Two-Tier Task Offloading for Satellite-Assisted Marine Networks: A Hybrid Stackelberg-Bargaining Game Approach

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Two-Tier Task Offloading for Satellite-Assisted Marine Networks: A Hybrid Stackelberg-Bargaining Game Approach Zhen Wang, Student Member, IEEE, Bin Lin, Senior Member, IEEE, Qiang (John) Ye, Senior Member, IEEE, Haixia Peng, Member, IEEE

arXiv:2611.13019v1 [cs.DC] 9 Nov 2026

Abstract—The proliferation of maritime activities has spurred the emergence of numerous computation-intensive and delay-sensitive marine applications and services. Given the inherent rationality, selfish nature, and limited computational abilities of marine devices, devising effective strategies to incentivize their participation in task processing become a critical challenge. In this paper, we investigate the satellite-assisted marine multi-access edge computing (MEC) and propose a two-tier task offloading scheme through a hybrid Stackelberg-Bargaining game approach to enhance offloading efficiency and maximize the utility of marine devices. Specifically, for the underwater acoustic communication, we consider the scenario where multiple autonomous underwater vehicles (AUVs), managed by maritime autonomous surface ships (MASSs), upload their collected data using non-orthogonal multiple access(NOMA) to optimize channel utilization. For the data transmission above the sea surface, we consider the scenario where a low earth orbit satellite (LEOS) functions as a space edge server to provide computing services, and MASS offloads workloads to LEOS through frequency division multiple access(FDMA) to prevent co-channel interference. we define the utility of AUVs, MASSs and LEOSs, and model the offloading process between AUVs and MASSs as a Stackelberg game, while representing the offloading interaction between MASSs and LEOSs as a Bargaining game. Additionally, we propose efficient algorithms to optimize AUV offloading strategies and MASS pricing strategies, while refining the bidding strategies for both MASSs and LEOSs. Simulation results demonstrate that the proposed algorithms significantly outperform benchmark schemes in achieving optimal solutions. Index Terms—Maritime MEC, two-tier task offloading, Stackelberg game, Bargaining game.

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I. I NTRODUCTION ITH the increasing scope of maritime activities, a wide array of marine wireless devices, such as underwater sen-

Copyright (c) 20xx IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. (Corresponding author: Bin Lin.) Zhen Wang is with the Department of Information Science and Technology of Dalian Maritime University, Dalian, China, and Communication Engineering of Dalian Neusoft University of Information, Dalian, China. E-mail: wangzhen jsj@neusoft.edu.cn. Bin Lin and is with the Department of Information Science and Technology of Dalian Maritime University, Dalian, China. E-mail: binlin@dlmu.edu.cn. Qiang (John) Ye is with the Department of Electrical and Software Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4. Email: qiang.ye@ucalgary.ca. Haixia Peng is with the School of Information and Communications Engineering, Xi’an Jiaotong University, Xi’an 710049, China. E-mail: haixia.peng@xjtu.edu.cn. This manuscript has been accepted by IEEE Internet of Things Journal, DOI:10.1109/jiot.2024.3523527.

sors, autonomous underwater vehicles (AUVs), vessels, buoys, and maritime autonomous surface ships (MASSs), has been deployed across the ocean. This proliferation has driven the rapid expansion of marine wireless networks, resulting in the generation of vast amounts of computation-intensive and delay-sensitive data [1], [2], [3]. For instance, in underwater exploration and surveillance, large volumes of hydrological data and monitoring images/videos must be collected and transmitted to designated equipment for processing. Similarly, during intelligent reconnaissance and maritime rescue operations, a large volume of collected real-time video footage requires prompt processing to enable timely decision-making. These applications have sparked stringent requirements on high-speed marine communication and powerful computing [4]. It is of utmost importance to establish an efficient marine communication and computing network for marine devices [5]. Nevertheless, existing marine communication and computing networks fall short in fulfilling the substantial demands of marine devices due to their low data rate and high latency [6], [7]. Multi-access edge computing (MEC) has emerged as an efficient solution to improve computing efficiency and reduce decision-making latency for maritime terminals [8], [9]. Recently, various research endeavors have been made in proposing diverse innovative approaches to enhance the overall performance and efficiency of maritime MEC systems. In [10], Hou et al. designed a multi-tier underwater computing framework for autonomous underwater vehicles (AUVs), aiming at collecting and forwarding data sensed by underwater devices to surfacestations. In [11], Wen et al. proposed an intelligent oceanic data collection scheme for multi-automatic underwater gliders in maritime wireless communication networks. To further enhance data collection and offloading efficiency across diverse transmission segments, non-orthogonal multiple access (NOMA) has been adopted in maritime MEC networks, especially for acoustic data transmissions [12], [13]. Six generation (6G) wireless technologies stand poised to revolutionize the wireless landscape by integrating satellite networks with ground networks, ushering in a new era of seamless connectivity and advanced functionality [14]. The edge computing paradigm holds significant potential for applications and services in satellite-assisted networks, enabling support for computation-intensive and delay-sensitive services in oceanic environments [15], [16]. Zeng et al. proposed an architecture for space-air-sea integrated networks aiming at enhancing the

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security of maritime communication networks for unmanned surface vehicles in [17]. Wang et al. proposed a space-air-sea integrated network architecture designed to provide secure MEC services for delay-sensitive applications for maritime mobile users [18]. Given the limited energy and computing resources of offshore equipment, integrating satellite and maritime networks with MEC presents a promising solution for enhancing the computing efficiency of marine applications. However, the features of a marine environment pose technical challenges in fulfilling various oceanic application requirements [19]. First, as an integral component of marine networks, underwater acoustic communication is typically affected by unfavorable factors, such as limited data rates, prolonged propagation delay, and elevated packet loss rates [20], [21]. It impedes the ondemand service provisioning and limits the potential of maritime applications in areas such as monitoring, exploration, and emergency response [22], [23]. Second, unlike terrestrial networks, oceanic communication and computing resources are extremely limited. Current standalone oceanic network infrastructures are unable to meet the demands of numerous computation-intensive and delay-sensitive tasks at sea. Third, due to the heterogeneity of satellite-marine integrated networks, different network service providers may lack sufficient incentives to offer edge computing services for different oceanic applications [20]. It is imperative to design an efficient maritime communication and computing scheme to overcome the aforementioned challenges and better serve the evolving demands of maritime applications and services. Currently, how to optimize the computation offloading for AUVs with respect to the space-sea integrated network architecture is still an open issue. Motivated by the above observations, in this paper, we propose a satellite-assisted maritime MEC architecture to enhance task offloading efficiency and optimize the utilization of marine wireless devices. Also, a two-tier task offloading scheme is exploited for AUVs through a hybrid Stackelberg-Bargaining game approach. The key contributions of this paper mainly include the following aspects: • Two-Tier Satellite-Assisted Maritime Task Offloading: We first propose a low earth orbit satellite (LEOS) assisted task offloading framework in maritime MEC, which consists of two transmission tiers, i.e., the underwater acoustic communication and the satellite-assisted wireless communication. For underwater acoustic communication, multiple AUVs collect and upload oceanic data to MASSs utilizing NOMA to improve the underwater acoustic channel utilization. For satellite-assisted communication, MASSs transmit partial workloads to LEOSs for further processing through FDMA to avoid co-channel interference. • Utility Maximization with Incentive-Driven Approaches: We employ an incentive-based framework to encourage marine wireless devices (i.e., AUVs, MASSs and LEOSs) to participate in task computing activities, with the goal of optimizing their respective profits. Specifically, for underwater acoustic communication, we model the offloading process as a Stackelberg game to optimize AUV offloading strategies and MASS pricing strategies. For MASS-toLEOS transmission, we model the offloading process as a

Bargaining game to refine the bidding strategies of MASSs and LEOSs, ensuring their mutual benefits. By analyzing the interactions among AUVs, MASSs, and LEOSs, we identify the game equilibrium that maximizes system efficiency and profitability. • Performance Evaluation: We perform extensive simulations to validate the efficacy of the proposed offloading and incentive schemes. Numerical results indicate that the proposed algorithms optimize participant utilities, demonstrating their effectiveness and efficiency compared to benchmark schemes. The remainder of this paper is organized as follows. Section II provides an overview of related works. The system model is presented in Section III. The problem formulation and solution design are given in Section IV. Section V presents the performance evaluation, and Section VI presents concluding remarks and future work. Table I outlines the key notations in the sequence of their initial appearance in the paper. II. R ELATED WORK In this section, we provide an overview of existing works in multi-tier task offloading schemes, satellite-assisted maritime networks, and game theory based MEC, respectively. For brevity, comparisons with representative existing works are summarized in Table II. A. Multi-tier Task Offloading Schemes Multi-tier task offloading has emerged as an efficient solution to improve the computing efficiency of marine devices [18]. Many studies have explored various task offloading strategies in marine networks, which is classified into two categories. One approach is shore-based task offloading schemes, which necessitates land-based stations to offer computing services to offshore devices, typically with the aid of relay devices like unmanned aerial vehicles (UAVs) to transmit offshore computing tasks to shore-based stations [22], [24]. Wang et al. established an MEC-enabled sea lane monitoring network architecture where the tasks generated by ships are offloaded to surface-stations and coastal base stations for processing in [25]. Dai et al. proposed a hybrid offshore and aerial-based MEC scheme where both offshore base-stations and UAVs can provide computing services for marine unmanned surface vehicles in [26]. Another type of approach is off-shore task offloading schemes, which involve unmanned devices (e.g., MASSs [3], AUVs [27] and UAVs [5], [28]) and high-altitude devices [29] facilitating edge computing services for offshore devices. Zeng et al. proposed an energyefficient USV fleets-assisted computation offloading framework, where UAVs serve as the requesters for computing services, and USV fleets are the helpers in [3]. In [27], Gjanci et al. focused on underwater multi-modal wireless sensor networks (UWSNs) for submarine surveillance and monitoring applications, where nodes offload data to an AUV through optical technology and employ acoustic communication for coordination. Lyu et al. proposed a computation offloading and resource allocation scheme for NOMA-UAV-assisted maritime emergency communications to minimize computation overhead in [5]. You et al. proposed a

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TABLE I K EY N OTATIONS Notation Υm λi Citot bi,n ϱ f gi,m Wi pi tts i,m dm,n θm,n vn αm gm χ ts Ei,n

Eicom εi /εm /εn tc Ei,m com Ei,m com Ei,n

ui ξi qi /qm /qn ui,m ωi,m ϕi,m (bi,n ) price ψi,m (bi,n ) µi,m γi,m

Description Spatial coordinates of MASS m Task generated by AUV i Number of CPU cycles for processing λi Ratio of offloading task λi from MASS m to LEOS n Coefficient of di,m Central frequency of the acoustic signal Acoustic uplink channel gain from AUV i to MASS m Allocated channel bandwidth of AUV i Transmission power of AUV i Transmission time of AUV i Distance between MASS m and LEOS n Elevation angle between MASS m and LEOS n Moving speed of LEOS n Bandwidth allocation factor Complex Gaussian variable

Notation Υi Ditot ai,m di,m Ω(f ) σ NB Ri,m si ts Ei,m ςm,n T max Rm,n pm βm

Path exponent

tts i,n

Description Spatial coordinates of AUV i Input data size (in bits) of λi Offloading ratio of AUV i to MASS m Distance between AUV i and MASS m Absorption coefficient Spreading factor Oceanic noise power spectrum density Link transmission capacity from AUV i to MASS m Underwater link quality indicator Energy consumption of AUV i for transmitting tasks Geocentric angle between MASS m and LEOS n Maximum communicate of each LEOS Transmission rate of MASS m Transmission power of MASS m Fading involving shadowing, rain, and other fading Communication latency for transmitting partial workloads of AUV i from MASS m to LEOS n

Energy consumption of MASS m for transmitting partial workloads of AUV i from MASS m to LEOS n Energy consumption Eicom of AUV i for computing Effective power consumption coefficient of AUV i /MASS m /LEOS n Energy consumption for transcoding data of MASS m Energy consumption of MASS m for completing the assigned task Energy consumption of LEOS n for completing the assigned task SoA function of AUV i Calibration factor of the SoA function Energy cost of AUV i /MASS m /LEOS n Satisfaction functions of MASS m Weighting parameter of MASS m Tender price of MASS m Final transaction price Discount factor of MASS m Patience coefficient of MASS m

tcom i

Computing time of AUV i

ρi /ρm /ρn

Computation capacity of AUV i /MASS m /LEOS n

ttc i,m

Transcoding time of MASS m

tcom i,m

Latency of MASS m to complete the assigned task

tcom i,n

Latency of LEOS n to complete the assigned task

Titot

Overall latency for completing AUV i’s workloads

ϖi Zi /Zm /Zn ki ui,n ωi,n ϕi,n (bi,n ) ηi µi,n γi,n

Initial satisfaction of AUV i Utility function of AUV i /MASS m /LEOS n Price for each bit of data paid by AUV i Satisfaction functions of LEOS n Weighting parameter of LEOS n Tender price of LEOS n Profit distribution ratio Discount factors LEOS n Patience coefficient LEOS n

computation offloading framework for uncertain marine tasks, where both UAVs and vessels provide computing services to marine Internet of Things (M-IoT) in [28]. Li et al. proposed a secure computation offloading scheme for M-IoT with the assistance of unmanned surface vehicles (USVs) subject to the eavesdropping attack, where the high altitude platform (HAP) performs computation offloading for marine devices in [29]. Different from existing offloading schemes, we propose a satellite assisted maritime MEC network for AUVs, to enable workload offloading to satellites for further computing, considering that satellites cover remote sea areas and have sufficient on-board energy capacity. We take the underwater acoustic communication into consideration and employ NOMA to optimize the underwater acoustic channel utilization. Additionally, we account for the underwater acoustic link quality when optimizing offloading decisions.

applications in [32]. To provide excellent quality of service for marine devices, Zhang et al. proposed a multi-domain virtual network embedding solution for SAGSIN in [33], while Lin et al. proposed a resource management scheme employing softwaredefined networking (SDN) controllers to provide services for marine application in SAGSIN in [34]. Simultaneously, individual scholars have delved into satellite-assisted maritime MEC. Lin et al. and Wang et al. leverage low altitude platforms (LAPs) [4] and UAVs [18], respectively, to assist in computing tasks, whereas some researchers primarily leverage satellites for signaling or navigation of the target area [5], [19], [28]. Inspired by the aforementioned studies, it is highly demanding to introduce satellite-assisted MEC into marine networks to provide oceanic devices with computation services by bringing the extensive computational resources of cloud servers to LEOSs.

B. Satellite-assisted Marine Networks To address the ubiquitous communication and computing demands of marine devices, satellite-assisted maritime networks has recently surfaced as a novel research topic [30], [31]. Li et al. proposed an energy-efficient scheme for the space-airground-sea-integrated network(SAGSIN), utilizing an intelligent autonomous underwater glider specifically designed for marine

C. Game theory based MEC Game theory has been extensively applied in MEC networks to establish distributed mechanisms and circumvent the high complexity inherent in centralized frameworks [5], [35], [36]. Zhang et al. formulated a Stackelberg game based three-tier multi-user multi-task offloading model by considering users as leaders and BSs and the cloud as followers in [37]. Niu et al.

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TABLE II R ELATED W ORK .

References [3] [4] [5] [18] [19] [22] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] Our work

Network type Air-sea integrated networks Space-air-ground-sea integrated networks Air-sea integrated networks Space-air-sea integrated networks Space-air-sea integrated networks Ground-sea integrated networks Air-ground-sea integrated networks Ground-sea integrated networks Air-ground-sea integrated networks Underwater wireless sensor networks Space-air-ground-sea integrated networks Air-ground-sea integrated networks Space-air-ground-sea integrated networks Space-air-sea integrated networks Space-air-ground-sea integrated networks Space-air-ground-sea integrated networks Space-air-ground-sea integrated networks Space-sea-underwater integrated networks

Offloading

USV→BS USV→UAV

Comparisons with existing studies The consideration is limited solely to the airspace segment, disregarding the underwater segment and space segment. Acoustic communication for underwater marine devices is not taken into consideration. The consideration is limited solely to the airspace segment, disregarding the underwater segment and space segment. Acoustic communication for underwater marine devices is not taken into consideration. Acoustic communication for underwater marine devices is not taken into consideration. The consideration is limited solely to the offshore area, disregarding the underwater segment and space segment. The consideration is limited solely to the offshore area and airspace segment, disregarding the underwater segment and space segment. The consideration is limited solely to the offshore area, disregarding the underwater segment and space segment. The consideration is limited solely to the offshore area and airspace segment, disregarding the underwater segment and space segment.

nodes→AUV

The consideration is limited solely to the underwater segment.

UAVs→USV fleets M-IoT→LAP→LEOS; M-IoT→BS→buoys M-IoT→UAVs M-IoT→BS M-IoT→UAV→LEOS Surveillance UAV →relay UAV Vessel→BS/buoy Vessel→BS relayed by UAVs Vessel→buoy→BS

M-IoT→UAV→vessel USV→HAP→BS

Acoustic communication for underwater marine devices is not taken into consideration. The consideration is limited solely to the offshore area and airspace segment, disregarding the underwater segment and space segment.

No task offloading

The focus is primarily on network performance optimization.

No task offloading

The focus is primarily on network performance optimization.

No task offloading

The focus is primarily on network performance optimization.

No task offloading

The focus is primarily on network performance optimization.

No task offloading

The focus is primarily on network performance optimization.

AUV→MASS→LEOS

A satellite assisted maritime MEC network for AUVs is proposed and the acoustic communication is taken into consideration.

formalized a potential game for multi-mobile devices and multibase stations to optimize latency sensitive tasks and latencytolerant tasksin [38]. Peng et al. leveraged a Stackelberg game to model the dynamic interaction between edge server providers and mobile users and proposed an alternating direction method of multipliers algorithm to derive the optimal strategie in [39]. The above studies have investigated the interaction between selfish game participants and achieved a mutually satisfactory optimization solution to maximize their profits. Motivated by the above incentive-based schemes, in this paper, considering the rationality and selfishness of marine wireless devices, we investigate the satellite assisted maritime MEC framework and propose a hybrid Stackelberg-bargaining game approach to maximize the utilities of game participants and improve the computing efficiency of marine networks. III. S YSTEM MODEL This section presents the scenario for the proposed two-tier task offloading in marine MEC networks including the system

model, communication model, computation model, and utility model as follows. A. Network model We consider a space-sea integrated network which consists of N LEOSs providing edge computing capabilities and robust communication coverage for MASSs, denoted by N = {1, 2, ..., n, ..., N }, where N denotes the total number of satellites within a constellation, as shown in Fig. 1. A group of AUVs, denoted by I = {1, 2, ..., i, ..., I}, are distributed on the seabed to monitor the marine environment and collect oceanic data (e.g., marine biological images, aquaculture monitoring videos, and intelligence reconnaissance videos). A set of MASSs equipped with computing capacities, denoted by M = {1, 2, ..., m, ..., M } are dispatched on the sea surface to receive the oceanic data collected by the AUVs. We consider four stages of uplink workload transmission and processing in the satellite-sea integrated system: in Stage I, AUVs execute local computing and upload a portion of their workloads to the corresponding MASS that they are associated with for further computation via NOMA;

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In Stage II, each MASS receives the offloaded data from its connected AUVs via underwater acoustic communication and then transcodes the data for further processing; In Stage III, the MASS processes partial workloads locally and transmits the remaining workloads to LEOS for further computation through FDMA; In Stage IV, each LEOS receives data offloaded from its connected MASSs through wireless transmission links and performs computation. To represent the locations of each AUV and MASS, a threedimension (3D) Cartesian coordinate system is employed. Denote Υm = (xm , ym , zm ) as the spatial coordinates of MASS m, where xm , ym , and zm represent its the longitude, latitude, and height, respectively. Correspondingly, the coordinates of AUV i is denoted as Υi = (xi , yi , zi ). We denote each task generated by AUV i as λi = {Ditot , Citot }, where Ditot denotes the input data size (in bits) and Citot indicates the number of CPU cycles needed to process the task λi . We assume that all tasks can be executed on different network terminals. Specifically, we denote variable ai,m ∈ [0, 1] as the offloading ratio of AUV i to MASS m. Then, the processing workload of AUV i is expressed as (1 − ai,m )Ditot . Denote bi,n ∈ [0, 1] as the ratio of offloading task λi from MASS m to LEOS n, then the workload for AUV i processed on MASS m is expressed as (1 − bi,n )ai,m Ditot .

Based on (1), the underwater acoustic uplink channel gain from AUV i to MASS m is calculated as 1 gi,m = . (3) H(di,m , f )NB Wi where NB is the oceanic noise power spectrum density and Wi denotes the allocated channel bandwidth for acoustic communications from AUV i to MASS m. Utilizing NOMA, the successive interference cancellation (SIC) necessitates an ordering based on their channel power gains relative to MASS m. The uplink channel gains at MASS m from different UAVs using NOMA are sorted in a descending order as g1,m > g2,m > ... > gi,m > ... > gI,m . According to Shannon theorem, the link transmission capacity from AUV i to MASS m can be calculated by ! pi gi si , (4) Ri,m = Wi log2 1 + P j∈I,j̸=i pj gj sj + NB where pi is the transmission power of AUV i and si represents link quality indicator during the offloading process of AUV i, which will be introduced in Section III-D. Then, the time to transmit a portion of task λi from AUV i to MASS m is calculated as ai,m Ditot tts . (5) i,m = Ri,m The corresponding energy consumption of AUV i is expressed as pi ai,m Ditot ts Ei,m = pi tts . (6) i,m = Ri,m (2) LOS Transmission from MASSs to LEOSs (i) Coverage Model of LEOSs: Different from terrestrial networks, LEOSs location dynamically vary, affecting the communication between MASSs and LEOSs. According to [42], the geometric relation between an LEOS and an MASS is depicted in Fig. 2, where h denotes the the altitude of the LEOS orbit, Re is the radius of the earth and dm,n represents the distance between MASS m and LEOS n, which is calculated as q (7) dm,n = Re2 + (Re + h)2 − 2Re (Re + h) cos ςm,n .

Fig. 1. The satellite-sea integrated network architecture.

B. Communication model (1) Underwater acoustic communication from AUVs to MASSs Based on the Urick’s model [40] [41], the transmission signal attenuation model tailored specifically for underwater acoustic communication between AUV i and MASS m is derived as: H(di,m , f ) = dσi,m Ω(f )ϱdi,m ,

(1)

where di,m is the distance between AUV i and MASS m, ϱ is the coefficient of di,m , Ω(f ) is the absorption coefficient, f denotes the central frequency of the acoustic signal, and σ is a spreading factor. The absorption coefficient Ω(f ) can be obtained according to the Thorp’s empirical formula in [41]. The distance between AUV i and MASS m is expressed as p di,m = (xm − xi )2 + (ym − yi )2 + (zm − zi )2 . (2)

In (7), ςm,n is the geocentric angle between MASS m and LEOS n, expressed as   Re · cos θm,n − θm,n , (8) ςm,n = arccos Re + h where θm,n is the elevation angle between MASS m and LEOS n, which is obtained by   Re + h θm,n = arccos · sin ςm,n . (9) dm,n Subsequently, we can determine the maximum communicate time between MASS m and LEOS n, denoted as T max =

2(Re + h) · ςm,n vn

(10)

q 0 where vn = RK is the moving speed of LEOS n and K0 is e +h the Kepler constant. Given the high-speed movement of LEOS,

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MASS m first receives ai,m Ditot of task λi from AUV i through acoustic communication and then transcodes the data for RF transmission. The transcoding time is ttc i,m =

δm ai,m Ditot ρm

(16)

where δm denotes the number of CPU cycles for processing one information bit of acoustic signal and ρm is the processing capacity of MASS m in CPU cycles per second. The energy consumption for transcoding data is expressed as Fig. 2. The geometric relation between LEOS n and MASS m in space.

tc 2 tot Ei,m = εm ρ3m ttc i,m = εm ρm δm ai,m Di .

the communication time between an MASS and an LEOS is constrained by the LEOS coverage duration. (ii) Communication Model from MASSs to LEOSs: The space segment comprises an LEO constellation, where each satellite is equipped with an MEC server to offer computing services to devices within its coverage area. Considering that all the MASSs share the spectrum resources of bandwidth W via FDMA, the transmission rate of MASS m is expressed as   pm | hm,n |2 . (11) Rm,n = αm W log2 1 + αm W N0 In (11), αm represents the proportion of bandwidth allocated to MASS m, pm denotes the transmission power of MASS m and hm,n = gm · βm · (dm,n )−χ , where gm is a complex Gaussian variable representing Rayleigh fading, βm denotes the fading involving shadowing, rain, and other fading, and χ is the path exponent. However, the distance between an MASS and an LEOS is relatively long, making the propagation delay non-negligible. Thus, the communication latency for transmitting partial workloads of AUV i between MASS m and LEOS n is calculated as tts i,n =

ai,m bi,n Ditot

2dm,n , c

(17)

(3) Local computing of MASSs: The latency of MASS m to complete the assigned task is denoted as (1 − bi,n )ai,m Citot . (18) tcom i,m = ρm The energy consumption for MASS m in terms of task computation is calculated as com 2 tot Ei,m = εm ρ3m tcom i,m = εm ρm (1 − bi,n )ai,m Ci ,

(19)

where εm is the effective power consumption coefficient of MASS m. (4) Local computing of LEOSs: The partial computation tasks of AUV i can be executed on the LEOS for further processing. We set ρn as the computation capacity (CPU cycles/s) of LEOS n and the execution time is calculated as ai,m bi,n Citot . (20) tcom i,n = ρn Similar to MASS, the energy consumption of LEOS n is calculated as com 2 tot Ei,n = εn ρ3n tcom i,n = εn ρn ai,m bi,n Ci ,

(21)

where c denotes the speed of light. The corresponding energy consumption of MASS m is expressed as   ai,m bi,n Ditot 2dm,n ts Ei,n = pm tts = p + . (13) m i,n Rm,n c

where εn is the effective power consumption coefficient of LEOS n in terms of task computation. The overall latency for completing AUV i’s workloads is calculated as   com ts tc com Titot = max tcom , tts . i i,m + ti,m + max ti,m , ti,n + ti,n (22)

C. Computation Model

D. Utility Model

(1) Local computing of AUVs: Regarding local computation, we denote ρi as the computation capacity (CPU cycles per second) of AUV i. The execution time of task λi is given by

(1) Utility function of AUVs: To express the level of satisfaction of AUVs (SoA) in performing computation offloading, we introduce a logarithmic function to reflect the computation offloading intention of AUVs [43]. The SoA function is concave and provides a quantitative assessment of the AUV’s satisfaction with offloading activities based on task offloading ratio ai,m to MASS m, given by

tcom = i

Rm,n

+

(1 − ai,m )Citot . ρi

(12)

(14)

The corresponding energy consumption Eicom for AUV i is computed as [25]: Eicom = εi ρ3i tcom = εi ρ2i (1 − ai,m )Citot , i

(15)

where εi is the effective power consumption coefficient of AUV i in terms of computation. (2) Data transcoding of MASSs:

ui = ln(1 + si ai,m ) + ϖi2

(23)

where si represents the link quality indicator during the offloading process of AUV i, and ϖi2 (ϖi ∈ [0, 1]) denotes the initial satisfaction of AUV i before the establishment of the MASS-assisted MEC system [43]. The value of ϖi2 is contingent upon the computing and communication capabilities of the

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neighboring MASS before the deployment of MEC system, as well as the AUV i’s individual computing requirements. The performance analysis of the satisfaction function is depicted in Fig. 3. When ϖi remains constant, AUV i’s satisfaction increases with the increase of si . When both ϖi and si are high, the satisfaction can reach its maximum even without offloading all tasks, as indicated by the blue line. When si is low (shown as the light blue line), the satisfaction rate increases slowly with the offloading rate, which means that if the signal quality is poor, AUV i may struggle to achieve high satisfaction even with substantial task offloading. The utility function of AUV i is 1 0.9

where qn denotes the cost of per unit of energy consumption of LEOS n. IV. P ROBLEM FORMULATION AND S OLUTION D ESIGN This section presents our problem formulation and the solution design devised to tackle the aforementioned challenges. We first describe the offloading strategies of AUVs and the pricing strategies of each MASS as a Stackelberg game. We then establish a Bargaining game model to capture the interaction between an MASS and an LEOS and determine their bidding strategies. Based on the aforementioned models in section-III, the following optimization problems are formulated to maximize the utilities of AUV i, MASS m, and LEOS n, respectively. For AUV i, the utility maximization problem is expressed as

0.8

(P1) : max Zi

Value of SoA

0.7

ai,m ,ki

0.6

s.t. (C1) − (C5).

0.5

Similarly, the optimization problem of MASS m is formulated as:

0.4 0.3

s=0.5, s=0.5, s=0.1, s=0.5, s=0.9,

0.2 0.1

=0.1 =0.9 =0.5 =0.5 =0.5

(P2) : max Zm ki ,bi,n

0 0

0.2

0.4

0.6

0.8

(27)

s.t. (C5) − (C8).

1

(28)

Offloading Ratio

For LEOS n, the optimization problem is formulated as: Fig. 3. Performance analysis of ui .

(P3) : max Zn

expressed as the difference between the SoA function of ui , the price paid to MASS m and the cost of completing its workload, given by ts Zi = ξi [ln(1 + si ai,m ) + ϖi2 ] − ki ai,m Ditot − qi (Ei,m + Eicom ),

(24) where ξi is a calibration factor of the SoA function to minimize the numerical discrepancy between ui and the associated workload processing cost, ki is the price for each bit of data that needs to be paid to MASS m and qi is the cost of per unit of energy consumption. (2) Utility function of MASSs: An MASS can assist in processing partial computation loads and its strategy is to determine the price for obtaining rewards from AUVs and the price paid to LEOS for assisting in computation workloads. For MASS m, the utility function is expressed as the difference between the revenue provide by AUV i, the price paid to LEOS, and the cost of processing its workloads, given by price ts tc com Zm = ki ai,m Ditot − ψi,m (bi,n ) − qm (Ei,n + Ei,m + Ei,m ), (25) where qm is the cost of per unit of energy consumption of MASS price and ψi,m (bi,n ) denotes the price paid to LEOS n given the offloading ratio bi,n , which will be introduced in Section IV-B. (2) Utility function of LEOSs: An LEOS can assist in workload computation to earn rewards from MASSs. For LEOS n, the utility function is expressed as the difference between the total revenue provide by MASS m and the cost of completing its workloads, given by price com Zn = ψi,m (bi,n ) − qn Ei,n ,

(26)

bi,n

s.t. (C6), (C9), (C10).

(29)

Where (C1) : 0 ≤ ai,m ≤ 1, ∀i ∈ I, ∀m ∈ M, ts (C2) : Eicom + Ei,m ≤ Eimax , ∀i ∈ I,

(C3) : Titot ≤ T max , ∀i ∈ I, (C4) : Zi ≥ 0, ∀i ∈ I, ∀m ∈ M, (C5) : 0 ≤ ki ≤ kimax , ∀i ∈ I, (C6) : 0 ≤ bi,n ≤ 1, ∀m ∈ M, ∀n ∈ N , com ts tc max (C7) : Ei,m + Ei,n + Ei,m ≤ Ei,m , ∀m ∈ M,

(C8) : Zm ≥ 0, ∀i, m, n, com max (C9) : Ei,n ≤ Ei,n , ∀m ∈ M,

(C10) : Zn ≥ 0, ∀m, n.

(30)

In (30), constraint (C1) and constraint (C6) indicate that the offloading ratio is in between 0 and 1. Constraint (C2), (C7) and (C9) guarantee that the energy consumption of each party cannot exceed the maximum value. Constraint (C3) ensures that the task completion time of AUV i cannot exceed the maximum LEOS coverage time. Constraint (C4), (C8) and (C10) guarantee the utility of each party be higher than or equal to 0. Constraint (C5) indicates that the price determined by AUV i cannot exceed the maximum value. Since the variables in (P1), (P2), and (P3) are closely coupled, solving the optimization problems is non-deterministic polynomial-time hard (NP-hard). The solution space for the formulated problem is immense, and as the number of AUVs escalates, the computational effort increases exponentially, which

8

is similar to the Traveling Salesman Problem (TSP, a well-known NP-hard problem) [44]. Finding the optimal solution through a centralized approach is not tractable in polynomial time. To overcome these challenges, we develop a hybrid StackelbergBargaining game framework to optimize the task offloading strategies and resource pricing policies in a distributed way with low computation complexity.

Algorithm 1: BSA Algorithm. Input: Given the tolerable computation-error δ; Output: The optimal value a∗i,m and the corresponding value of Zi (a∗i,m ); l 1 Initialization: Set the lower bound as ai,m , set the upper h bound as ai,m ; h l 2 while |ai,m − ai,m | > δ do 1 h l 3 Update the current value of acur i,m = 2 (ai,m + ai,m ); ′ 4 Obtain the value of Zi (acur A. Stackelberg Game Formulation between AUVs and MASSs i,m ); ′ cur 5 if Z (a ) < 0 then i i,m We describe the interaction between an AUV and an MASS Update the upper bound of the search range as as a Stackelberg game model. An MASS, say MASS m, is the 6 ahi,m = acur i,m ; leading player responsible for establishing the pricing strategies 7 else for task processing and reward acquisition. Subsequently, an ′ if Zi (acur AUV, say AUV i, as the follower, determines its offloading 8 i,m ) > 0 then 9 Update the lower bound of the search range ratio in response to the price established by MASS m, with the l cur as a objective of optimizing its overall revenue. Given the predefined i,m = ai,m ; else pricing strategies of MASS m, our initial step is to analyze the 10 Set a∗i,m = acur offloading ratio of AUV i to optimize its utility. In accordance 11 i,m ; Calculate the value of Zi (a∗i,m ); with the objective function of the problem, we derive the first- 12 13 end order derivative of Zi with respect to ai,m as 14 end ξi si qi pi Ditot ∂Zi (ai,m ) = − ki Ditot + qi εi ρ2i Citot − . 15 end ∂ai,m 1 + si ai,m Ri,m (31) Then, the second derivative of Zi with respect to ai,m is Algorithm 2: LSA Algorithm. calculated as cur 1 Initialization: j = 0, the current best value Zm , the cur ∂ 2 Zi (ai,m ) ξi s2i current best price ki , the step size π; =− . (32) min ∂a2i,m (1 + si ai,m )2 2 Set ki (j) = ki ; max 3 while ki (j) < ki do As the second derivative of the utility function is negative, Zi 4 Invoke Algorithm 1 to obtain a∗i,m ; is identified as a strictly concave function with respect to ai,m , Calculate Zm (ki (j)) according to Eq. (26); and the first derivative of Zi decreases with ai,m , which proves 5 cur 6 if Zm < Zm (ki (j)) then the existence of Stackelberg equilibrium. cur ← Zm (ki (j)); 7 Update Zm Then, we obtain cur 8 Update ki ← ki (j); ′ end lim Zi (ai,m ) = ξi si − A (33) 9 ai,m →0 10 j ← j + 1; 11 Update ki (j) with ki (j + 1) = ki (j) + π; and ′ ξi si 12 end lim Zi (ai,m ) = −A (34) cur ∗ cur ∗ ai,m →1 1 + si 13 Obtain the optimal price ki = ki , Zm = Zm ; ∗ ∗ 14 Return ki and Zm ; ′ where Zi (ai,m ) = ∂Zi (ai,m )/∂ai,m and A = ki Ditot − qi εi ρ2i Citot + qi pi Ditot /Ri,m in (33) and (34). The maximum utility of AUV i is expressed as  B. Bargaining Game Formulation between MASSs and LEOSs  if ξi si − A < 0 Zi (0), We model the interaction between an MASS and an LEOS ξi si max Zi = Zi (a∗i,m ), if 1+s − A ≤ 0 ≤ ξi si − A (35) i ai,m  as a Bargaining game, where MASS m is the buyer intending  ξi si Zi (1), if 1+s −A>0 i to purchase computation services for processing workloads, ′

where a∗i,m is the root of Zi (a∗i,m ) = 0. In Algorithm 1, we propose a binary search algorithm (BSA) to obtain the value of a∗i,m . After obtaining the optimal offloading strategy of AUV i, similarly,we analyze (P2) to derive the pricing strategies of MASS m. To find the optimal value of ki , we propose a linear search algorithm (LSA) within the given interval [0, kimax ] to numerically obtain the optimal solution of MASS m, as shown in Algorithm 2.

while LEOS n serves as the seller to get revenue by providing computation resources. The satisfaction functions of MASS m and LEOS n are expressed, respectively, as ! 1 ui,m = ωi,m ln 1 + com (36) ti,n and ui,n = ωi,n ln (1 + bi,n ) ,

(37)

9

where ωi,m and ωi,n are the weighting parameters indicating the degrees of satisfaction of MASS m and LEOS n, respectively. On this basis, we define the tender price for MASS m as ϕi,m (bi,n ) = min {B, ui,m } ,

(38)

ts tc com where B = ki ai,m Ditot − qm (Ei,n + Ei,m + Ei,m ). Similarly,

the tender price for LEOS n is formulated as  com ϕi,n (bi,n ) = max qn Ei,n , ui,n .

(39)

For MASS m, its satisfaction degree is higher if LEOS n completes its offloaded workloads within a shorter time. For LEOS n, its satisfaction degree increases with the offloaded workload volume, indicating higher revenue. The final transaction price is calculated as price ψi,m (bi,n ) = ηi ϕi,m (bi,n ) + (1 − ηi )ϕi,n (bi,n )

(40)

where the weighting parameter ηi (0 ≤ ηi ≤ 1) determines the weights of profit distribution between MASS m and LEOS n. The optimal transaction price is determined through a Bargaining game, which involves two bargainers negotiating the distribution of the Bid-ask Spread ϕi,m (bi,n ) − ϕi,n (bi,n ). If ϕi,m (bi,n ) < ϕi,n (bi,n ), the transaction is cancelled, as the bidding price of MASS m is less than that of LEOS n. If ϕi,m (bi,n ) = ϕi,n (bi,n ), the transaction price is determined as ϕi,m (bi,n ) or ϕi,n (bi,n ). The bargaining game exists only when the bidding strategy satisfies ϕi,m (bi,n ) > ϕi,n (bi,n ). In this case, MASS m intends to minimize its expenses, while LEOS n aims for maximizing its profit earning. Basically, it is a zero-sum game on the total transaction surplus ϕi,m (bi,n ) − ϕi,n (bi,n ). After the transaction, price LEOS n obtains the remaining ψi,m (bi,n ) − ϕi,n (bi,n ), and price MASS m obtains the remaining ϕi,m (bi,n ) − ψi,m (bi,n ). According to Rubinstein’s bargaining model [45], in an infinite round of Bargaining game, we complete the bargaining process within the first round and obtain the distinct subgame Nash equilibrium as µi,n (1 − µi,m ) , (41) ηi∗ = 1 − µi,m µi,n where µi,m ∈ [0, 1] and µi,n ∈ [0, 1] are the discount factors which represent the respective patience levels exhibited by MASS m and LEOS n. A higher patience level corresponds to a higher discount factor value, indicating a greater willingness to negotiate, while a lower patience level corresponds to a lower discount factor value, reflecting more impatience [46]. Since MASS m aims to complete its computation workloads efficiently, its discount factor increases as the completion time for workload computation decreases. Then, µi,m is formulated as   1 ln(1 + tcom ) − ln 1 + com i,n ti,n   . (42) µi,m = γi,m 1 com ln(1 + ti,n ) + ln 1 + tcom i,n

Similarly, LEOS n also strives to reap greater benefits by efficiently completing workloads and its discount factor µi,n increases with the increase of the offloading ratio bi,n , given by   1 ln(1 + bi,n ) − ln 1 + bi,n   . µi,n = 1 − γi,n (43) 1 ln(1 + bi,n ) + ln 1 + bi,n

γi,m and γi,n indicate the the patience coefficients of MASS m and LEOS n, respectively. Obviously, both players aim to reach a consensus on the proposed scheme for the transaction surplus distribution, as their utilities are diminished over time. Based on the hybrid Stackelberg game and Bargaining game, we propose a two-tier task offloading algorithm (TTA) based on pricing-based incentive mechanisms, as described in Algorithm 3. The algorithm consists of two stages: the first stage (from step 2 to step 5) is to obtain the Stackelberg equilibrium of (P1) and (P2), and the second stage (from step 8 to step 15) to obtain the bargaining equilibrium of (P2) and (P3). Algorithm 3: TTA Algorithm. Input: Given the tolerable computation-error δ, the step size π; ∗ Output: Zm and Zn∗ ; 1 Stage 1: Stackelberg equilibrium of (P1) and (P2); max 2 for ki ∈ [0, ki ] do 3 Invoke Algorithm 1 to calculate the value of a∗i,m ; 4 Invoke Algorithm 2 to obtain the optimal price ki∗ ; 5 end  ∗ ∗ 6 Input: the Stackelberg equilibrium as ai,m , ki ; 7 Stage 2: Bargaining equilibrium of (P2) and (P3); ∗ tot 8 Calculate the offloading workload ai,m Di ; ∗ 9 if ai,m ∈ (0, 1] then 10 Calculate ηi∗ with Eq.(41); 11 Calculate ϕi,m (bi,n ) and ϕi,n (bi,n ) with Eq.(38) and Eq.(39); price 12 Calculate the optimal bidding price ψi,m (bi,n ) with Eq.(40); 13 else 14 (P2) and (P3) are infeasible; 15 end We analyze the computational complexity of the proposed algorithms. The complexities of Algorithm 1 and Algorithm 2 largely depend on the number of iterations required for the algorithms to converge. We denote the number of iterations of Algorithm 1 and Algorithm 2 as J and Q, respectively. Then, we obtain the computation complexity of Algorithm 1 as O(I log2 (J)) for I AUVs. Similarly, the computational complexity of Algorithm 2 is O(QM )∗O(I log2 (J)) for I AUVs and M MASSs. For Algorithm 3, to obtain the Bargaining equilibrium of (P2) and (P3) for the tasks of I AUVs, the computational complexity is O(I). Therefore, the overall computational complexity of the proposed algorithms is O(QM ) ∗ O(I log2 (J)). V. P ERFORMANCE E VALUATION In this section, we conduct simulations to validate the effectiveness of our proposed scheme. Specifically, we assess the impact of key parameters on the utility of each party and compare the performance of our proposed method with other benchmark approaches. A. Simulation setup We conduct all the simulations with MATLAB on a PC configured with a Core i7-10510U 1.80 GHz CPU and 8 GB

10

TABLE III S IMULATION PARAMETER S ETTINGS Parameters The central frequency of the acoustic signal, f [47] The ocean noise power, NB [12] The air noise power, N0 Transmission power of AUV i, pi Transmission power of MASS m, pm The coefficient of di,m , ϱ [20] The elevation angle, θ [48] The computation capacity of AUV i, ρi The power consumption coefficient of AUV i, εi The computation capacity of MASS m, ρn The power consumption coefficient of MASS m, εm The computation capacity of LEOS n, ρn The power consumption coefficient of LEOS n, εn The number of CPU cycles for processing one bit of data in MASS m, δm [12]

Values 1kHz 1 × 10−4 dBm −174dBm/Hz 0.1W 0.5W 0.001 30◦ 1 × 106 cycles/s 5 × 10−20 4 × 106 cycles/s 1.5 × 10−22 6 × 108 cycles/s 2 × 10−23

• Random Pricing Scheme (RPS): In this scheme, the tender prices of MASS m and LEOS n are randomly determined in the bargaining game [3]. B. Numerical Results and Analysis Fig. 4 illustrates the variation in offloading ratio of AUV i as the number of iterations increases under different link quality. The proposed scheme consistently converges to a fixed value to achieve the optimal ai,m with the increasing number of iterations. Moreover, ai,m also increases as the link quality intensifies, indicating that the better the link quality, the more tasks tends to be offloaded by AUV i to conserve its energy consumption. The results presented in Fig. 4 also confirm the efficiency of the proposed BSA algorithm. 1 0.9

Offloading ratio of AUV i

of RAM. We consider a satellite-assisted maritime network comprised of one LEOS and five MASSs, which are deployed in a 500 × 500 × 500 m3 area, together with 5-30 AUVs capable of autonomous navigation. In the considered scenarion, AUVs make decisions regarding the amount of offloading tasks based on the pricing strategies issued by MASS. We assume AUV i has a total task volume of 50 Mbits. Each AUV communicates with MASS via NOMA, utilizing a channel bandwidth of 1 MHz, and each MASS communicates with LEOS through FDMA, employing a channel bandwidth of 10 MHz. The remaining simulation parameters are listed in Table III.

0.8 0.7 0.6 0.5 0.4 0.3

si=0.5

0.2

si=0.7

0.1

si=0.9

0

1 × 104 cycles

1

3

5

7

9

11

13

15

Number of iterations

Fig. 4. The variation of ai,m under different link quality.

Fig. 5 demonstrates how the utility of AUV i varies with the number of iterations and link quality. As the number of iterations increases, the algorithm converges to a fixed value for maximum utility. Additionally, the utility function of AUV i escalates as link quality intensifies. 108

4

si=0.5 si=0.7

3.5

Utility of AUV i

To validate the effectiveness and efficiency, we further compare the utility performance of the proposed scheme with the following benchmark schemes. • OFDMA based transmission scheme (OTS) [49]: In this scheme, each AUV uploads its workloads to an MASS via OFDMA through underwater acoustic communication, and the communication bandwidth is evenly allocated to each AUV. • Offloading Scheme based on Fixed Proportion (OSFP): In this scheme, the offloading ratio ai,m is predetermined and remains constant when AUV i transmits workloads to MASS. • Offloading Scheme based on Random Proportion (OSRP): Similar to [50], in this scheme, the offloading ratio ai,m is randomly determined when AUV i transmits workloads to MASS. • Offloading Scheme based on Linear Proportion (OSLP): In this scheme, the offloading ratio ai,m varies linearly with the total amount of data when AUV i transmits workloads to MASS. • Hierarchical Adaptive Search Algorithm (HAS) [51]: In this scheme, the optimal solution is progressively attained through iterations. • Linear Pricing Scheme (LPS): In this scheme, the tender prices of MASS m and LEOS n are linear with the offloading ratio bi,n in the bargaining game [12]. • Fixed Pricing Scheme (FPS): In this scheme, the tender prices of MASS m and LEOS n are predetermined and remains constant in the bargaining game.

si=0.9

3

2.5

2 1

3

5

7

9

11

13

15

Number of iterations

Fig. 5. The variation of Zi under different link quality.

Fig. 6 illustrates the variation in offloading ratio of AUV i as the number of iterations increases under different task volumes. This figure indicates that the proposed algorithm can always converge to a constant value within a finite number of iterations to attain the maximum utility, regardless of how much total workload needs to be processed.

11

1

2.5

108

0.8

proposed =0.5 =0.6

2

0.7

Utility of MASS

Offloading ratio of AUV i

0.9

0.6 0.5 0.4 0.3

D tot =45Mbit i D tot =50Mbit i D tot =55Mbit i

0.2 0.1 3

5

7

9

11

13

1

0.5

0 1

1.5

0.1

15

0.2

0.3

0.4

0.6

0.7

0.8

0.9

i,n

Fig. 8. Comparison of the utility of MASS under different bi,n .

Fig. 7 depicts the variation in the utility of both MASS and AUV throughout the iterations. As the number of iterations increases, their utilities converge to fixed values to obtain their respective maximums. The utility of MASS m increases with higher prices, while the utility of AUV i decreases as prices rise. Nevertheless, once the price surpasses a specific point, both settle into a Stackelberg equilibrium. This figure also verifies the effectiveness of the proposed LSA algorithm.

2

108 proposed =0.1 =0.2

1.8 1.6

Utility of LEO

Fig. 6. The variation of ai,m under different task volumes.

0.5

Offloading ratio b

Number of iterations

1.4 1.2 1 0.8 0.6 0.4

8

108

0.2 0.1

Utility of MASS m Utility of UUV i

7

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Offloading ratio bi,n

6

Fig. 9. Comparison of the utility of LEOS under different bi,n . Utility

5 4

cooperative nature of the game between AUVs. In contrast, the average utility of MASS increases rapidly as the number of AUVs increases. This is because, with more AUVs, MASS can process more computation tasks, thereby boosting profit margins and enhancing its utility.

3 2 1 0 5

10

15

20

25

30

Number of iterations

108 3.5

TTA OTS OSFP OSRP OSLP

Fig. 7. The variation of the utility of MASS m and AUV i. Average utility of AUV

3

Fig. 8 and Fig. 9 illustrate the comparison of the utilities of MASS and LEOS under varying bi,n and ηi , respectively. The benchmark is set using different proportion ηi for the Bargaining game. As bi,n increases, the utility of MASS decreases, while the utility of LEOS rises, due to the fact that the expenditure paid by MASS escalate with bi,n . When bi,n remains constant, an increase in ηi leads to a decrease in the utility of MASS and an increase in LEOS’s utility, as a larger share of the profits is allocated to LEOS with higher ηi . The proposed scheme can achieve better utility than others. Fig. 10 and Fig. 11 demonstrate the utility comparison of the proposed algorithms for AUV and MASS with different number of AUVs. As the number of AUVs escalates, we observe that our proposed scheme has the maximum utility for both the MASS and AUVs, because the proposed scheme takes the optimal offloading ratio ai,m and the optimal pricing strategies of ki into account. Moreover, as the number of AUVs escalates, the average utility of AUVs rises very slowly due to the non-

2.5 2 1.5 1 0.5 0 05

10

15

20

25

Number of AUVs

Fig. 10. Comparison of the average utility of AUVs with the number of AUVs.

Fig. 12 and Fig. 13 illustrate the utility comparison of our proposed scheme for MASS and LEOS under different values of the offloading ratio bi,n . With the increment of bi,n , we observe that the utility of MASS decreases, while the utility of LEOS increases. The rationale is that as bi,n increases, a greater

12

9

2

2 TTA OTS OSFP OSRP OSLP

1.8 1.6

1.5

1.4

Utility of LEOS

Average utility of MASS

8

10

1.2 1 0.8 0.6

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TTA HAS LPS FPS RPS

1

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0 05

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20

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25

0.3

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Offloading ratio b i,n

Number of AUVs

Fig. 11. Comparison of the average utility of MASSs with the number of AUVs.

Fig. 13. Comparison of the utility of LEOS under different bi,n .

proportion of workloads are offloaded to LEOS n, prompting MASS m to offer higher expenditure to LEOS n. Consequently, this enhances the utility of LEOS n while diminishing the utility of MASS m. The proposed scheme attains approximate optimal performance due to its consideration of the most advantageous bidding prices for both MASS m and LEOS n. In addition, we see that HAS outperforms the proposed TTA at times in terms of optimization performance, which stems from HAS’s ability to progressively converge towards the optimal solution by leveraging global information. However, acquiring global information in real-world applications is challenging, and centralized solutions often entail high time complexity.

optimize the pricing strategies of each MASS, to maximize their respective profits. Subsequently, for MASS-to-LEOS transmission, we consider the scenario where each MASS delegates a portion of its workloads to an LEOS via FDMA to avoid the co-channel interference. We formulate the interactions between an MASS and an LEOS as a Bargaining game to optimize their bidding strategies and maximize their respective revenues. Numerical results are presented to validate the efficiency and effectiveness of our proposed scheme. For future work, we will investigate efficient resource management for satellite-marine integrated networks to improve the overall system performance. In addition, we will explore the development of intelligent algorithms using deep reinforcement learning to improve the adaptability of decision-making process for task offloading in dynamic marine environments.

108 TTA HAS LPS FPS RPS

Utility of MASS

2

ACKNOWLEDGMENT

1.5

This work was supported by the National Natural Science Foundation of China under Grant 62371085, Grant 51939001 and Grant 62301411.

1

0.5

R EFERENCES 0 0.1

0.3

0.5

0.7

0.9

Offloading ratio b i,n

Fig. 12. Comparison of the utility of MASSs under different bi,n .

VI. C ONCLUSION AND F UTURE W ORK In this paper, we have considered a space-sea integrated network architecture and proposed a two-tier task offloading scheme for AUVs using a hybrid Stackelberg-Bargaining game approach to improve the efficiency of task offloading process. Initially, we implement a multi-access task offloading strategy through underwater acoustic communication, enabling AUVs to delegate their workloads to MASSs via NOMA. We formulate the task offloading interactions between AUVs and MASSs as a Stackelberg game to refine the AUV offloading strategy and

[1] M. Dai, C. Dou, Y. Wu, L. Qian, R. Lu, and T. Q. S. Quek, “Multi-UAV aided multi-access edge computing in marine communication networks: A joint system-welfare and energy-efficient design,” IEEE Transactions on Communications, vol. 72, no. 9, pp. 5517–5531, 2024. [2] Y. Liu, J. Yan, and X. Zhao, “Deep reinforcement learning based latency minimization for mobile edge computing with virtualization in maritime UAV communication network,” IEEE Transactions on Vehicular Technology, vol. 71, no. 4, pp. 4225–4236, 2022. [3] H. Zeng, Z. Su, Q. Xu, R. Li, Y. Wang, M. Dai, T. H. Luan, X. Sun, and D. Liu, “Usv fleet-assisted collaborative computation offloading for smart maritime services: An energy-efficient design,” IEEE Transactions on Vehicular Technology, vol. 73, no. 10, pp. 14718–14733, 2024. [4] Z. Lin, J. Yang, Y. Chen, C. Xu, and X. Zhang, “Maritime distributed computation offloading in space-air-ground-sea integrated networks,” IEEE Communications Letters, vol. 28, no. 7, pp. 1614–1618, 2024. [5] T. Lyu, H. Xu, F. Liu, M. Li, L. Li, and Z. Han, “Computing offloading and resource allocation of NOMA-based UAV emergency communication in marine internet of things,” IEEE Internet of Things Journal, vol. 11, no. 9, pp. 15571–15586, 2024. [6] G. Yue, C. Huang, and X. Xiong, “A task offloading scheme in maritime edge computing network,” Journal of Communications and Information Networks, vol. 8, no. 2, pp. 171–186, 2023.

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[7] H. Li, S. Wu, J. Jiao, X.-H. Lin, N. Zhang, and Q. Zhang, “Energy-efficient task offloading of edge-aided maritime UAV systems,” IEEE Transactions on Vehicular Technology, vol. 72, no. 1, pp. 1116–1126, 2023. [8] Q. Ye, W. Shi, K. Qu, H. He, W. Zhuang, and X. Shen, “Joint RAN slicing and computation offloading for autonomous vehicular networks: A learning-assisted hierarchical approach,” IEEE Open Journal of Vehicular Technology, vol. 2, pp. 272–288, 2021. [9] Y. Chen, K. Li, Y. Wu, J. Huang, and L. Zhao, “Energy efficient task offloading and resource allocation in air-ground integrated MEC systems: A distributed online approach,” IEEE Transactions on Mobile Computing, vol. 23, no. 8, pp. 8129–8142, 2024. [10] X. Hou, J. Wang, T. Bai, Y. Deng, Y. Ren, and L. Hanzo, “Environmentaware AUV trajectory design and resource management for multi-tier underwater computing,” IEEE Journal on Selected Areas in Communications, vol. 41, no. 2, pp. 474–490, 2023. [11] J. Wen, J. Yang, W. Wei, and Z. Lv, “Intelligent multi-AUG ocean data collection scheme in maritime wireless communication network,” IEEE Transactions on Network Science and Engineering, vol. 9, no. 5, pp. 3067– 3079, 2022. [12] M. Dai, Z. Luo, Y. Wu, L. Qian, B. Lin, and Z. Su, “Incentive oriented two-tier task offloading scheme in marine edge computing networks: A hybrid stackelberg-auction game approach,” IEEE Transactions on Wireless Communications, vol. 22, no. 12, pp. 8603–8619, 2023. [13] M. Dai, Y. Wu, L. Qian, Z. Su, B. Lin, and N. Chen, “UAV-assisted multi-access computation offloading via hybrid NOMA and FDMA in marine networks,” IEEE Transactions on Network Science and Engineering, vol. 10, no. 1, pp. 113–127, 2023. [14] J. Zhang, Q. Ye, K. Qu, Y. Sun, Y. Tang, D. Zhao, and T. Ye, “Learningassisted dynamic VNF selection and chaining for 6G satellite-ground integrated networks,” IEEE Transactions on Vehicular Technology, pp. 1– 17, 2024. [15] Q. Pan, S. Lin, W. Lu, Z. Wang, L. Wu, Y. Zou, B. Ai, and Z. Zhong, “Space-air-sea-ground integrated monitoring network-based maritime transportation emergency forecasting,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 3, pp. 2843–2852, 2022. [16] X. Fang, W. Feng, Y. Wang, Y. Chen, N. Ge, Z. Ding, and H. Zhu, “NOMAbased hybrid satellite-UAV-terrestrial networks for 6G maritime coverage,” IEEE Transactions on Wireless Communications, vol. 22, no. 1, pp. 138– 152, 2023. [17] H. Zeng, Z. Su, Q. Xu, and R. Li, “Security and privacy in space-air-ocean integrated unmanned surface vehicle networks,” IEEE Network, vol. 38, no. 3, pp. 48–56, 2024. [18] D. Wang, T. He, Y. Lou, L. Pang, Y. He, and H.-H. Chen, “Double-edge computation offloading for secure integrated space–air–aqua networks,” IEEE Internet of Things Journal, vol. 10, no. 17, pp. 15581–15593, 2023. [19] S. Qi, B. Lin, Y. Deng, X. Chen, and Y. Fang, “Minimizing maximum latency of task offloading for multi-UAV-assisted maritime search and rescue,” IEEE Transactions on Vehicular Technology, vol. 73, no. 9, pp. 13625–13638, 2024. [20] Z. Luo, M. Dai, Y. Wu, L. Qian, B. Lin, and Z. Su, “UAV-aided two-tier computation offloading for marine communication networks: An incentivebased approach,” in 2023 IEEE Wireless Communications and Networking Conference (WCNC), pp. 1–6, 2023. [21] H. Wu, Y. Shen, X. Xiao, G. T. Nguyen, A. Hecker, and F. H. P. Fitzek, “Accelerating industrial IoT acoustic data separation with In-Network computing,” IEEE Internet of Things Journal, vol. 10, no. 5, pp. 3901– 3916, 2023. [22] T. Yang, Z. Cui, A. H. Alshehri, M. Wang, K. Gao, and K. Yu, “Distributed maritime transport communication system with reliability and safety based on blockchain and edge computing,” IEEE Transactions on Intelligent Transportation Systems, vol. 24, no. 2, pp. 2296–2306, 2023. [23] L. Qian, M. Li, P. Ye, Q. Wang, B. Lin, Y. Wu, and X. Yang, “Secrecydriven energy minimization in federated-learning-assisted marine digital twin networks,” IEEE Internet of Things Journal, vol. 11, no. 3, pp. 5155– 5168, 2024. [24] Y. Dai, B. Lin, Y. Che, and L. Lyu, “UAV-assisted data offloading for smart container in offshore maritime communications,” China Communications, vol. 19, no. 1, pp. 153–165, 2022. [25] Z. Wang, B. Lin, Q. Ye, Y. Fang, and X. Han, “Joint computation offloading and resource allocation for maritime MEC with energy harvesting,” IEEE Internet of Things Journal, vol. 11, no. 11, pp. 19898–19913, 2024. [26] M. Dai, N. Huang, Y. Wu, L. Qian, B. Lin, Z. Su, and R. Lu, “Latency minimization oriented hybrid offshore and aerial-based multi-access computation offloading for marine communication networks,” IEEE Transactions on Communications, vol. 71, no. 11, pp. 6482–6498, 2023.

[27] P. Gjanci, C. Petrioli, S. Basagni, C. A. Phillips, L. Bölöni, and D. Turgut, “Path finding for maximum value of information in multi-modal underwater wireless sensor networks,” IEEE Transactions on Mobile Computing, vol. 17, no. 2, pp. 404–418, 2018. [28] J. You, Z. Jia, C. Dong, L. He, Y. Cao, and Q. Wu, “Computation offloading for uncertain marine tasks by cooperation of UAVs and vessels,” in ICC 2023 - IEEE International Conference on Communications, pp. 666–671, 2023. [29] M. Li, L. P. Qian, X. Dong, B. Lin, Y. Wu, and X. Yang, “Secure computation offloading for marine IoT: An energy-efficient design via cooperative jamming,” IEEE Transactions on Vehicular Technology, vol. 72, no. 5, pp. 6518–6531, 2023. [30] X. Guo, Y. Luo, N. Yan, W. An, and K. Ma, “Multibeam transmit-reflectarray antenna using alternating transmission and reflection elements for space–air–ground–sea integrated network,” IEEE Transactions on Antennas and Propagation, vol. 71, no. 11, pp. 8668–8676, 2023. [31] S. S. Hassan, D. H. Kim, Y. K. Tun, N. H. Tran, W. Saad, and C. S. Hong, “Seamless and energy-efficient maritime coverage in coordinated 6G space–air–sea non-terrestrial networks,” IEEE Internet of Things Journal, vol. 10, no. 6, pp. 4749–4769, 2023. [32] Z. Li, J. Wen, J. Yang, J. He, T. Ni, and Y. Li, “Energy-efficient space–air–ground–ocean-integrated network based on intelligent autonomous underwater glider,” IEEE Internet of Things Journal, vol. 10, no. 11, pp. 9329–9341, 2023. [33] Y. Zhang, P. Zhang, C. Jiang, S. Wang, H. Zhang, and C. Rong, “QoS aware virtual network embedding in space-air-ground-ocean integrated network,” IEEE Transactions on Services Computing, vol. 17, no. 4, pp. 1712–1723, 2024. [34] Y. Lin, Z. Xu, J. Li, J. Wang, C. Li, Z. Huang, and Y. Xu, “Resource management for QoS-guaranteed marine data feedback based on space–air–ground–sea network,” IEEE Systems Journal, vol. 18, no. 3, pp. 1741–1752, 2024. [35] H. Wu, J. Nie, Z. Xiong, Z. Cai, T. Zhou, C. Yuen, and D. Niyato, “A gamebased incentive-driven offloading framework for dispersed computing,” IEEE Transactions on Communications, vol. 71, no. 7, pp. 4034–4049, 2023. [36] Y. Chen, J. Zhao, Y. Wu, J. Huang, and X. S. Shen, “Multi-user task offloading in UAV-assisted LEO satellite edge computing: A game-theoretic approach,” IEEE Transactions on Mobile Computing, vol. 24, no. 1, pp. 363–378, 2025. [37] X. Zhang, Z. Wang, F. Tian, and Z. Yang, “Stackelberg-game-based multiuser multi-task offloading in mobile edge computing,” IEEE Transactions on Cloud Computing, vol. 12, no. 2, pp. 459–475, 2024. [38] Z. Niu, H. Liu, Y. Ge, and J. Du, “Distributed hybrid task offloading in mobile-edge computing: A potential game scheme,” IEEE Internet of Things Journal, vol. 11, no. 10, pp. 18698–18710, 2024. [39] K. Peng, Y. Yang, S. Wang, P. Xiao, and V. C. M. Leung, “Reliability-aware proactive offloading in mobile edge computing using stackelberg game approach,” IEEE Internet of Things Journal, vol. 11, no. 9, pp. 16660– 16671, 2024. [40] R. Ma, R. Wang, G. Liu, W. Meng, and X. Liu, “UAV-aided cooperative data collection scheme for ocean monitoring networks,” IEEE Internet Things J., vol. 8, no. 17, pp. 13222–13236, 2021. [41] D. E. Lucani, M. Stojanovic, and M. Medard, “On the relationship between transmission power and capacity of an underwater acoustic communication channel,” in Proc. MTS/IEEE Kobe Techno-Ocean, pp. 1–6, 2008. [42] B. Elbert, Introduction to Satellite Communication. Norwood, MA, USA: Artech House, 2008. [43] M. Wang, L. Zhang, P. Gao, X. Yang, K. Wang, and K. Yang, “Stackelberggame-based intelligent offloading incentive mechanism for a multi-UAVassisted mobile-edge computing system,” IEEE Internet of Things Journal, vol. 10, no. 17, pp. 15679–15689, 2023. [44] M. R. Garey and D. S. Johnson, “Computers and intractability: A guide to the theory of np-completeness,” W. H. Freeman, 1983. [45] R. A, “Perfect equilibrium in a bargaining model,” Econometrica, vol. 50, no. 1, pp. 97–109, 1982. [46] Z. Sun, G. Sun, Y. Liu, J. Wang, and D. Cao, “Bargain-match: A game theoretical approach for resource allocation and task offloading in vehicular edge computing networks,” IEEE Transactions on Mobile Computing, vol. 23, no. 2, pp. 1655–1673, 2024. [47] R. Ma, R. Wang, G. Liu, W. Meng, and X. Liu, “UAV-aided cooperative data collection scheme for ocean monitoring networks,” IEEE Internet of Things Journal, vol. 8, no. 17, pp. 13222–13236, 2021. [48] Q. Tang, Z. Fei, B. Li, and Z. Han, “Computation offloading in LEO satellite networks with hybrid cloud and edge computing,” IEEE Internet of Things Journal, vol. 8, no. 11, pp. 9164–9176, 2021.

14

[49] L. Wu, Z. Liu, P. Sun, H. Chen, K. Wang, Y. Zuo, and Y. Yang, “DOT: Decentralized offloading of tasks in OFDMA-based heterogeneous computing networks,” IEEE Internet of Things Journal, vol. 9, no. 20, pp. 20071–20082, 2022. [50] X. Lin, A. Liu, C. Han, X. Liang, K. Pan, and Z. Gao, “LEO satellite and UAVs assisted mobile edge computing for tactical Ad-Hoc network: A game theory approach,” IEEE Internet of Things Journal, vol. 10, no. 23, pp. 20560–20573, 2023. [51] T. Zhou, Y. Yue, D. Qin, X. Nie, X. Li, and C. Li, “Joint device association, resource allocation, and computation offloading in ultradense multidevice and multitask iot networks,” IEEE Internet of Things Journal, vol. 9, no. 19, pp. 18695–18709, 2022.

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