 Research
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Nonorthogonal multiple accessbased MEC for energyefficient task offloading in ecommerce systems
Journal of Cloud Computing volumeÂ 13, ArticleÂ number:Â 117 (2024)
Abstract
Mobile edge computing (MEC) reduces the latency for end users to access applications deployed at the edge by offloading tasks to the edge. With the popularity of ecommerce and the expansion of business scale, server load continues to increase, and energy efficiency issues gradually become more prominent. Computation offloading has received widespread attention as a technology that effectively reduces server load. However, how to improve energy efficiency while ensuring computing requirements is an important challenge facing computation offloading. To solve this problem, using nonorthogonal multiple access (NOMA) to increase the efficiency of multiaccess wireless transmission, MEC supporting NOMA is investigated in the research. Computing resources will be divided into separate subcomputing that will be handled via ecommerce terminals or transferred to edge sides by reutilizing radio resources, we put forward a Group Switching Matching Algorithm Based on Resource Unit Allocation (GSMRUA) algorithm that is multidimensional. To this end, we first formulate this task allocation problem as a longterm stochastic optimization problem, which we then convert to three shortterm deterministic subprogramming problems using Lyapunov optimization, namely, radio resource allocation in a large timescale, computation resource allocating and splitting in a smalltime frame. Of the 3 shortterm deterministic subprogramming problems, the first subprogramming problem can be remodeled into a 1 to n matching problem, which can be solved using the blockshiftmatchingbased radio resource allocation method. The latter two subprogramming problems are then transformed into two continuous convex problems by relaxation and then solved easily. We then use simulations to prove that our GSMRUA algorithm is superior to the stateoftheart resource management algorithms in terms of energy consumption, efficiency and complexity for ecommerce scenarios.
Introduction
With mobile edge computing (MEC) and the explosive growth of mobile Internet industries, the majority of shoppers are increasingly turning to the Internet for their shopping needs as ecommerce gains traction. Furthermore, expert ecommerce services are offered for every facet of transactions, hence cutting down on transaction expenses. As a result, an increasing number of conventional offline businesses are aggressively transforming into online businesses. Around 32.7 trillion yuan worth of transactions took place in Chinaâ€™s ecommerce business in 2019. Even with ecommerceâ€™s enormous expansion perspective, there remain quite several important issues which have to be tackled. The difficulties associated with ecommerce are examined from three angles in this paper: system complexity, taskscheduling energy consumption, and data transmission energy consumption.

(1)
Server load challenges to energy efficiency : I. High load leads to surge in energy consumption: Ecommerce platforms usually need to handle a large number of user requests and data exchanges, especially during peak hours, when server load increases significantly. High load means that the server needs to invest more computing resources and power to maintain normal operation, resulting in a sharp increase in energy consumption. II. Inefficient energy utilization: During peak server load periods, due to unbalanced and unreasonable allocation of system resources, some servers may be overloaded while other servers are idle. In this case, energy utilization efficiency is low, resulting in unnecessary waste of energy.

(2)
Challenges to energy efficiency caused by mobile device resource constraints: I. Limited battery life: The battery life of mobile devices is one of the key factors limiting their energy efficiency. Ecommerce platform applications often require frequent interactions with the network, which can lead to rapid battery drain on mobile devices. In the case of limited battery life, users may not be able to use the ecommerce platform for a long time, thus affecting the user experience and the energy efficiency of the platform. II. Processing power and memory limitations: Mobile devices have relatively limited processing power and memory and cannot compare to servers. This results in mobile devices potentially experiencing delays when processing complex tasks or large amounts of data. To cope with this situation, ecommerce platforms may need to optimize their applications to reduce resource consumption, but this often affects the functionality and performance of the application.
To address these issues, this study presents mobile edge computing (MEC) to facilitate MECbased ecommerce, where users can offload their tasks to neighboring edge servers [1,2,3,4]. Nevertheless, computing offloading in MEC systems is complicated and influenced by several variables [5, 6].
There are a few important factors to take into account when selecting an edge server for ecommerce: 1. Performance and processing capabilities: In order to handle the large amounts of data that ecommerce websites process, the high volume of concurrent access, and the demands of realtime trading, edge servers must be sufficiently performant and process capable. 2. Low latency and high availability: Because ecommerce websites must meet very strict realtime performance and availability standards, edge servers must have both of these qualities.
Regarding task scheduling, the MEC system needs to optimize task allocation to ensure that tasks are assigned to the most appropriate edge computing nodes for processing. This requires consideration of multiple factors such as node computing power, storage resources, network bandwidth, and task characteristics. Therefore, it is necessary to design an efficient task scheduling algorithm and formulate an optimal task allocation plan by analyzing the matching relationship between tasks and resources to achieve optimal utilization.
As the number of users in ecommerce scenarios increases, the resource collision problem becomes more and more serious. Nonorthogonal multiple access (NOMA) technology introduces interference information to achieve simultaneous transmission on the same frequency [7, 8], and uses serial interference removal technology for signal demodulation and interference elimination, effectively solving the resource collision problem caused by the increase in the number of users. However, there are still some challenging issues to be resolved. First, NOMA technology enables the simultaneous use of the same frequency and temporal resources by several users. This increases spectrum efficiency in ecommerce applications by enabling several users to transmit and interact with data simultaneously. This lessens the problems with resource conflicts brought on by an increase in user numbers. Secondly, NOMA technology achieves separation and correct demodulation of multiuser signals through power multiplexing and serial interference cancellation (SIC) technology. In ecommerce scenarios, when the number of users is large and resources are limited, interference may occur between signals, leading to resource conflicts. However, through the power multiplexing and SIC technology of NOMA technology, the signals of different users can be distinguished at the receiving end and multiaccess interference is eliminated, thereby ensuring that each user can obtain stable communication quality.
The joint optimization of multidimensional resources in ecommerce based on NOMA mobile edge computing (NOMAMEC) has attracted more and more research attempts. In the literature [9], Kiani et al proposed a computing resource offloading scheme that can implement user clustering based on NOMA and has the feature of low energy consumption. In the literature [10], the authors proposed the NOMAbased edge computing offloading problem and brought up a heuristic algorithm to reduce the energy required for computation by jointly optimizing power and time. However these initiatives only take shortterm objectives into account, and efficiency degradation is expected when applying them to problems that require longterm optimizing.
Inspired by findings from the previously mentioned research, the article puts forward a method for multitimescale multidimensional resource allocation for NOMAMEC for ecommerce platforms. The paper aims to optimize resource unit allocation and task decomposition simultaneously to minimize continuous utilization of all ecommerce platform devices depending on longterm queue delay restrictions. As a result, this work first divides the longterm stochastic joint optimization challenge into three shortterm deterministic tasks (i.e., task computation, task partitioning, and wireless spectrum allocation) applying the Lyapunov method [11].
Ecommerce devices and resource units are particularly grouped by employing clusteringbased methods to reduce complexity. The allocation of wireless spectrum is characterized as a largescale, onetomany matching process that is dealt with at the base station (BS) level. Resource unit allocation should be implemented via group swap matching. Switching and matching occur inside each group after the devices and resource units for the ecommerce platform have been separated into multiple groups. Subsequently, tasks are divided, and computer resources are distributed and assigned in shorter time intervals on the device side. The contributions of the work are as follows:

(1)
Optimization decomposition of multidimensional problems: Three feasible deterministic problems are derived from the longterm stochastic multidimensional optimization task employing Lyapunov optimization.

(2)
Group switch matching for resource allocation: The group swap matchingbased resource allocation techniques offers a practical, straightforward, and flexible solution to the interdependency problem between various resources and ecommerce terminals.
The organization structure of this paper is as follows: IntroductionÂ section is an introduction, Related workÂ section is related work, System modelÂ section is the system model, Problem description and analysisÂ section is problem description and analysis, task division and resource allocation are in Partitioning tasks and allocating resourcesÂ section, and analysis of experimental results is in Simulation resultsÂ section, ConclusionÂ section is the conclusion, Funding is the acknowledgments.
Related work
MEC provides cloud and ITrelated services at the radio access network (RAN) near mobile users (MUs). [12, 13]. To supply contextually aware services and services that offer distinctive mobile browsing experiences, app designers and content vendors can leverage the RAN edge, which offers an ultralow latency and highbandwidth service setting. Additionally, applications have instant access to realtime wireless data from the network (such as locationbased data, cell loads, etc.). By enabling resource organization [14, 15] and service architecture [16], MEC enhances edge response by accelerating content, services, and apps. Thus, by running networks and services more efficiently, the user experience can be enhanced.
Edge computing is gaining popularity as a complement to, and expansion of cloud computing [17]. By adopting a distributed computing strategy, edge computing eliminates the need for devices to upload data to cloud servers and server power consumption, and enhances security, and latency. Usersâ€™ computing duties are divided across several servers located throughout the network [18]. This method tries to solve the problem of network congestion and significant transmission delay brought on by cloud computingâ€™s centralized computation. Additionally, the realtime performance of the data calculating process is further ensured by the edge serverâ€™s ability to respond to the userâ€™s request and task in a shorter amount of time [19]. At order to reduce the large data transmission delay experienced during longdistance communication, the server is placed in a network edge node that is closer to the device.
The following studies include the use of edge computing in a consumer IoT environment. To achieve the optimal distribution of widely distributed green and energysaving computer resources, time and energy costs are optimized in the literature [20]. The offloading issue of multihop computing jobs in a hybrid edge cloud computing environment is researched in the literature [21], and the offloading technique that satisfies the service quality requirements is accomplished through the game method. A hybrid computing structure with intelligent resource planning is suggested in the literature [17] to meet realtime needs. In conclusion, edge computing, which is installed near ecommerce devices at the networkâ€™s edge, offers suitable computing resources for these devices, which can lower system expenses and satisfy task service quality requirements in a range of situations.
In short, the resource limitations of mobile devices such as processor performance, memory size, and battery capacity prompt ecommerce application developers to pay more attention to resource optimization. By optimizing strategies, reducing unnecessary resource consumption and improving resource efficiency, developers can provide users with a smoother and more responsive application experience, thereby improving user satisfaction.
System model
The basic idea of NOMA is to allocate nonorthogonal communication resources to different users at the transmitting end. In the orthogonal scheme, if a piece of resource is evenly allocated to N users, then subject to the constraints of orthogonality, each user can only be allocated \(\frac{1}{N}\) resources. NOMA gets rid of the limitation of orthogonality, so the resources allocated to each user can be greater than \(\frac{1}{N}\). In the extreme case, each user can be allocated to all resources to realize resource sharing among multiple users. The conventional NOMA technology is based on the condition that the userâ€™s CSI is known and correct when conducting theoretical analysis. This work is carried out based on the above conditions.
Consider concerning the NOMA and MEC combined ecommerce platform situation shown in Fig.Â 1, which consists of N access points (APs) and a base station (BS). Singleantenna architecture has been widely adopted in various MEC networks. However, the optimization scenarios proposes in the work can be extended to scenarios involving multiple antenna ensembles. The wireless channel connects each AP in the system to the base station, which is regarded as the user m of the AP. It provides a set of singleantenna services and provides wireless access and computing services to \(\mathcal {M}\) ecommerce terminal devices. The system model is represented by M nodes: \(\mathcal {M}=\left\{ 1,2,...,m,...M ...\right\}\). The terminal tasks under the ecommerce platform are either partially offloaded or offloaded to a nearby BS for processing.
In contrast to [22], this work considers a discrete time slot structure in which the optimization method is divided into \(\mathcal {K}\) time slots, with a \(\kappa\) duration for each time slot. The formula \(\mathcal {K}=\left\{ 1,...,k,...,K\right\}\) indicates a sequence of time slots. Investigate a case that is nearly static, in which the CSI changes from slot to slot but doesnâ€™t change within a slot. \(t\in T, t=\left\{ 1,...,T\right\}\) denotes a time epoch that is associated with each successive \(K^{\prime }\) slot.
The expression \(\mathcal {K}(t)=\left\{ (t1)K^{\prime }+1,...,tK^{\prime },tK^{\prime }+1,...(t+1)T^{\prime }\right\}\) specifies the tth time epoch. \(\mathcal {P}=\left\{ 1,...,p,...,P\right\}\) is the collection of the resources, which are split into P timefrequency resource components, B bandwidth, and \(K^{\prime }\) time period. Challenges of splitting and multidimensional resource distribution are examined. On the primary time scale, the unlimited resource allocation strategy is optimized at the start of every time period. The binary indicator \(\varvec{I(t)}=\left\{ I_{m}^{p}(t), m\in \mathcal {M}, p\in \mathcal { P}\right\}\), where \(I_{m}^{p}(t)=1\), reflects the resource allocation strategy. In the tth time interval, \(I_{m}^{p}(t)=1\) indicates that resource unit p is assigned to device m; else, \(I_{m} ^{p}(t)=0\). Subsequently, combined optimization computation of resource allocation and splitting is carried out on a small time scale, depending on the resource unitâ€™s allocation technique used for each time slot.
First, the time epoch provides a globally consistent time base so that various parts of the system can be synchronized more accurately. This is especially important for realtime processing systems that require a high degree of coordination. Second, in systems that require dynamic allocation of resources, time epochs can help manage resources more efficiently.
A. Traffic model on the device A task splitting approach is used in the paper [23] that permits the division of each task into independent subtasks of size \(X_{0}\) (bits). W orthogonal channels are shared by W users who are active without any cochannel interruption. It is assumed that during the kth time slot, the \(a_{m}^{max}(t)\) subtask reaches device m. The division of arriving tasks into two distinct and parallel types can be done: for local operations, \(a_{m}(k)\) subtasks and for task offloading, \(a_{m}^{max}(k)a_{m}(k)\) subtasks. Taking everything into consideration, the task to be split at device m during time slot k is specified as
where \(X_{m}^{L}(k)\) denotes the length of the task that device m is currently processing locally. The task length when device m performs compute offloading at time k is denoted by \(X_{m}^{O}(k)\). The local processing and resource offloading are executed using \(Q_{m}^{L}(k)\) and \(Q_{m}^{O}(k)\), respectively. \(Q_{m}^{L}(k)\) and \(Q_{m}^{O}(k)\) [24] vary as you can observe in Fig.Â 1.
where \(d_{M}^{L}(k)\) and \(d_{M}^{O}(k)\) respectively indicate the volume of data departure \(Q_{m}^{L}(k)\) and \(Q_{m}^{O}(k)\).
B. Locally task data processing scheme The kth time slotâ€™s local processing amount of data is specified as
where the number of CPU cycles assigned to device M within the kth time slot is denoted by \(f_{m}(k)\). \(l_{m}\) stands for the amount of processing, or the number of CPU cycles needed for each bit. The local operating computing delay and associated energy consumption produced by the device m in the kth time slot are specified as
where the chip structure regulates a constant power coefficient named \(\tau _{m}\).
C. Computing offload processing method interference cancellation (SIC). The BS correctly sequences the decoding of signals from devices which have greater channel gains, but all other communications are regarded as interference. \(h_{m}^{p}(k)\) is the uplink channel gain connecting device m to resource unit p within the kth time slot. The following is the signaltonoise ratio (SNR) data that the BS acquired:
The power of transmission is g. The first component of the denominator is the additive white Gaussian noise power, yet the second item is intracell interference from other lower channel gain devices.
Note: First, the base station decodes the signal strategy, that is, the base station decodes the signal in order of channel gain. This is an optimization strategy designed to improve decoding efficiency and accuracy, especially in the presence of multiple signals with interference between them. Second, it was mentioned that users seem to treat all signals in Eq.Â 7 as interference. This reflects the way users actually handle signal processing, that is, users may not adopt a decoding strategy like the base station, but instead treat all signals as potential interference.
Consequently, the following formulas are used to compute the data amount of the task that can be offloaded in the kth time slot and the device mâ€™s transmission speed applying the resource unit p.
First, in edge computing networks, resources are limited, and by arranging users in descending order, the system can more easily identify and handle those users that have the greatest impact on performance. This descending order helps ensure resources are allocated to users who need them most, optimizing overall network performance. Secondly, by giving better services to users with higher priority (such as higher data transmission rates, lower delays, etc.), the service quality of these users can be improved.
All mobile user devices are arranged in decreasing order in accordance with the \(\varepsilon _{i}^{p_{*}}_{\sigma (p_{i})=m_{s}}\), \(\forall m_{s}\in \mathcal {M}\) criterion to produce the preference set \(\xi (p_{i})=\left\{ ..., m_{s}, m_{p},...\right\}\). When all B2B pairs are available, they are sorted according to \(\varepsilon _{s}^{m_{*}}_{\sigma (m_{s})=p_{i}}\) to produce \(\xi (m_{s})\), which stands for the preference profile of \(m_{s}\). Create \(\Xi =\left\{ \xi (p_{1}),...\xi (p_{m}),\xi (m_{1}),...,\xi (m_{S})\right\}\) to represent the entire set of preferences.
Here, arranging \(\varepsilon _{s}^{m_{*}}\) in descending order means that the services with the highest matching degree are placed first, so that those services with the highest matching degree can be prioritized to improve user experience. Generating a preference set \(p_{i}\) means that it is convenient for users to make decisions, so that they can find services that meet their needs more quickly and reduce selection costs.
The following indicates the corresponding energy consumption that device m produced during the kth time slot:
The composition of the modeling given above is the construction of traffic on the device, local task processing and task offloading scheme, and various mathematical symbols and formulas to be used are also given.
Problem description and analysis
First, queuing delay restrictions are introduced in this section. This is followed by the idea put forward of the multidimensional resource allocation and task splitting optimization problem.
A. Queued delay constraint To guarantee the efficiency and promptness of task offloading, manage queuing delay restrictions. According to Littleâ€™s law [25], the following formula is used to determine the queuing delays of \(Q_{m}^{L}(k)\) and \(Q_{m}^{O}(k)\).
where \(MA_{m}^{L}(k)\) and \(MA_{m}^{O}(k)\) are the average data arrival rate of moving time of \(Q_{m}^{L}(k)\) and \(Q_{m}^{O}(k)\), respectively. \(D_{m,max}^{L}\) and \(D_{m,max}^{O}\) are their respective maximum tolerable queuing delays.
B. Problem definition The aim is to minimize the total accumulated longterm energy consumption of all devices, according to queue latency restrictions, by centrally optimizing resource unit allocation, partitioning, and computing task scheduling.
The resource group allocation vector is denoted by \(\varvec{I=\left\{ I(t)\right\} }, t\in \mathcal {T}\), the wireless dividing of resources vector is expressed by \(\varvec{a=\left\{ a(k ) \right\} }, k\in \mathcal {K}\). The vector for assigning computing resources is indicated by \(\varvec{a(k)}=\left\{ a_{m}(k), m\in \mathcal {M }\right\}\), and \(\varvec{f}=\left\{ \varvec{f(k)}=f_{m}(k),m \in \mathcal {M}, k\in \mathcal { K}\right\}\). The restriction on resource dividing is \(C_{1}\). \(C_{2}\) is an expression of the deviceâ€™s computing resource allocations constraint. Each device is allowed to utilize a maximum of one resource entity, denoted by \(C_{3}C_{5}\). At most \(M_{p}\) devices can acquire the resource group p. The resource groups assigned to device m must be achieved by \(C_{6}\) to guarantee that the SNR acquired at the BS exceeds the minimal allowed \(SNR_{m}\). \(C_{7}\) ensures that \(m_{s}\)â€™s power allocation does not go beyond the maximum permitted transmission power \(max (g_{s}^{m})\), \(C_{8}\) ensures that \(p_{i}\)â€™s power allocation does not go beyond the maximum permitted transmission power \(max (g_{i}^{p})\).
C. Transformation of the problem It is challenging to find a direct solution for P1, a nondeterministic polynomial (NP) hard situation.
Lyapunov optimization is usually applied to dynamic systems such as resource allocation problems and scheduling problems with stability and performance optimization requirements. It can be used to solve practical problems such as how to maximize network throughput, minimize user average delay, and minimize total network power consumption. Since the Lyapunov function can effectively handle system uncertainty, it can show good robustness to a certain extent.
In the model, multiple shortterm determinate subproblems are derived from the original longterm stochastic optimization problemsolving through the application of Lyapunov optimization [26, 27]. The queue stability restriction condition of the virtual queue theory can be determined by Eqs. (11) and (12). \(\Delta _{m}^{L}(k)\) and \(\Delta _{m}^{O}(k)\) are matching virtual queues that can be transformed into
Formula (11) and (12) are inevitably preserved once the average rates of \(\Delta _{m}^{L}(k)\) and \(\Delta _{m}^{O}(k)\) remain stable. Accordingly, problem \(P_{1}\) will be converted into
s.t. \(C_{1}\)  \(C_{8}\)
We may deduce that P2 will be split up into three subtasks of optimization: SP1, which is the subproblem of resource group allocation; SP2, which is the subproblem of task splitting; and SP3, which is the subproblem of computing the allocation of resources.
Partitioning tasks and allocating resources
This section provides an overview of the claimed schemes before introducing the three deconstructed subschemes and the corresponding reactions.
A. Resource unit allocation optimization Device m along with BS decide a resource group allocation technique at the start with every interval in SP1. Since the values of \(h_{m}^{p}(k)\), \(Q_{m}^{O}(k)\), and \(R_{m}^{p}(k)\) differ over the time slot, their experience \(\overline{h_{m}^{p}(k)}\) is the mean value.There are two considerations: \(\overline{Q_{m}^{O}(k)}\) and \(\overline{R_{m}^{p } (k)}\). Consequently, SP1 will refer to:
s.t. \(C_{3}\)  \(C_{8}\)
The typical approach for SP1 is a onetomany matching between devices and resource groups. The following is the performance of the onetomany matching algorithm \(\eta\) that we symbolizes here:
The restrictions \(C_{4}\) and \(C_{5}\) are discussed in the scenarios (1) and (2) above, whereas the third situation demonstrates that resource unit p is allocated to device m and vice versa if device p and resource unit p match. Specifically, there is a close relationship between \(\upsilon\) and the resource unit allocation rating \(I_{m}^{p}(t)\).
The following are the utility functions for device m and resource unit p:
It is not feasible to match every device and resource unit as a result of the high matching complexity of a largescale ecommerce network. Consequently, we start by grouping the resource units and devices into collections. Devices and resource groups are specifically classified into Y sets, i.e., \(\mathcal {M}=\left\{ \mathcal{M}\mathcal{G}_{1},..., \mathcal{M}\mathcal{G}_{y},.., \mathcal{M}\mathcal{G}_{Y}\right\}\), in accordance with the clustering technique [28].The expressions \(\mathcal {P}=\left\{ \mathcal{P}\mathcal{G}_{1}\right\}\) and \(\mathcal{P}\mathcal{G}_{y}\). Devices and resource groups (\(M_{g}=M/y\) and \(P_{g}=P/y\), respectively) are available to each group. Regulated resource units, \({PG}_{Y}\), are resources that are commonly assigned to \({MG}_{Y}\) for offloading by devices inside each union. After then, switch matching is carried out in a semidistributed fashion in each group in order to prioritize devices and resource units based on their utility, ranking them from high to low. By group switching and matching at the two points, the resource unit allocation constraint is thereby resolved.
Definition 1
Matching \(\upsilon\) and two device resource group pairings \((m,p), (v,l)\in \upsilon\) are defined as follows: \(\upsilon (p)=m\) and \(\upsilon (v)= l\), \(\forall m\ne v\) and \(m,v\in \mathcal{M}\mathcal{G}_{s}\), \(\forall p\ne l\) and \(p,l \in \mathcal{P}\mathcal{G}_ { s}\), if they satisfy
The equation \(\upsilon _{mv}^{pl}=\left\{ \upsilon \setminus (m,p), (v,l))\right\} \cup \left\{ (m,l), (v, p)\right\}\) illustrates the method of exchanging variables \(\upsilon\) and \(\upsilon _{mv}^{pl}\succ \upsilon\).
Definition 2
The matched \(\upsilon\) is bilaterally interchangestable if there isnâ€™t a swap match.
The details of the group swap matchingbased resource unit allocation technique are compiled in Algorithm 1. Devices and resource groups are assigned to Y unions during initialization, and each device unity is given a collection of resource units, denoted as \(\mathcal{M}\mathcal{G}_{y}\leftarrow \mathcal{P}\mathcal{G}_{y}\). Next, the allocation groupâ€™s devices and resource groups will be paired at arbitrary, provided that all of the conditions in Eq. (15) are satisfied. Formula (20) determines the preferences generated by every device and resource group.
When transfer matching occurs, the program moves to its preferred position in \(PG_{y}\) , the resource group l for every device m in \(MG_{y}\) that presently matches resource group p in \(PG_{y}\). The new matching \(\upsilon _{mv}^{pl}\) replaces the old matching \(\upsilon\) for each current device v in \(MG_{y}\) that matches l in \(PG_{y}\) if and only if \(\upsilon _{mv}^{pl}\succ \upsilon\) and satisfies (15). In every other scenario, \(\upsilon\) keeps the same. Till no matches are swapped, the process will terminate.
To determine the resource unit allocation indicator \(I^{*}(t)\), the ultimate \(\upsilon\) is transformed into it using formula (19).
B. Task splitting and resource allocation optimization The following factors are crucial for the joint optimization of task splitting and computing resource allocation in the context of ecommerce: (1) High task calculation volume, high data processing volume, and high complexity tasks necessitate more splitting and refinement; (2) For tasks requiring quick response, splitting should guarantee that each subtask can be finished in a shorter amount of time.
The following is the formulation of the task splitting challenge. The task splitting decisionmaking between local operations and offloading is assigned by SP2 in the kth time slot.
s.t. Â Â Â \(C_{1}\)
The amount of CPU cycle frequencies that each device assigns for local processing in the kth time slot is managed by the computing allocation of resources subscheme SP3, and this quantity is determined by the following procedure.
s.t. Â Â Â \(C_{2}\)
Lagrangian dual decomposition provides an easy way to address convex optimization challenges such as SP2 and SP3.
According to the above conditions, the original constrained problem is transformed into an unconstrained problem through the Lagrangian function. If the original problem is difficult to solve, the dual problem is used to replace the original problem under the condition of satisfying KKT, which makes the problem solving easier.
This study introduces a onetoone matching model to address problem \(P_{1}\). This model matches users in accordance with their shared preferences and blocktoblock pairs (B2B). This allows the original NPhard problem to be split into two distinct subproblems and addressed in a straightforward manner. In this study, the created matching problem is represented by the triplets \((\mathcal {N}, \mathcal {M}, \mathcal {P})\), where \(\mathcal {P}\) is the collection of shared preferences and \(\mathcal {M}\) and \(\mathcal {N}\) are two finite and distinct sets of B2B couples and users, respectively. In order to improve energy efficiency, both B2B pairs and individual devices work to establish an appropriate channel reuse cooperative relationship within the confines of QoS and transmit power.
Definition 3
In the case of a match \((\mathcal {N}, \mathcal {M}, \mathcal {P})\), \(\sigma\) is represented as a pointwise mapping from \((\mathcal {N}, \mathcal {M}, \mathcal {P})\) to itself. In other words, \(\forall n_{k}\in \mathcal {N}\) and \(\forall m_{i}\in \mathcal {M}\), \(\sigma (n_{k})\in \mathcal {M}\cup \left\{ n_{k}\right\}\) and \(\sigma (m_{i})\in \mathcal {N}\cup \left\{ m_{i}\right\}\). \(\sigma (n_{k})=m_{i}\) iff \(\sigma (m_{i})=n_{k}\).
In the case of \(\sigma (m_{i})=m_{i}\) or \(\sigma (n_{k})=n_{k}\), then \(m_{i}\) or \(n_{k}\) maintains a single value. According to their preferences, either \(m_{i}\) or \(n_{k}\) can send a request to create a partnership with their selected partner and then show how the assigned transmission power for the resulting partnership (i.e., the power allocation subproblem) works. Both \(m_{i}\) and \(n_{k}\) make the assumption that they are just interested in their own pairings and are not very interested in the pairings of others.
The resource allocation technology based on group switch matching algorithm has good scalability in ecommerce scenarios, specifically: First, the resource allocation technology of group switch matching achieves flexible allocation of resources by dividing resources into different groups and matching and switching between these groups. This technology can adapt to the increase in the number of users by increasing the number of groups or adjusting the size of the groups. At the same time, as the number of computing tasks increases, this technology can ensure efficient resource utilization and delayed response by optimizing the matching algorithm and exchange mechanism.
C. Stable and energyefficient matching In order to match B2B pairs and user equipments, the study proposed Algorithm 2, which employs the GS method after obtaining \(P(m_{i})\) and \(P(n_{k})\), \(\forall m_{i}\in \mathcal {M}\), \(\forall n_{k}\in \mathcal {N}\) [29, 30]. In the initial iteration, each \(m_{i}\in \mathcal {M}\) sends a collaboration request to its most preferred user equipment \(max \left\{ \varepsilon _{i}^{m_{*}}_{\sigma (m_{i})=n_{k}, \forall n_{k}\in \mathcal {N}}\right\}\). The request is then received by each \(n_{k}\in \mathcal {N}\), which, if it has a superior candidate, rejects the B2B pair. If \(m_{i}\in \mathcal {M}\) accepted as a candidate at this point has not been rejected by the user. The user with the highest priority in the set of users who have not yet issued a refusal receives a fresh request from \(\forall m_{i}\in \mathcal {M}\) that has been refused in the following phase. When a B2B pair receives rejections from all of its preferred users, it gives up and stops sending requests. Only the most favored B2B pair is accepted for \(\forall n_{k}\in \mathcal {N}\) after all incoming requests, including candidate requests kept from earlier steps, have been compared. When \(\forall m_{i}\in \mathcal {M}\) has found a mate or has had all of its requests denied by users, the request sending and rejection procedure comes to a conclusion. The best candidate preserved at any step may subsequently be eliminated if a better candidate appears, which is a feature of Algorithm 2.
D. Our proposed algorithm The three steps in the put forward algorithm are as follows:

First: Define all resource unit allocation rules and queue backlog indicators to zero.

Second: In accordance with Algorithm 1, each device partially distributes the optimal resource group allocation \(\varvec{I^{*}(t)}\) and employs the amount of resource unit that has been assigned to transmit data.

Third: Every device gathers up the best techniques for allocating tasks and resources. Power consumption, queue overflow, queue latency, and updates for \(Q_{m}^{L}(k+1), Q_{m}^{O}(k+1), VQ_{m}^{L}(k+1)\), and \(VQ_{m}^{O}(k+1)\) will all be taken into consideration for each device. These factors will then be taken into account using the formulas (2), (3), (13) and (14) . The iteration continues between the second and third phase until \(k>K\).
The optimization decomposition approach may break down the complicated energy consumption problem into a number of smaller issues, allowing it to optimize each smaller issue in terms of energy consumption. In addition, the network topology is optimized. For example, edge computing technology is used to integrate the data centers of various ecommerce platforms, therefore reducing the quantity and distance of data transmission, which can also efficiently cut energy consumption.
Therefore, the optimization decomposition method significantly lowers energy usage and raises the caliber of services provided by ecommerce platforms. It makes it possible to optimize and enhance the platform more precisely, which lowers energy consumption and raises service quality, by breaking down complicated difficulties into a number of smaller problems.
Simulation results
The following part assesses the proposed method using simulations. The investigation looked at a single cell that has a radius of 2000 US dollars millimetres. 20 devices make up each of the 100 groups; this division of resource units and devices is consistent.Specific simulation parameters are listed in TableÂ 1.
We contrast two cuttingedge algorithms. The first is the resource unit allocation algorithm (SMRA) inspired by switch matching that was put forth by [16], which the basic idea is to study the energy efficiency of an uplink hybrid system integrating NOMA into OMA (HMA) to support a large number of ecommerce devices. It is significant to notice that SMRA energy efficiency maximization is replaced in the scenarios with energy consumption minimization. The creation of the Access Control and Resource Allocation Algorithm (ACRA) is the cause of the second. ACRA relies on pricing matching and Lyapunov optimization, and in order to determine the optimal decision, it needs a perfect GSI. In this case, still it presumes that only the CSI of the prior slot is available, meaning that the CSI contains outofdate information. The local computer resources are configured to the largest value possible between SMRA and ACRA, and the task partitioning step is assigned arbitrarily.
Discuss the computational complexity of the work. For the initial stage, \(O(n^{2}M)\) operations are required. In the exchangematching stage, it means that the number of iterations to reach the final match is \(I_{1}\). In each iteration, all possible exchange combinations should be considered, which requires \(O(n^{2})\) operations. Indicates that the computational complexity of devices for computing energy efficiency is O(x), and then, the total complexity of the swapmatching stage is \(O(I_{1}n^{2}X)\).
In order to achieve the minimal energy consumption and minimum delay requirements, the GSMRUA algorithm in this article is designed with the following measurement parameters in mind: (i) average handover delay (i.e., the average time of all successful handovers). (ii) The total energy used during the simulation process as well as the average energy used during the switching procedure.
The average energy consumption of edge devices as an index of time slots is illustrated in Fig.Â 2. Both SMRA and ACRA have a task splitting percentage of 0.85, meaning that \(85\%\) of the jobs are handled locally. GSMRUA performs significantly better than SMRA and ACRA when \(t = 80\). Because it simultaneously optimizes resource allocation and deviceside task splitting, GSMRUA runs at its best and contributes significantly to the reduction of energy consumption in local computing.
The average queue backlogs for \(Q_{n}^{L}\) and \(Q_{n}^{O}\) with time slots shown in Figs.Â 3 and 4, respectively. Since SMRA only takes energy consumption optimization into account and is unable to address highdimensional optimization that involves large state and action space challenges, it performs poorly when it comes to task offloading, offloading fewer tasks from \(Q_{n}^{O}\) to the server than GSMRUA and ACRA. As consequently, SMRA has a larger average backlog of \(Q_{n}^{O}\). Offloading more subtasks from devices to edge servers can reduce queue backlog owing to the queueagnostic and stable computing resource allocation methodology.
The average queuing delay of \(Q_{n}^{L}\) and \(Q_{n}^{O}\) with time slots, respectively, are displayed in Fig.Â 5 and 6. According to the simulation results, \(Q_{n}^{L}\) and \(Q_{n}^{O}\) queuing delays are significantly reduced by GSMRUA when compared to ACRA. Due to the acquisition of queue awareness and combined optimization of resource allocation and task offloading, GSMRUA performs better when it comes to queuing delays.
In Fig.Â 7, for \(Y=10\) users and \(P=10\) B2B pairings, the average effective energy consumption performance is shown against the maximum B2B transmission distance \(d_{max}\). The suggested approach achieves the best effective performance across the entire region, according to simulation findings. Concerning the random power allocation method and the power greedy algorithm, the suggested approach outperforms both by \(135\%\) and \(208\%\), respectively, when \(d_{max}=30\)m. The reason why random assignment performs second best is because it has a larger likelihood of consuming more energy than powerhungry algorithms, which always make the best use of any available power. The gain of the SE algorithm brought about by raising transmit power is insufficient to offset the accompanying effective energy loss. There are two reasons why the powergreedy algorithm performs the least efficiently in terms of energy use among the three. First, when allocating resources, electricity use is completely disregarded. Furthermore, in an environment with little interference, boosting transmit power beyond the node where the SE algorithm performs best results in neither an enhancement of the SE algorithm nor a notable reduction in effective energy usage. It is important to note that when B2B transmission distance increases, all algorithmsâ€™ effective energy performance declines since more transmission power is needed to keep the QoS performance at the same level as in the shortdistance situation.
When \(d_{max}=30\)m, Fig.Â 8 illustrates the relationship between the average effective energy consumption performance of B2B pairs and the number Y of active users and the number P of B2B pairs. The number of user and B2B pair activations grows linearly in relation to the average effective energy performance of all algorithms. The explanation is that as the number of users grows, there are more orthogonal channels overall and each B2B pair has more options than the original B2B pair in the expanded matching market. There is a higher chance that B2B pairs will be matched with superior relationships in the wider matching market. In comparison to the heuristic algorithm, the proposed method has the highest slope, indicating that it may gain more from a variety of options. The powergreedy algorithm has the smoothest slope since the benefits of selection variety are not completely utilized and power consumption is not taken into account when allocating resources.
Discussion
The impact of the research results on the current stateoftheart resource management algorithms and their applicability in reallife ecommerce scenarios can be analyzed from the following aspects:

(1)
First of all, the impact of the research results on the current most advanced resource management algorithms is mainly reflected in algorithm design and optimization. The innovation of the GSMRUA algorithm in resource unit allocation and group switching matching may inspire other researchers to improve existing resource management algorithms or propose new algorithms.

(2)
Secondly, ecommerce scenarios usually face challenges such as high concurrency, low latency, and dynamic changes in resources. The GSMRUA algorithm helps ecommerce platforms improve system throughput and reduce latency by optimizing resource allocation and handover matching, thereby improving user experience and platform performance. Then it may be widely used in ecommerce scenarios.
Conclusion
NOMA technology further increases spectral efficiency by enabling multiple users to perform nonorthogonal transmission on the same time and frequency resources. Edge computing and the combination of NOMA technology can intelligently select offloading strategies based on task characteristics and requirements. Edge computing already gives ecommerce platforms powerful computing capabilities and lowlatency services.
This work investigates the joint optimization of resource units, largeconnection computing resources, and task splitting on ecommerce platforms using NOMA. Based on energy consumption and queue backlogs, our suggested technique is intended to dynamically optimize multidimensional resource allocation to reduce energy consumption. To maximize the achievable effective energy usage under the highest transmit power, the cooperation problem is constructed while taking the userâ€™s preferences into account. The ideal energy usage for a certain match is modeled as its userâ€™s choice. The experimental results demonstrate that our proposed algorithm effectively achieves the tradeoff between complexity and network capability, outperforming the current SMRA and ACRA in the \(Q_{m}^{L}\) queue backlog and in the \(Q_{m}^{O}\) queue backlog, respectively, A fresh thought for the research topic of allocating resources for B2B communication is also offered by the matching approach. Future research will investigate how to organize devices in ecommerce more effectively. Additionally, it incorporates the expansion of onetomany matching, user preference modeling from a big data standpoint, and content caching with context awareness.
Availability of data and materials
No datasets were generated or analysed during the current study.
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Funding
This Research is funded by Researchers Supporting Project Number (RSPD2024R947), King Saud University, Riyadh, Saudi Arabia.
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Xiao Zheng and Muhammad Tahir: Writingoriginal draft, conceptualization, methodology, data curation, visualization, writingreview, and editing. Khursheed Aurangzeb: supervision, resources, project administration, validation, writing, review, and editing. Muhammad Shahid Anwar: Resources, Formal Analysis, WritingReview and Editing, Resources. Muhammad Aamir: supervision, project administration, writing, review, and editing. Ahmad Farzan: Resources, Validation, Writing, Review, and Editing. Rizwan Ullah: formal analysis, supervision, writingreview and editing, Project administration.
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Zheng, X., Tahir, M., Aurangzeb, K. et al. Nonorthogonal multiple accessbased MEC for energyefficient task offloading in ecommerce systems. J Cloud Comp 13, 117 (2024). https://doi.org/10.1186/s13677024006802
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DOI: https://doi.org/10.1186/s13677024006802