Service Pricing and Selection for IoT Applications Offloading in the Multi-Mobile Edge Computing Systems

With the rapid developing of Internet of Things (IoT) technologies, various kinds of IoT devices are connected over the Internet. Consequently, how to meet the requirements of executing IoT applications is becoming a critical issue. Offloading the IoT applications to the public cloud is an efficient approach to enhance the computing capabilities of these IoT devices. However, as there is a long distance from the IoT devices to the remote public cloud, transmission delay will be caused. Mobile edge computing (MEC) provides an effective solution to this issue since IoT devices are near to the servers of the MEC systems. Pricing and load balancing are two important factors for cloud service provision. Pricing is of paramount importance for cloud service provision, and load balancing is fully considered when cloud users select an edge cloud service provider (ESP) as it has a direct relation with the quality of cloud service. In multi-cloud systems, a cloud service broker (CSB) reserves cloud resources from multiple CSPs to provision cloud services to users. While existing work has put a lot of attention on IoT applications offloading to the MEC, many of them only considered one edge cloud scenario, ignoring the multi-MEC scenario. In this article, we investigate service pricing and selection for IoT applications offloading in a multi-MEC system with multiple ESPs. Specifically, we take load balancing into account. The studied problem is formulated as a Stackelberg game, where CSB first sets service price and load balancing strategies for the cloud services trying to get its maximized revenue. Then, IoT users make their decisions on which ESP they select service. By applying the backward induction approach, the optimal solutions are derived. The proposed scheme is verified through simulation results.


I. INTRODUCTION
In recent years, the Internet of Things (IoT) has received a significant amount of attention in the academic and industrial The associate editor coordinating the review of this manuscript and approving it for publication was Takuro Sato.
fields [1]. With the technologies of IoT rapidly growing, various kinds of IoT devices, such as smart phones and vehicles, have been connected by the Internet [2], [3]. The explosive growth of applications generated from the IoT devices has stringent demands of computation resources and real-time processing [4], [5]. However, the IoT devices generally have not enough computing resources, and their battery lives are short. Offloading the IoT applications from the IoT devices to be processed in the servers of remote public cloud is considered as a solution to address the above issue. However, the IoT devices are far away from the public clouds; long transmission time will cost [6]. To overcome this shortcoming, mobile edge computing (MEC) is proposed to solve the challenging problems of limited computing resources and short battery lives of IoT devices [7]. Compared with the public cloud, the edge cloud is near to the IoT devices, therefore, the low latency requirements for the IoT applications can be met. In the last few years, with the demand for edge cloud services proliferating, more and more edge cloud service providers (ESPs) are emerging. For example, China Telecom and Huawei are two ESPs in China.
In the beginning, the model of single ESP dominates the cloud market. With the demands of IoT users' application requests on computing resources increasing dramatically, and at the same time, the applications of IoT users become more and more complex, IoT users may consider using services from different ESPs in order to meet their demands. Under this circumstance, multi-cloud systems, have emerged as practical platforms to address this problem [8].
In a multi-cloud system, a cloud service broker (CSB) acts as a mediator between IoT users and cloud service providers (CSPs). The CSB aggregates integrates and coordinates resources from multiple CSPs and to provide services to IoT users so that not only the demands for cloud services are satisfied, but also that there is enough capacity left for future application requests [9]. A study estimated that the global brokerage market of cloud services had reached 10.5 billion US dollars by the year 2018 [10].
In the cloud system, pricing is of critical importance for service provision, as an important economic factor for CSPs. From the viewpoint of the ESP, how to set its service price is a non-trivial issue. If they pricing services too high, potential IoT users might not select the service from this provider. When the prices are set too low, ESPs might not obtain enough revenue. Many existing works have focused on designing better pricing schemes to maximize the profits or revenue of CSPs in public clouds, such as [11]. From the perspective of CSPs, besides prices, guaranteeing Quality of Service (QoS) measured as the average queueing response time to IoT users is also quite important, as the applications of IoT users need realtime processing [12].
Response time is recognized as an important metric for evaluating the performance of the online cloud services, which is the time between the sending application requests and receiving a response [13]. Besides response time, QoS also includes reliability, security and so on [14]. Response time is used as the main QoS metric, where the assumption is widely made, such as [15]. Besides response time, load balancing is a crucial factor for cloud computing systems. Cloud-based applications have more requirements on load balancing compared to the traditional enterprise applications, and load balancing is an important factor which is fully  considered by users when they choose a CSP [16]. From the perspective of CSPs, load balancing has a direct impact on their revenue as it has a close relation with the quality of service.
Motivated by the concept of multi-cloud systems, this study explores service pricing and selection in a multi-MEC system by taking the different valuations of IoT users' applications on services into account, as shown in Fig.1. The problem that this study tries to address is illustrated in Fig.2. For the CSB, its main objective is to maximize revenue by making optimal pricing and load balancing decisions. On the IoT users' side, based on pricing and load balancing information, they will select services from these ESPs for processing their application requests.
The contributions of this article are summarized as follows.
• Unlike the previous studies that ignored IoT users' different types and load the balancing strategies, this study investigates and analyzes the problem of service pricing and selection for IoT applications offloading in a multi-MEC system taking both pricing and load balancing factors into account.
• Given the prices of cloud services and load balancing strategies of the ESPs in the multi-MEC system, we analyze IoT users' service selection policies based on which we get the effective arrival rate of application request at each ESP. Then, the CSB's revenue maximization problem is formulated. By carefully analyzing the objective function of the problem, we first express the load balancing index as the function of the effective arrival rate of application requests and then propose a dual decomposition method to solve it.
• The proposed method is compared with the proportional scheme (PS) and the resource allocation method of some recent works that did not consider load balancing. The simulation results demonstrate that the proposed method (PM) VOLUME 8, 2020 can achieve a lower mean response time. We also analyze the effect of reward value on users' arrival rate and the revenue of CSB.
The rest of the paper is structured as follows. Related works are reviewed and discussed in section II. System models are introduced in the section III. The application arrival rate of IoT users' decisions and the CSB's revenue maximization problem are analyzed in the section IV. Simulations are presented in the section V. Section VI presents the conclusions.

II. RELATED WORK
Applications offloading in mobile cloud computing (MCC) and mobile edge computing (MEC) have been extensively in the existing works. In [17], non-orthogonal multiple access (NOMA) is considered as an enabling technology in the future generation communication systems, the authors studied the effect of NOMA on the application offloading in MEC. In [18], the authors developed a unified framework that can minimize the overall outage probability when offloading applications to the public cloud. In [19], Li and Cai proposed an incentive mechanism based framework for the design of collaborative application offloading in MEC. In [20], Pham et al. studied the problem of application offloading in the MEC system based on NOMA by using the coalition game. A low-complexity algorithm is developed to get the solution. In [21], Wang et al. proposed a multiantenna NOMA MEC system with multiple users having computation-intensive applications to be offloaded. Minimizing energy consumption from all users is their goal. In [22], Bonadio et al. studied the performance of analysis of an SaaS MEC system, which is modelled as a queuing system Markov with multiple servers. However, the authors only considered a single cloud system.
In the cloud systems, pricing provides a useful tool for service provision. Many efforts have been devoted to investigating service price in MEC and MCC without considering load balancing. For example, in [23], the authors proposed a two-stage game-theoretic framework to capture cloud users' demand preferences for cloud capacity and pricing. In [24], Chen et al. studied pricing and resource allocation in MEC. They proposed a Stackelberg game-based approach to solving the problems of revenue maximization for MEC and utility maximization for users. In [25], Wu et al. investigated how to model the utility of cloud users given the pricing strategy of services of CSPs. In [26], the authors studied task offloading in vehicular fog computing. Two algorithms based on matching-learning and pricing are proposed to minimize the total network delay.
Load balancing is directly related to service quality (e.g., response time) for the cloud users, and it is seriously considered when they select a CSP [16]. Load balancing has been extensively studied in a great number of works with different goals. Nonetheless, many of the existing works ignored pricing factor, which is an intrinsic economic characteristic of cloud services. An energy-aware model is introduced by Paya and Marinescu in [27], which is used for load balancing and application scaling. In [28], Abdelltif et al. proposed an SDN-based load balancing service for cloud servers. Their objective was to maximize the utilization of cloud resources and at the same time minimize the response time that cloud users experience. However, they mainly studied from the perspective of cloud users without considering the benefits of CSPs. In [29], Huang et al. studied load balancing for caching fairness in edge computing environments by proposing two caching algorithms.
Resource management and service provision in multicloud and federated cloud systems have been attracted great attention in recent years. In [30], the authors proposed two algorithms by respectively applying the genetic algorithms and evolutionary game theory for forming the cloud federation. A cooperative cloud market is proposed in [31], where a cloud market broker decides which CSP's resources are employed to be allocated to minimize the cost users. In [32], Li et al. proposed a multiple cloud intermediary framework for providing cloud services from different CSPs to users for streaming big data processing. Lin et al. proposed a brokerage-based framework in the cloud computing systems, where the CSB takes the responsibility of recommending the best available services to users [33]. In [34], Mei et al. studied the problem of profit maximization for a cloud broker. The cloud broker buys reserved VM instances from a multiple of cloud providers and delivers services to the users. However, these previous studies neglected user type heterogeneity and response time, which are not practical as different types of applications may have different preferences for cloud services and different requirements for processing deadlines. In [35], the authors presented a novel framework to secure the access to IoT services in a multi-cloud system without considering user heterogeneity, pricing factor and load balancing strategy. In [36], Zhou et al. studied the problem of edge computing service provisioning for energy-efficient workload offloading in vehicular networks, and proposed a consensus ADMM approach to solve it. However, these works did not consider the pricing factor.
From the analysis of the works above, it can be found that many of the previous works on IoT applications offloading did not jointly study pricing and load balancing. Furthermore, these previous works neglected IoT users' heterogeneity, as different IoT users types may show different preferences for cloud services [11]. This study compares with several closely related work on service provision in multi-cloud and federated cloud systems, which is summarized in Table 1. '' '' means that this factor is considered and ''×'' means that this factor is ignored. It can be observed from Table 1 that the main related studies only considered part of the factors, whereas, our study fully consider these factors.

III. SYSTEM MODELS
This section introduces the system models consisting of IoT users and CSB. Consider a multi-MEC system with a CSB who reserves cloud resources from multiple ESPs and provisions cloud services to IoT users. Each IoT user will make a determination on which ESP's service it should select from to process its application requests.

A. CSB's MODEL
We suppose that the number of ESPs that a CSB integrates and coordinates resources from is N , each of which is modelled by one M/M/1 queue, the processing capacity of whom is represented by its service rate µ i (in application requests per second), i ∈ {1, 2, . . . , N }. Without loss of generality, it is also assumed that µ 1 ≥ µ 2 ≥ . . . ≥ µ N ≥ 0. For each ESP i , CSB sets the price per application request as p i , and broadcasts load balancing indicator s i to the IoT users. Based on this information, IoT users will decide whether to subscribe to cloud services from one of the ESPs or not.

B. THE MODEL OF IoT USERS
We made such an assumption that IoT users' application requests are generated with the arrival rate λ (measured by the application requests per second) according to Poisson process [36], and these application requests are processed based on the first-come-first-served (FCFS) queueing discipline. The recent studies on the analysis of cloud data centers show that the arrival rate of users' application requests follows Poisson distribution [15], [39]. We also assume that each IoT user generates a distinct application request upon arrival. Therefore, the number of application requests reflects the number of IoT users. IoT user and application request are used interchangeably throughout the paper.
Remark: It is important to remark that an M/GI/1 PS system can also be adopted or an M/M/1 FCFS system. However, the problem can be simplify analyzed by considering an M/M/1 FCFS system. The detailed reason can be referred to the work of [40].
Each IoT user is assumed to be associated with a specific application request by the parameter α k having uniform distribution in the range [0, 1], and its probability distribution function (PDF) and cumulative distribution function (CDF) are denoted as f (·) and F(·), respectively [11]. The value of α k represents this IoT user's preference for cloud services. Based on the above assumptions, given the service price p i and load balancing indicator s i of ESP i , the utility that this IoT user α k gets is where r denotes the reward that this IoT user obtains from using cloud service, and it is proportional to the application request size of this IoT user [23], [41], c is the delay cost which reflects the urgency of users' application requests [15], [23], and d i (λ i )=1/(µ i − λ i ) is the average response time (including queueing time plus processing time) incurred by the arrival rate λ i . As µ i and λ i are both measured by application requests per second; therefore, the average response time is measured by seconds per application request. It is obvious that serving an application request with larger size means that this IoT user can gets a higher reward. For ease of presentation, the notations of this article are summarised in Table 2.

IV. PROBLEM FORMULATION AND SOLUTION METHOD
In this section, the interaction between IoT users and CSB are investigated and analyzed by applying a two-stage Stackelberg game [42], the illustration of which is shown in Fig.2. In this game, the CSB sets service prices and load balancing strategies to have the maximized revenue in the first stage, and IoT users make determinations on the number of their generated application requests in the second stage. Based on the method of backward induction, this game can be solved easily. In the first stage, based on service prices and load balancing indicators that set by the CSB, we study how IoT users make their determinations on which ESP's cloud service should be selected and the number of application requests they generate. In the second stage, we study how CSB maximizes its revenue according to IoT users' decisions in the first stage.

A. STAGE II: IoT USERS' STRATEGIES
Recall that the arrival rate of IoT users' application requests is rate λ, which is assumed to follow poisson process, and these application request are executed based on the discipline of FCFS queueing.
For the type α k IoT user, after generating application requests, a decision will be made as to which ESP's service it selects from. It joins the ESP only if the utility it gets is positive, which means that (2) VOLUME 8, 2020 from which we get α k >α * k where Therefore, the effective application request arrival rate of IoT user α k at ESP i is where s i denotes the fraction of the number of application requests dispatched to ESP i , and denotes the load balancing indicator of this ESP.

B. STAGE I: CSB's REVENUE MAXIMIZATION
After the effective arrival rate λ i is got, the problem of revenue optimization for CSB is Problem 1: where the first constraint is the effective application arrival rate of IoT user α k at ESP i , and the second one is the constraint of load balancing. By solving Problem1, the following results can be obtained, the proof of which are shown in Appendix. Proposition 1. The unique optimal pricing and load balancing strategies from solving the revenue maximization problem are

V. SIMULATION RESULTS
Consider a multi-MEC system with a CSB who reserves cloud resource from N = 5 ESPs and provisions edge cloud services to a number of IoT users. We present simulation results to evaluate and compare our proposed method (PM) with some main recent work on cloud service provision. We compare the following benchmark schemes with our algorithm: Proportional Scheme (PS): PS dispatches application requests of IoT users to ESPs according to their processing rates [43]:

Homogeneous User Scheme (HUS):
HUS assumes that all the IoT users have a homogeneous preference for cloud services.
Random Scheduling Scheme (RSS): RRS dispatches application requests of IoT users to ESPs randomly. We assume that the number of application requests dispatched to the ESPs according to the following load balancing strategies: s 1 = 2/5, s 2 = 1/5, s 3 = 1/5, s 4 = 1/20, s 5 = 1/20. The IoT users are assumed to be homogeneous under PS. We analyze the effect of the reward value, the effect of arrival rate, and the effect of system size on CSB's revenue and IoT user's total utility. The Discussion of the setting for parameter values. We let µ i denote the service rate for the ESP i reflecting the application request this provider's processing capacity.  The value of λ denotes the number of application requests. r is the reward of this IoT user obtained from using edge cloud services, which is directly related with the data size of the application request. It is obvious that processing an application request with larger size means that this IoT user can get more reward. Similar to the work of [44], we let the value of r represent the size of application request of the cloud user. The varying values of r reflect the different sizes of application requests. The values selected for the parameters are only for the purpose of demonstration. Similar results can also be obtained by choosing other values of parameters.

B. COMPARISON OF MEAN RESPONSE TIME
We first compare PM with the benchmark methods in terms of mean response time that IoT users experience in each ESP and the revenue that each ESP gets. For the HUS, we set the values of all the IoT users' types as α k = 1. Fig.3 shows the comparison of the PM with PS, HUS and RSS in terms of the mean response time experienced in each ESP. From  Fig.3, we can see that PM achieves much lower response time compared with the benchmark methods, which means that the PM can provide cloud services with better QoS.   3 also suggests that these ESPs with more cloud resources can provision services with better QoS than those with less cloud capacities in the multi-MEC system.

C. COMPARING LOAD BALANCING STRATEGIES
We next compare load balancing strategies set by CSB for different ESPs under our proposed method PM and PS. From  Fig.4, we observe that the PM assigns more service requests to the ESPs with more cloud resources than these ESPs with fewer ones. One main reason is that PM considers IoT users' different types, which are ignored in PS.

D. EFFECT OF REWARD VALUE
We analyze how reward value r impacts IoT users' arrival rate of application requests and CSB's revenue. Figs.5(a), (b) and (c) depict the impact of reward value r on IoT users' arrival rate at each ESP with different delay costs in the multi-MEC system. It is easily seen from the three figures that IoT users with larger sizes of application requests are prone to use cloud services under the condition that delay costs are the same, and IoT users are more likely to choose VOLUME 8, 2020 these ESPs who provide low delay costs. These figures also indicate that these ESPs with abundant cloud resources can process more application requests from IoT users than those with less cloud capacities as delay costs increase. No IoT user chooses ESP 5 due to its not enough cloud resources.
The impact of reward value r on CSB's revenue is shown in Fig.6. It is observed in this figure that the revenue of CSB increases with reward value increasing, which indicates that CSB can gain more revenue if the provided edge cloud services can process requests with higher sizes. Fig.6 also shows that higher delay costs will lead to the loss of revenue. Fig.7 shows the comparison of our proposed scheme with benchmark method under different reward values. This figure suggests that CSB earns the least revenue under the proposed schemes comparing with benchmark methods. This is due to the reason that the proposed scheme considers IoT users' different tastes for cloud services, which is more practical; in contrast, the benchmark methods assume that all the IoT users have the same valuation on cloud services.

VI. CONCLUSION AND FUTURE WORKS
We have presented a joint study of the problem of service pricing and selection for IoT applications offloading in a multi-MEC system. The problem is investigated and analyzed as a Stackelberg game, under which the CSB first sets service prices and load balancing strategies for the purpose of maximizing revenue. Then, IoT users makes their application requests arrival rate decisions based on the information provided by CSB. This game is solved by applying the technique of backward induction, in which the CSB determines service prices and load balancing strategies in Stage II and IoT users decide which ESP's service they choose in Stage I. The simulation results demonstrate that in a comparison with the benchmark methods, the proposed method (PM) achieves much lower mean response time and provides a more effective load balancing strategy.
Several research aspects can still be further explored as future works. For example, the ESPs in the multi-MEC system may compete or cooperate to provision edge cloud services. Therefore, considering the relationship of these ESPs is an interesting future work. Our work can also be extended to analyze IoT users' different sensitivity to delay into account.

APPENDIX PROOF 1
The objective function of the revenue maximization problem is not convex, and it is difficult to be solved.
According to the first constraint, we have Therefore, we can eliminate the first constraint of Problem1 by substituting Eq.(9) into the objective function, and the original problem is equivalently written as, Problem 2: Before introducing solution method, we first give a lemma which is proved in [45], based on which our solution method is proposed. Lemma 1. We always have sup wheref (x)=sup y f (x, y). Lemma 1: means that we could always first minimize a function through minimizing over some of the variables, and minimizing the remaining ones later [45].
According to Lemma 1, we can solve Problem2 by maximizing over s i and λ i sequentially. For any given λ i , the above problem is transformed into Problem 3: It is obvious that Problem3 is a convex problem, from KKT conditions [45], the solution is obtained as follows By substituting Eq.(12) back into Eq.(10) and denoting N n=1 λ i = λ t , we have an equivalent problem The objective function of Problem4 is convex with respect to λ i , and the Lagrangian function is where v denotes the dual variable associating with the first constraint of Problem4. Denoting It is obvious that Eq.(15) is a concave function of λ t for a given v, and Eq.(16) is a concave function of λ i for a given v. From the first-order condition [45], we have Therefore, the optimal solutions of Eqs. (15) and (16) for a given v are respectively expressed as where [x] + is max{0, x}, g(v) and h(v) are given as It is evident that for v ∈ (c/µ i , r), h(v) is an increasing and positive function, and g(v) is a decreasing and positive function. Therefore, we can get the optimal solutions of λ t (v) and λ i (v) by calculating the optimal value of dual variable v * . By substituting Eqs. (21) and (22) into the first constraint of Problem4, we have Eq.(23) is difficult to be solved, but we can try to solve it by numerical analysis. As illustrated in Fig.3, the two lines intersect at a unique point where the optimal value of v is obtained. The values of r = 2, c = 1, N = 5, µ i (i = 1, 2, . . . , 5) are set respectively as 10, 8, 6, 4, 2, and λ = 20.
After getting the unique v * , we can obtain the unique solutions λ i (v * ) and λ t (v * ) from Eqs. (14) and (15), respectively, which are also global optimal solutions of Problem4, as v * , λ i (v * ) and λ t (v * ) satisfy the sufficient and necessary KKT conditions [45]. By substituting these values into Eqs. (6) and (9), we get s * i and p * i , respectively. Therefore, Proposition 1 is proved.