmission is completed and the downlink transmission takes place after task processing. We extend the initial formulation in (7) to promote a balanced utilization of resources across the IoT-edgecloud continuum. This extension is aimed at mitigating load concentration and resource bottlenecks under high traffic conditions, while preserving the Deterministic operation of the scheme. In this case, the objective function is still minimizing the overall penalty cost, but this cost is now expressed as: (10) 𝛨𝐷𝐷 = ∑𝑖𝜖𝐼 Λ(𝜏𝑖 ) + 𝜆1 ∑𝑚𝜖𝑀 𝑁𝑚 . |𝛽̅ − 𝛽𝑚 | + 𝜆2 ∑𝑚𝜖𝑀(1 − 𝜂𝑚 ), where the first term corresponds to the penalty function HD in (7) and accounts for tasks whose execution exceeds their deadline. The second term in (10) promotes a more balanced utilization of computing resources across the continuum by penalizing deviations from the continuum’s average usage ratio. 𝑁𝑚 denotes the set of tasks assigned to computing unit 𝑚, and 𝛽𝑚 represents the usage ratio of computing unit 𝑚: ∑𝑖𝜖𝐼 𝑐𝑖 𝑎𝑖,𝑚 𝛽𝑚 = , (11) Χ𝑚 where 𝛽̅ is the average usage ratio across different computing units, which is computed as: THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

1 (12) ∑ 𝛽𝑚 . 𝑀 𝑚𝜖𝑀 By weighting the deviation |𝛽̅ − 𝛽𝑚 | with 𝑁𝑚 , this second term in (10) places greater emphasis on load imbalance affecting computing units that serve a larger number of tasks. The second term in (10) discourages load imbalance and excessive task concentration in certain computing units. Finally, the third term in (10) penalizes low task satisfaction at each computing unit by weighting the fraction of tasks whose execution time 𝑇𝑖 exceeds their deadline. This fraction is equal to 1 𝜂𝑚 , where 𝜂𝑚 is defined as the task satisfaction ratio for computing unit 𝑚. The satisfaction ratio is defined as the ratio of tasks completed within their deadlines. The third term is hence defined to encourage high perunit satisfaction ratios and prevent the concentration of poorly served tasks on individual computing units. The second and third terms in (10) use 𝜆1 and 𝜆2 as weighting factors to control the importance of the terms. The objective function for the task offloading and resource allocation problem is then defined as: (13) 𝑀𝑖𝑛 𝛨𝐷𝐷 𝛽̅ =

𝑠. 𝑡.

𝐶1 − 𝐶13 ,

where 𝐶1 − 𝐶13 are the constraints defined in (9). The objective function is further extended to incorporate task prioritization so that high-priority tasks can still be completed within their deadline under resource-constrained conditions. In this case, the penalty cost is defined as follows: 𝐻 (14) 𝛨𝑃𝐷𝐷 = ∑𝑖𝜖𝐼 Λ𝑃 (𝜏𝑖 ) + 𝜆1𝐻 ∑𝑚𝜖𝑀 𝑁𝑚 . |𝛽̅ − 𝐻∑ 𝐻 𝛽𝑚 | + 𝜆2 𝑚𝜖𝑀(1 − 𝜂𝑚 ), where Λ𝑃 (𝜏𝑖 ) is defined as: 0, 0 ≤ 𝜏𝑖 ≤ 1, (15) Λ 𝑃 ( 𝜏𝑖 ) = { Π , 𝜏 > 1, 𝑃𝑖 𝑖 where 𝑃𝑖 𝜖 {𝐿, 𝐻} denotes whether task 𝑓𝑖 is of low (L) or high (H) priority. The penalty values satisfy 𝛱𝐿 ≪ 𝛱𝐻 , thereby enforcing a stronger penalty for deadline violations of high-priority tasks and biasing the optimization toward their timely completion under resource-constrained conditions. The second and third terms in (14) extend (10) by focusing specifically on 𝐻 high-priority tasks. To this end, in (14), 𝑁𝑚 denotes the number of high-priority tasks assigned to computing 𝐻 unit 𝑚, while 𝜂𝑚 represents the satisfaction ratio of high-priority tasks at unit 𝑚. By weighting the load 𝐻 imbalance with 𝑁𝑚 , the second term discourages concentration of high-priority tasks on individual computing units and promotes a balanced distribution of critical workloads across the IoT–edge–cloud continuum. The parameters 𝜆1𝐻 , 𝜆𝐻 2 are weighting factors controlling the relative importance of load

6 Submitted to Future Generation Computer Systems Journal (Elsevier)

V. EVALUATION SCENARIO Algorithm I : Genetic algorithm 1. For gen = 1 to G do 2. Initialize population {𝑎𝑖,𝑗 , 𝑎𝑖,𝑞 , 𝑎𝑖,c } satisfying 𝐶1 − 𝐶5 , 𝐶12 . 3. For each individual: 𝑈𝐿 4. Allocate 𝑏𝑖,𝜅 under 𝐶7 , 𝐶9 , 𝐶11 ⟶ 𝑖 compute 𝑡𝑈𝐿 . 5. Calculate 𝑡𝑝𝑖 using (1). 𝐷𝐿 6. Allocate 𝑏𝑖,𝜅 under 𝐶8 , 𝐶10 , 𝐶13 ⟶ 𝑖 compute 𝑡𝐷𝐿 . 7. Evaluate objective functions of (9), (13), (16). 8. Select top 25% as elite. 9. Generate 75% via crossover (elite). 10. Mutate 20% of new individuals. 11. End For 12. Return best {𝑎𝑖,𝑗 , 𝑎𝑖,𝑞 , 𝑎𝑖,c } across G generations balancing and maximizing the number of high-priority tasks completed by their deadlines per computing unit. The final objective function for the joint task offloading and resource allocation problem is defined subject to constraints 𝐶1 − 𝐶13 in (9) as: (16) 𝑀𝑖𝑛 𝛨𝑃𝐷𝐷 𝑠. 𝑡.

𝐶1 − 𝐶13 .

The optimization problem in (16) is NP-hard, and we use the genetic algorithm in Algorithm I to obtain nearoptimal solutions [16]. The algorithm runs for G =10 generations (line 1) with a population size of 1,000 individuals per generation. This configuration is sufficient because the large population size allows for broad exploration of the search space, leading to rapid convergence. By the tenth generation, the variation in the objective values stabilizes to less than 1%, indicating that further iterations would yield negligible improvements. Algorithm I initializes the population based on constraints 𝐶1 − 𝐶5 and 𝐶12 (line 2). The objective functions are evaluated in lines 3 to 7. For each generation, 25% of the top-performing (elite) individuals are selected for crossover to form the next generation (lines 8 and 9). Additionally, in line 10, mutation is introduced in 20% of the population to enhance solution diversity and improve convergence toward a near-optimal solution [18].

THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

We consider two representative IoT-edge-cloud scenarios from the connected mobility and smart manufacturing verticals to evaluate the ability of the task offloading schemes to adapt to heterogeneous operational environments. These scenarios exhibit fundamentally different characteristics in terms of device heterogeneity, local processing capabilities, and reliance on network-assisted computation. The connected mobility scenario includes 𝐽𝑣1 =4 smartwatches, 𝐽𝑣2 =4 smartphones, and 𝐽𝑣3 =2 vehicles, resulting in a total of 𝐽𝑣 =10 IoT devices. Tasks are generated by these devices at proportions of 𝛼𝑣1 =0.1, 𝛼𝑣2 =0.5 and 𝛼𝑣3 =0.4, respectively. These values align with the standard distribution of tasks commonly observed across these specific device categories [19]. The computational workload of each task is modeled as a uniformly distributed random variable whose range depends on the originating device type. Tasks generated by smart vehicles are more computationally demanding, ranging from 75 to 150 Mcycles. In contrast, tasks generated by smartwatches and smartphones range from 25 to 35 Mcycles and from 30 to 60 Mcycles, respectively, reflecting the less demanding applications they support [20]. Following the specifications of commercial off-the-shelf products, the local processing capabilities are set to 400 MHz for smartwatches, 3 GHz for smartphones, and 12 GHz for vehicles, capturing the large disparity in onboard computing power across device types. In the smart manufacturing scenario, we consider a medium-size industrial deployment [21] with 𝐽𝐼1 = 5 mobile IoT devices, 𝐽𝐼2 = 6 assembly robots, 𝐽𝐼3 = 6 advanced factory robots, and 𝐽𝐼4 = 6 automated guided vehicles, for a total of 𝐽𝐼 = 23 IoT devices. The four device types generate tasks with proportions of 𝛼𝐼1 =0.1, 𝛼𝐼2 =0.3, 𝛼𝐼3 =0.3, and 𝛼𝐼4 =0.3, respectively, reflecting the heavier workloads produced by robotic systems compared to simple sensing devices [22]. Their workloads are modeled as uniformly distributed random variables with ranges depending on the device type and their processing needs ([23], [24]): (25–35) Mcycles for mobile IoT devices, (30–100) Mcycles for assembly robots and advanced factory robots, and (60–120) Mcycles for autonomous guided robots. Their local processing power is set to 400 MHz for mobile IoT devices, 1.2 GHz for assembly robots, 2 GHz for advanced factory robots, and 2.5 GHz for autonomous guided vehicles [25]. In both scenarios, the infrastructure includes one edge computing node and one cloud server, with processing capacities of 70 GHz and 150 GHz, respectively [26].

7 Submitted to Future Generation Computer Systems Journal (Elsevier)

Different workload scenarios are analyzed with the number of parallel tasks ranging from 35 to 80 every 100 ms, and tasks generated uniformly over time. The task deadlines are uniformly distributed between 50100 ms for the connected mobility scenario, and 50-90 ms for the smart manufacturing scenario [27]. Representing typical payloads for sensing and control data [20], task sizes are uniformly distributed in the range of 1–2 Mbits, and the size of processed results is set to 𝜌=0.15 of the original task size. We consider two task priority classes. The penalty values Π𝑃𝐻 and Π𝑃𝐿 in (15) for high- and low-priority tasks are set to 100 and 1, respectively. The regularization factors in (10) and (14) are 𝜆1 = 𝜆1𝐻 = 2 and 𝜆2 = 𝜆𝐻 2 = 2, respectively. These values are chosen to give equal importance to satisfying latency deadlines in each computing unit and ensuring balanced workload distribution across the continuum. The FDD-based OFDMA wide area network is configured with a 100 MHz bandwidth, 30 kHz subcarrier spacing (SCS) and a time slot duration of 0.5 ms, typically used in 5G NR environments representing aggregated FDD carriers. Diverse communication conditions are analyzed by varying the SINR between devices and the base station in the range of 15 – 30 dB. VI. PERFORMANCE EVALUATION This section compares the performance of the deterministic task offloading and resource allocation proposal against three benchmark schemes. With the first one (Local), all tasks generated by IoT devices are processed by the devices themselves. This scheme represents scenarios where task offloading is not

(a) Satisfaction ratio as a function of the number of tasks (SINR= 30 dB)

feasible - e.g. when devices are not connected to the wide-area network - and local processing is the only option. The second scheme (Offload) offloads all tasks generated by the IoT devices for processing at edge nodes or cloud servers. This scheme represents scenarios where local computing resources are insufficient, and tasks must rely entirely on networkassisted processing. The third benchmark scheme (Minimum) follows the principles of [6]-[9] and jointly manages communication and computing resources with the objective of minimizing the execution time 𝑇𝑖 of individual tasks 𝑓i . The objective function is defined as: (17) 𝛨 =∑ 𝑇 , 𝑀

𝑖𝜖𝐼

and we apply the same constraints 𝐶1 − 𝐶13 in eq. (9) for a fair comparison with the Deterministic problem. The optimization problem is then defined as follows, and we apply the same genetic algorithm for its resolution: (18) 𝑀𝑖𝑛 𝛨𝑀 𝑠. 𝑡.

𝐶1 − 𝐶13 .

Figure 1 compares the satisfaction ratio achieved by the Deterministic and benchmark schemes under varying traffic loads and channel quality conditions in the connected mobility scenario. Unless otherwise stated, the Deterministic proposal is configured with the penalty value Π in (8), assigned to tasks that are not completed by their deadlines equal to 100; this value is chosen to be higher than the maximum number of tasks to impose a sufficiently high penalty. The satisfaction ratio is defined as the ratio of tasks completed within their deadlines. Figure 1 shows that the Deterministic

(b) Satisfaction ratio as a function of the SINR (number of tasks=50)

Figure 1. Satisfaction ratio in the connected mobility scenario. THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

𝑖

8 Submitted to Future Generation Computer Systems Journal (Elsevier)

(a) Communication resources usage

(b) Computing resources usage

Figure 2. Resources usage ratio as a function of number of tasks for SINR= 30 dB in the connected mobility scenario. proposal achieves the highest satisfaction ratio across all considered traffic loads and channel quality conditions. This confirms the effectiveness of explicitly targeting deadline satisfaction when allocating communication and computing resources. Figure 1 also highlights the benefits of exploiting an integrated IoTedge-cloud continuum with the Deterministic and Minimum schemes compared to Local and Offload. The latter experience a pronounced degradation as the number of tasks increases, since they are restricted to using only IoT or edge/cloud computing resources, which can saturate earlier. The effective exploitation of computing resources across the IoT–edge–cloud

(a) Connected mobility

continuum requires coordinated management of both computing and communication resources, as evidenced by the performance gap between the benchmarks and the Deterministic proposal depicted in Figure 1 for both varying system loads and channel conditions. Figure 1(a) shows that the Deterministic proposal can support a larger number of tasks satisfactorily than schemes trying to minimize the execution time of individual tasks. For example, the Deterministic proposal can achieve full task satisfaction for up to 60 tasks, whereas the Minimum scheme reaches complete satisfaction only up to 45 tasks. The impact of channel conditions reported in Figure 1(b) further highlights the

(b) Smart manufacturing

Figure 3. Task execution time distribution for different number of tasks in the connected mobility and smart manufacturing scenarios.

THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

9 Submitted to Future Generation Computer Systems Journal (Elsevier)

(a) Offloading ratio as a function of the number of tasks (SINR= 30 dB)

(b) Offloading ratio as a function of the SINR (number of tasks=50)

Figure 4. Ratio of offloaded to non-offloaded tasks. benefits of the proposed Deterministic scheme. As the SINR decreases, schemes that rely heavily on offloading suffer from reduced data rates and increased communication congestion. In contrast, the Deterministic proposal adapts its task allocation decisions by leveraging local processing when communication resources become constrained. For example, when SINR=15 dB, Minimum is offloading 53% of the tasks while the Deterministic proposal reduces this percentage to 40%. The higher satisfaction ratios achieved with the Deterministic scheme stem from its better management and more balanced workload and resource utilization across the continuum, which it achieves by flexibly

(a) Satisfaction ratio as a function of the number of tasks (SINR= 30 dB)

exploiting task deadlines. Figure 2 depicts the average ratio of occupied communication (Figure 2(a)) and computing (Figure 2(b)) resources out of the total resources available between the task arrival time and its deadline. Figure 2 shows that the Deterministic proposal balances communication and computing resources usage depending on the workload by spreading tasks more evenly across available resources. In low-load scenarios, the Minimum scheme utilizes fewer communication resources and prefers processing more tasks locally compared to the Deterministic proposal. However, as the workload increases, the Minimum scheme relies excessively on the edge/cloud processing to reduce task’s execution time. This

(b) Satisfaction ratio as a function of the SINR (number of tasks=50)

Figure 5. Satisfaction ratio in the smart manufacturing scenario. THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

10 Submitted to Future Generation Computer Systems Journal (Elsevier)

(a) Satisfaction ratio of high-priority tasks as a function of the number of tasks (SINR= 30 dB)

(b) Satisfaction ratio of high-priority tasks as a function of the SINR (number of tasks=50)

Figure 6. Satisfaction ratio of high-priority tasks in the connected mobility scenario. excessive offloading leads to bottlenecks in the communication links under high loads, resulting in a drop in the satisfaction ratio, as illustrated in Figure 1. Figure 3 illustrates the task execution time for the Deterministic and Minimum schemes as a function of the traffic load for both the connected mobility (Figure 3(a)) and smart manufacturing (Figure 3(b)) scenarios. The results are presented as box plots to capture both the median execution time and the variance experienced by the tasks. Specifically, the central mark indicates the median, while the bottom and top edges of the box represent the 25th and 75th percentiles, respectively. The whiskers extend to the minimum and maximum values to capture the variance of task execution times. Under low traffic conditions (e.g., 35 to 45 tasks), the benchmark Minimum scheme achieves lower median execution times than the proposed Deterministic scheme. This behavior is expected, as the Minimum scheme targets the minimization of individual task execution times, exploiting resources when they are available. However, as the number of tasks increases, the performance of the Minimum scheme degrades. It leads to resource congestion, resulting not only in higher median execution times but also in an increased execution time variance, as indicated by the elongated upper whiskers in both scenarios at loads of 70 to 80 tasks. In contrast, the proposed Deterministic scheme demonstrates superior scalability. By explicitly managing resources to satisfy deadlines rather than minimizing individual execution times, the Deterministic scheme prevents severe congestion. Consequently, at high traffic loads, it maintains lower median execution times and a tighter variance compared to the Minimum scheme. THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

Figure 4 compares the operation of the Deterministic and Minimum task offloading and resource allocation schemes under the connected mobility and smart manufacturing scenarios. Both scenarios differ in the computing resources available locally at the IoT devices, which directly influences the balance between local processing and task offloading decisions. Figure 4 depicts the ratio of offloaded to locally processed tasks as a function of the traffic load (Figure 4(a)) and channel conditions (Figure 4(b)). The results show that the Deterministic scheme dynamically adjusts its offloading decisions according to both the workload and available local computing capacity in each scenario. As the number of tasks increases or the SINR decreases, the Deterministic scheme balances the use of local and edge/cloud resources to prevent early resource saturation. In particular, it offloads a higher fraction of tasks to the edge-cloud in the smart manufacturing scenario than in the connected mobility one. This reflects the more constrained local processing capabilities in the smart manufacturing scenario. The difference in offloading ratios between the two scenarios reaches a maximum relative difference of 21% under the highest load condition (i.e. 80 tasks), where computing resources are more stressed. Under these conditions, the Deterministic scheme processes locally a larger proportion of tasks in the connected mobility scenario, leveraging its stronger onboard computing resources. This trend is also visible when analyzing how the offloading ratio evolves with increasing workload. The proportion of offloaded tasks decreases by only 11% in the smart manufacturing scenario while it decreases by more than 21% in the connected mobility scenario. The capacity of the

11 Submitted to Future Generation Computer Systems Journal (Elsevier)

Deterministic scheme to dynamically adjust its allocation decisions results in high task satisfaction ratios for both the connected mobility (Figure 1) and smart manufacturing (Figure 5) scenarios. In contrast, the benchmark Minimum scheme does not explicitly account for differences in local computing capabilities across scenarios in its target to minimize the task execution latency. As a result, it shows largely unchanged offloading behavior despite variations in operating conditions, offloading a similar proportion of tasks in both scenarios (Figure 4). However, since the two scenarios differ in their local processing resources, the Minimum scheme achieves a lower satisfaction ratio in the smart manufacturing scenario than in the connected mobility scenario. The Minimum scheme achieves a 100% satisfaction ratio in the connected mobility scenario for up to 45 tasks, while in the smart manufacturing scenario, it could not achieve 100% even with 35 tasks. The previous analysis considers scenarios where all tasks have the same priority. Figure 6 compares the satisfaction ratio of high-priority tasks as a function of the number of tasks (Figure 6(a)) and channel conditions (Figure 6(b)) in the connected mobility scenario with equally mixed high- and low-priority tasks. The figure shows that the Deterministic proposal can better guarantee deterministic service levels for high-priority tasks under constrained scenarios. In particular, it can satisfy the deadlines of all highpriority tasks, even when there is a high traffic load (i.e., 80 tasks in Figure 6(a)) and constrained communication conditions (SINR=15 dB in Figure 6(b)). On the other hand, trying to minimize the execution time of all tasks reduces the capacity to support deterministic service levels for high-priority tasks. For example, the Minimum scheme can only guarantee the execution of 45 high-priority tasks within their bounded deadlines under good communication conditions (SINR= 30 dB). This number reduces by more than 35% when the communication link degrades (SINR=15 dB). VII. CONCLUSIONS This study presents a Deterministic task offloading and resource allocation scheme for the joint management of communication and computing resources in the IoT–edge–cloud continuum. The proposed scheme prioritizes meeting task deadlines rather than minimizing individual task latency. By leveraging the heterogeneity of task latency requirements, it enables efficient workload distribution and supports a higher number of tasks within their deadlines. In contrast, schemes that aim to minimize THIS IS AN AUTHOR-CREATED POSTPRINT VERSION

the latency of each individual task may fail to efficiently exploit the resources of the IoT–edge–cloud continuum or may impose excessive loads on specific resources. The conducted evaluation demonstrates that a Deterministic scheme of task offloading, and resource allocation better adapts to variations in operating conditions, as well as to changes in resource availability and characteristics across the continuum. By dynamically adjusting the balance between local processing and offloading according to scenariospecific capabilities, the Deterministic scheme efficiently utilizes available resources across the continuum in diverse operational settings and can guarantee deterministic service levels for high-priority tasks, even under resource-constrained scenarios. REFERENCES [1] B. Mao, et al., “AI-assisted edge caching for metaverse of connected and automated vehicles: Proposal, challenges, and future perspectives,” IEEE Vehicular Technology Magazine, vol. 18, no. 4, pp. 66–74, 2023. [2] M. Serror, et al., “Challenges and opportunities in securing the industrial internet of things,” IEEE Transactions on Industrial Informatics, vol. 17, no. 5, pp. 2985–2996, 2021. [3] U. Mikko, et al. “European Vision for the 6G Network Ecosystem”, 6G-IA Vision Working Group’ White Paper, Nov. 2024. [4] G. P. Sharma et al., "Toward deterministic communications in 6G networks: state of the art, open challenges and the way forward," IEEE Access, vol. 11, pp. 106898–106923, 2023. [5] P. Gkonis et al., “A survey on IoT-edge-cloud continuum systems: Status, challenges, use cases, and open issues,” Future Internet, vol. 15, no. 12, p. 383, 2023. [6] W. Fan et al., “Joint task offloading and resource allocation for multi-access edge computing assisted by parked and moving vehicles,” IEEE Transactions on Vehicular Technology, vol. 71, no. 5, pp. 5314–5330, 2022. [7] W. Fan et al., “Joint task offloading and resource allocation for vehicular edge computing based on V2I and V2V modes,” IEEE Transactions on Intelligent Transportation Systems, vol. 24, no. 4, pp. 4277–4292, 2023. [8] W. Feng et al., “Latency minimization of reverse offloading in vehicular edge computing,” IEEE Transactions on Vehicular Technology, vol. 71, no. 5, pp. 5343–5357, 2022. [9] J. Cai et al., “Multitask multi objective deep reinforcement learning-based task offloading

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[22] J. Li et al., "ODTRA-Based Task Offload Optimization for Industrial Internet of Things: Improving Efficiency and Performance with Digital Twins," IEEE Access, vol. 12, pp. 5179651810, 2024. [23] Industrial Internet Consortium, "Industrial Internet Reference Architecture (IIRA)," v1.10, 2022, [Online]. [24] F. Zhang et al., “Secure data offloading and resource allocation against hybrid intrusions for IIoT: A fully decentralized framework,” IEEE Internet of Things Journal, vol. 12, no. 7, pp. 9218– 9237, Apr. 1, 2025. [25] Z. Kuang, et al., "SDN-Assisted Mobile Edge Computing for Collaborative Computation Offloading in Industrial Internet of Things," IEEE Internet of Things Journal, vol. 9, no. 14, pp. 12513-12526, July 2022. [26] Intel, "Case Study of Scaled-Up SKT 5G MEC Reference Architecture", White Paper, 2022. [27] Q. Li et al., “Cloud-edge collaboration for industrial internet of things: Scalable neurocomputing and rolling-horizon optimization,” IEEE Internet of Things Journal, vol. 12, pp. 19929 - 19943, June 2025.

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