A Sequential Game Approach for Computation-Offloading in an UAV Network Mohamed-Ayoub Messous1, Amel Arfaoui1, Ahmed Alioua2, Sidi-Mohammed Senouci1 1
DRIVE EA1859, Univ. Bourgogne Franche Comté, F58000, Nevers, France. 2 LSI, Computer Science Department, USTHB, Algiers, Algeria {ayoub.messous; amel.arfaoui; sidi-mohammed.senouci}@u-bourgogne.fr;
[email protected] Abstract—Small drones are currently emerging as versatile nascent technology that can be used in exploration and surveillance missions. However, most of the underlying applications require very often complex and time-consuming calculations. Although, the limited resources available onboard the small drones, their mobility, the computation delays and energy consumption make the operation of these applications very challenging. Nevertheless, computation-offloading solutions provide feasible resolves to mitigate the issues facing these constrained devices. In this context, we address in this paper the problem of offloading highly intensive computation tasks, performed by a fleet of small drones, in order to improve the energy overhead and decrease the execution delay. We adopt a theoretical methodology based on a sequential game where three different types of players (drone, base station and edge server) carry out the heavy computation tasks. Compared to literature, as far as we know, we are the first to consider a computationoffloading problem with three different devices. Each player has a set of possible strategies, depending on the previous actions that the other players might undertake in a sequential game. Furthermore, we prove the existence of a Nash Equilibrium and design an offloading algorithm that converges to this optimal point. Extensive simulations gave promising results where the sequential game based model outperforms comparable approaches in terms of global utility, which pledges the best possible tradeoff between energy consumption and achievable delay. Keywords—Small drones network; Computation-offloading; Sequential game.
I. INTRODUCTION UAVs (Unmanned Aerial Vehicles), also known as drones, continue to attract much attention. While initially intended for strategic and defense programs, recent technological advances have led to the emergence of smaller and significantly cheaper UAVs, which made the technology easier to acquire, maintain and handle. Thanks to this, their usage was democratized in civil applications and UAVs proved to be versatile and quite useful in rescue missions, target detection, remote sensing, surveillance, service delivery, pollution detection and farming [1][4]. Nevertheless, many issues are yet to be overcome, for instance in order to be fully operational in surveillance applications, UAVs need to detect, classify and identify objects or situations beforehand. Consequently, UAVs are brought to deal with highly intensive computation tasks such as video preprocessing, pattern recognition and feature extraction, which typically require complex calculation and dedicated processors. However, despite the ever-increasing UAVs’ capabilities, the applications’ resource requirements can often transcend what is
available within a single UAV. Therefore, performing a computationally intensive task onboard a constrained UAV may result in slow response times and considerable energy usage, which might eventually affect mission success, especially for real-time applications such as forest fire detection or research and rescue missions. In this context, a cloud-based solution would offer a pertinent solution in order to address the issues related to the limited resources and the intermittent connectivity in UAV networks [5]. Several literature studies prescribed offloading from constrained devices to closely located or even to remote powerful cloud computing resources [6]. Providing unrestricted computing capabilities at the edge of the access networks, mobile edge cloud is one of the new paradigms that are taking a large magnitude throughout industry and academia. In the last few years, Mobile Edge Computing (MEC) was revealed as a very promising concept in order to enhance network performance, as well as the user experience. Due to the limitations of mobile devices in terms of processing power and battery life, MEC-based solutions offer an attractive approach to address these shortcomings. Indeed, when intensive computation tasks are offloaded to an edge server, some significant performances can be achieved [7-10]. Existing research works, summarized in [7] and [8] considered computation-offloading to servers in the cloud or in the edge of the access network. The work presented in [9] suggests using a cloudlet-based infrastructure in order to further reduce power consumption and network delay when using mobile cloud computing. We address throughout this study the challenges related to energy and time sensitive applications where computationally intensive tasks are performed by a fleet of small drones. Furthermore, we tackle the problem of computation-offloading and adopt a theoretical game methodology to solve it. We consider a set of three different types of players, namely, (i) drone, (ii) Base station, and (iii) edge server. Besides, each player participates in a sequential game and has a set of different possible strategies. We also define a new utility function, which takes as input a weighted combination between energy consumption and time delay. To the best of our knowledge, we are the first to ever consider three different offloading approaches, while using a sequential game approach, rather than classical two approaches-based models. Hence, a task in our computation scheme can be either treated: (i) in the drone, (ii) offloaded to a neighboring base station, or (iii) offloaded to an edge server.
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The main contributions of the present paper are as follow: We formulate an all-new computation-offloading solution based on a theoretical game. Moreover, we model the interactivity among three different players as a sequential offloading decision game with a set of different strategies. The players work together in order to optimize a global utility function, which is defined as the best possible combination between energy consumption and time delay. We show the existence of a Nash equilibrium and provide a compatible algorithm to resolve the problem. Besides, simulation results prove the model effectiveness compared to other approaches. The rest of the paper is organized as follows: we first present the system model is Section II. Section III provides details about our sequential computation-offloading game, the existence of a Nash Equilibrium and an algorithm to attain this equilibrium. Results achieved through simulation work are presented and discussed in Section IV. Section V summarizes relevant related works and section VI concludes the paper. II. SYSTEM MODEL We present in this section the system model and the computation-offloading problem formulation. We consider throughout our study a set of small UAVs performing an exploration mission that involve computing highly intensive computation tasks. Each task Ti is defined through two numerical values {Ci, Di} representing respectively the number of computation cycles indicating the task’s complexity and the data size specifying the amount of data necessary to achieve this computation task. Besides the required input parameters for the computation, Di can even contain the task’s source code which can be either executed in the drone or offloaded to a more powerful distant device if necessary. Furthermore, the network model throughout this paper is composed of three different entities: (i) a drone, (ii) a base station and (iii) an edge server (see Figure 1). In the following subsections, we first present and justify the communication model of the entailed network. Then, we highlight the different possible computation scenarios. Finally, we detail the utility function and the different inputs required to compute its values. A. Network Model Wi-Fi is the most recognized wireless technology that uses a set of standards for implementing wireless local area network (WLAN) communication. It can create a wireless link between a mobile device and an access point or between two wireless devices. Furthermore, this technology has been widely used in UAV related applications [4][11-13]. For instance, it has been used in [11] to implement a flight control scheme with a realtime data such as photo and video transmission between UAVs and devices on the ground. This line of work supports the feasibility of offering Wi-Fi services through flexible UAV platforms. Another study, presented in [12], focused on enhancing Wi-Fi bandwidth for communications between UAV and ground stations. Furthermore, the experimental work results presented in [13] showed the viability of using 802.11 interfaces for UAV-based networking. Since cellular access is widely spread, we consider in the sketch shown in Figure 1 that the drone has a cellular network access along with a second 802.11 wireless interface. Communications between the drone and the base station is achieved via Wi-Fi whereas a cellular network (4G/LTE) is
Fig. 1. System architecture
used to access the server at the edge of the access network. Likewise, even the base station uses a cellular link to communicate with the edge server, this assumption holds in order to consider a general use case and a more generic scenario where the base station is mounted in a ground mobile vehicle. Moreover, since our prime focus in this paper is on the computation-offloading problem in its wide form, we consider an orthogonal wireless channel selection based on devices placements, signal strength and background interferences to compute the actual communication data rate. Given the space limitation, further details can be found in [14]. B. Computation Models In the set of drones, each device has one or more highly intensive computation tasks. Each task Ti is characterized by the number of CPU cycles Ci necessary to perform the calculation and the size of required data, Di. The latter can include both the input parameters necessary for the computation and the program code to be executed. UAVs have to decide whether to execute their computation tasks either locally or offload them to one of two possible remote devices: (i) a Base Station or (ii) an Edge Server. Therefore, three possible choices with three different utility values are available for each UAV: (i) perform their tasks locally, (ii) offload them via a local wireless connection to a neighboring base station, or finally (iii) through a cellular connection to a more powerful server at the edge of the access network. Besides, the base station on its turn, when it receives a computation task through the Wi-Fi interface from a neighboring UAV, can either compute it locally or offload it once more to an even more powerful server through the cellular link. Subsequently, the two possible choices of action for the base station are: (i) perform the task locally, (ii) offload it via a cellular connection to the edge server. Finally, the edge server can either accept or refuse the requests it would receive from both the drone and the base station. The details related to all the possible cases for each device and how they would affect the energy and delay performances are provided in Section IV. C. Utility Funtion We defined our cost function as a combination of two performance metrics: energy and delay. Since all mobile devices are battery powered, their available energy still is a limited resource. Therefore, the wise management of this constrained resource is quite crucial for the device lifetime. Moreover, intensive computation tasks are known to require a considerable amount of time to complete their execution, even with slightly powerful processors. For these reasons, we drew a global utility function as a joint equation of computation and
communication delays along with energy consumption. Resulting function for each task is given as: = + (1) Where α and β represent the weighting factors for delay and energy respectively and α+β=1. , are the maximum values for delay and energy, which are used in order to normalize these two disjoint values. Furthermore, the drive behind the use of α and β is to enhance the flexibility and address specific requirements for different potential applications. Thus, the values of the weighting parameter can be adapted according to the intended scenarios or even to handle specific situations. For instance, a delay sensitive task would require a higher value for α in order to reduce the response time, whereas, to put the emphasis on energy consumption in case of energy shortage β would take a higher value. We tackle throughout our work the problem of offloading highly intensive computation tasks from constrained, less powerful, network nodes to more powerful and less constrained devices. Based on the system model presented above, we formulate in the following section our computation-offloading solution using a theoretical game approach. We implement a sequential game based on three different types of player, where each player has a set of different possible strategies. III. SEQUENTIAL GAME FOR COMPUTATION-OFFLOADING Computation-offloading offers a promising solution for constrained mobile devices, such as UAVs in our case, to achieve better performances when processing heavy computation tasks. Based on the previously presented computation and communication models, we can state that possible action choices for the different entities in the network are mutually related. This means that each device decision will have a direct impact on the other devices in the network. In order to address how to achieve the best possible computationoffloading decision, we present in more details throughout the following subsections the proposed theoretical game model. A. Sequential Game Formulation One of the main reasons for choosing game theory as an enabling framework is the decentralized nature of the decision making process achieved by the network nodes [15]. Since the latter may have different requirements and eventually do not pursue the same interest, a decentralized scheme is required. In addition, game theory is perceived as a powerful tool to analyze the interactions among multiple players that are supposed to act toward achieving their own interests. Each player chooses the best possible strategy to achieve its own goals. Thus, by leveraging the intelligence of each individual device, decentralized schemes are devised with low complexity. Consequently, players ought to self-organize into a mutually satisfactory solution such that no player has the incentive to deviate unilaterally. Therefore, it would indeed ease the burden of implementing a more complex centralized system. This mutually satisfactory solution where no player has the incentive to individually change its strategy is called Nash Equilibrium [16]. The sequential game is defined as the 3-tuple SG (N, S, U); where: N={UAV, BaseStation, Server} represents the set of players, S={ , , } are the set of respective strategies for each player and finally U are their global utility function. The values of the global utility function are governed
Fig. 2. Synoptic scheme of the utility and the strategies for each player
by the decisions made by the players and their respective utilities. B. Strategies per player Figure 2 shows a synoptic depiction for the whole system. We recognize three players in the game, namely: (i) UAV, (ii) BaseStation, and (iii) Server. Each player has a specific set of possible strategies, shown in equation 2, which would eventually dictate the values of their local utility functions. More details are given in the following. ={ , , } } ={ , (2) = , 1) UAV player As shown in Figure 2, three possible computation choices for each drone are possible, ): In this case the a) Local Computing ( computation tasks are executed locally within the drone, therefore no actual data ought to be sent via wireless interfaces. Subsequently, the amount of time required to execute a task Ti= {Ci, Di} if the CPU frequency of the drone is is given shown in equation (1) along with which represents the expected energy consumption. = / (3) = ∗ Where, is a coefficient representing the energy consumed per CPU cycle. ): This strategy is the b) Offload to Base Station ( second possible action for the UAV. The computation task is offloaded through the wireless access point to the nearby base station. In this case, the time delay and energy cost for the UAV are given respectively as: = / (4) = ∗ Where, is the effective data rate achieved through the represents the coefficient wireless local network and measuring the energy necessary to send one data unit through the available access point network to the base station. c) Offload to Server ( ): represents a second offloading approach and the third possible choice for the UAV. In which the drone sends the computation task via the cellular network to a server at the edge of the access network. This latter
will compute the received task instead of the mobile node. Similar to the previous option, the resulting delay and energy are correlated to the size of data being send. Therefore, the equation for the required time and energy would be written as: = / (5) = ∗ is the effective data rate achieved through the Where, cellular network and denotes the consumption coefficient required to send one unit of data through the cellular network from the drone to the edge server. 2) Base Station player As part of the network architecture, this device has the possibility of computing the tasks that may arrive from the drones. On its turn, the base station has two possible choices: a) Local Computing ( ): Since the base station has more powerful computation resources and less constrained energy resources compared to the UAVs, computing the task locally would achieve better performance. Subsequently, the energy and delay in this case are computed as follow: = / (6) = ∗ denotes the CPU frequency available within the Where, base station and is the energy consumption parameter for each CPU cycle. ): The second possible action b) Offload to Server ( performed by the base station is to offload the computation task to the edge server rather than executing it locally. In some cases, this second choice can outperform the performance of the first choice of the base station, especially for highly intensive tasks with small limited data size. The corresponding delay and energy equations, provided in the flowing, are only related to the size of data Di. = / (7) = ∗ is the cellular network data rate within the base Where, station and is the coefficient measuring the energy necessary to send one unit of data through cellular link from the base station to the server at the edge of the access network. 3) Edge server player As the third player in our game, the edge server has two possible strategies. On the first hand, it can accept to perform the tasks that it may receive from the UAV or from the base station. On the other hand, it might, in some extreme cases, refuse the execution. In this case, the originating device of the computation task, after being receiving a decline message from the server, would perform the task locally. a) Accept ( ): Even though the energy resource is abundantly available for the server when compared to the drone and even to the base station, its wise management is still important. = / (8) = ∗ represents the frequency of the server’s CPU, Where, which in practice is very big compared to the running frequency for the mobile devices CPUs. b) Reject ( ): In this second strategy, the edge server would decine the computation task. Thus, the delay and time would be equal to null. Wheareas, the computation would be achieved within the originating device of the task.
TABLE I.
NORMAL-FORM REPRESENTATION OF GLOBAL UTILITY
Base Station Server U1 UAV
U2 U5
U3 U5
U6
U4 U6
UAV S
U1
S S Server
Base Station
S
S
S
U2
U5
Server S
U6
S U3
Fig. 3.
S
U4
Extensive-form representation of global utility
= 0
(9) = 0 As many previous studies [17-19], we neglect the delay overhead required to send back the computation result to its respective initiator. In the vast majority of cases, the size of the resulting data for an intensive computation task is considered very small and eventually insignificant compared to the size of the input data. This assumption holds for many scenarios such as video processing, feature extraction and pattern recognition algorithms, where the program codes and input parameters size are much bigger than the input data. C. Global Utility Functions Based on the system model provided above, we propose the sequential game formulation shown in Figure 3. The decisionmaking process, for each player, is always govenred by the environmental conditions change. The multi-objective utility function, presented in section II, implements a correlation between delay and energy consumption. A global utility funtion needs to consider all the different strategies for each player involved in the computation scenario. As shown in Table I, six possible strategy profiles reflecting the different conceivable scenarios can be enumerated, which are given as follows: = = ={
,∗ ,∗ , ,
,∗ ,
}
= = ={
,
, ,∗, ,∗,
}
The global utility funtions, depictecd in Figure 3 for each strategy profile, are given as follow: = ) + ( = + ) ( + + = ( + + ) + + + = ( + + + ) + = ( + ) + + = ( + + )
D. Equilibirum Analyisis and Offloading Algorithm We investigate, in this subsection, the existence of an emerging equilibrium point and implement an offloading algorithm for the sequential game presented in previous sections. A strategy profile is called a Nash equilibrium if no player can achieve a better utility by unilaterally changing its strategy. This equilibrium point grants a mutually satisfactory solution for all the players, such that no player has the incentive to deviate individually [20]. This optimal satisfactory solution would be eventually reached in order to get the best possible performances. Theorem.1 Dynamic games where players have finite action sets and act only a finite number of times are equivalent, and every finite extensive-form game with perfect information has a pure-strategy Nash equilibrium. [20] Theorem 1 indicates that the proposed sequential game for the computation-offloading problem has a Nash equilibrium. Furthermore, this equilibrium point would be reached within a finite number of iterations. The proof for theorem 1 is provided in [21]. Based on this, Algorithm 1 shows the implementation of the computation-offloading solution. Within each decision slot, the players estimate the values of their respective utility function based on the current decision profile. Eventually, when a stat of equilibrium is reached each player will execute its corresponding optimal strategy = { , , }. Moreover, thanks to the NE theorem presented above, Algorithm 1 would achieve an equilibrium within a finite number of iterations. Even though this algorithm is executed simultaneously by all the players, the decision making process uses a sequential scheme. In order to implement this latter, we proposed exchanging small messages to notify the adjoining players of each player current decision. Algorithm 1: Sequential Game for Computation-Offloading A set of heavy computation tasks: {Task i (Ci, Di)} Inputs: ={ , , Optimal strategy profile Outputs: Optimal Utility value 1 Initialization 2 select an initial strategy: from (2) 3 compute the initial value U0 of utility function (1) 4 end initialization 5 Begin 6 for each (Task i ) 7 while an Equilibrium is not yet reached do 8 get the current network status and strategy profile 9 select the new best strategy: 10 compute the new value for Ui+1 11 if (Ui+1< Ui ) then : 12 update strategy 13 compute the new utility value: 14 else 15 & utility keep the previous strategy 16 end while 17 ={ , , } get strategy profile 18 execute the computation task based on 19 end for 20 End
IV. EXPERIMENTAL RESULTS ANALYSIS This section presents the performance analysis of the experimental results obtained through an extensive simulation work. We provide a comparative study between the proposed theoretical game approach compared to three main approaches, namely: (i) Local Computing, (ii) Offloading to a Base Station, and (iii) Offloading to the edge Server. Furthermore, the six different possibilities, enumerated in the previous section, are taken into account. In the first and sixth models, U1 and U6, computation tasks are executed in the drone. Whereas, in the second and fourth scenarios, U2 and U4, tasks are executed in the base station. Finally, the third and fifth scenarios (U3 and U5) are treated by the edge server. Furthermore, as depicted in Figure 3 for the models U3 and U4, the base station offloads a second time the computation tasks it received from the drone to the edge server via a cellular link. Similarly, the drone uses a cellular connection to send its computation tasks to the edge server in U5 and U6. Even though, the tasks are offloaded to the base station through a wireless access network in the second, third and fourth (U2, U3 and U4) approaches, only on the third scenario (U3) the tasks are computed in the edge server after being offloaded. To evaluate each model, we consider the global utility function, presented previously in section III.C. Furthermore, we give an equal importance to energy and delay, therefore we chose α = β = ½. Moreover, to study the impact that computation complexity and data size might have on the overall utility, we varied the number of computation cycles required to achieve a given task along with data size offloaded to remote devices. Simulation parameters are summarized in Table II. We consider the processing power of the base station ( ) ) to be respectively three and ten and the edge server ( ). As for energy times the CPU frequency of the drone ( consumption coefficients, we chose realistic parameters, where sending one data unit through the wireless local area network ) requires a thousand time more energy than interface ( computing one CPU cycle in the drone ( ). Whereas, ) needs sending the same data using the cellular interface ( 20% more energy than Wi-Fi. Subsequently, we fixed the achievable data rates for Wi-Fi and LTE ( , ) at 10 and 5 mb/s respectively. Furthermore, since the drone has more restrictive energy resource, is twice as much as in the base station . Yet, because the edge server has no restrictions in terms of energy, the value of is much smaller than both and
. TABLE I.
Parameters Tasks: Ci Di (α , β ) ( , , ) ( , , ) ( , ) ( ,, )
SIMULATION PARAMETERS
Values [5, … 50] (x105) CPU Cycles [1, … 10] (x103) data unit (½ , ½ ) (1, 3, 10) Ghz (2,1, 0.01) units (10,5) mb.s-1 (1000, 1200) units
The bar diagram shown in Figure 4 demonstrates the effectiveness of the sequential game (SG) approach compared to the six other models in terms of average global utility. This is because our model always chooses the most efficient strategy, which achieves the best possible tradeoff between energy
0.1
Energy (x10^6)
Average Utility
0.15
U1 U2 U3 U4 U5 U6
12
U1 U2 U3 U4 U5 U6 SG
10 8 6 4 2 0
0.05
(a)
Impact on the average energy consumtpion
20
Delay (x10^2)ms
0 Fig. 4. Average utility values per apporach
efficiency and response time. Furthermore, since global utility considers both energy consumption and delay, we show in Figure 4, the impact of each model on these two metrics independently. In Figure 5.(a), the proposed model (SG) outperforms all the other models in achieving the lowest average energy overhead. Whereas, the third and fifth model (U3, U5) achieved better average delay in Figure 5.(b) because the computation tasks were executed in the edge server. Moreover, we see that U1 and U6 are the least efficient models in terms of average delay, yet U1 still manage to achieve acceptable average energy consumption. Besides, U4 consumes the greatest energy while outperforming U1 and U6 in terms of delay and achieving comparable execution time compared to U 2. In order to investigate the impact that computation complexity and data sizes for different tasks have on the proposed approach, we show through Figure 6 an evaluation of these two parameters. In Figure 6.(a), we fixed the number of CPU cycles, Ci, while changing each time the size of data, Di. Results show that the average utility achieved through SG approach outperforms the other models in all cases. The obtained results were even better for very intensive computation tasks. Besides, the average utility values for the proposed model increases much slower compared to U1, U4 and U6, because as the number of processing cycles increases, more tasks are offloaded in order to mitigate the heavy cost of local computing. Average Utility
0.3
U1
0.25
U2
U3
U4
U5
U1 U2 U3 U4 U5 U6
15 10 5 0 (b) Impact on average time delay Fig. 5. Energy and delay evaluation
Figure 6.(a) also shows that the local computing in the drone and in the base station (U1 and U2) are most suitable for less intensive computation tasks. Inversely, offloading to server (U5) is more appropriate for highly intensive tasks. As for Figure 6.(b), it illustrates the impact that data sizes might have on the global utility. We run different simulations while changing each time data size. Figure 6.(b) shows that the average utility increases with respect to data sizes for all the offloading scenarios, due to the fact that big data induces high transmission overhead. Nevertheless, local computation model U1 is not as affected as much the other models. Besides, the theoretical game approach achieves comparable utility to U5 model when data size is small, whereas, it definitely outperforms this offloading approach when data size becomes bigger. V. RELATED WORKS Mobile-Edge Computing technology improves the computation performances and the network resources U6
SG
0.2 0.15 0.1 0.05 0 5
10
20
CPU Cycles (105)
30
40
50
7
10
Average Utility
(a) Impact of complexity of tasks on the average utility 0.2
U1
U2
U3
U4
U5
U6
SG
0.15 0.1 0.05 0 1
2
3
Data sizes (103)
5
(b) Impact of different data sizes on the average utility Fig. 6. Average utility
utilization by moving the computation resources at the edge of the network closer to their users. In this line of work, the emerging concept of computation-offloading has attracted a particular attention from researchers. Furthermore, many recent studies, that influenced the most our work, have used theoretical game methodology to address the decision-making process in computation-offloading problems. In [18], authors proposed a multi-user computation-offloading game to model a distributed computation-offloading scheme between mobile devices in a multi-channel wireless environment. They used a potential function in order to prove the existence of a Nash Equilibrium, which can be achieved through their distributed algorithm. In [22], authors studied the computation-offloading problem in a multi-cell mobile edge computing environment with the aim of achieving a tradeoff between energy consumption and computation delay. Besides, they proposed an adaptive sequential multi-user offloading game where mobile users sequentially make offloading decisions based on the current network interference and the available computation resources. Likewise, [23] shows a two-stage sequential theoretic game approach between a single provider and multiple users. The authors investigated the economic aspects for adopting delayed Wi-Fi network for an offloading application. In [24] and [25], the authors suggested a two stage sequential game and studied the economic impacts that a user-oriented Wi-Fi offloading would have on two market models: a monopoly with a single provider and a duopoly with multi-service provider. Finally, in [26], a two-stage nested sequential game was adopted to solve a delay-sensitive computation-offloading problem. The suggested game model was implemented with an application partitioning game and cloud resource-selection game in the Mobile Cloud and Internet of Things environment respectively. VI. CONCLUSION Small UAVs are emerging as versatile nascent paradigm that can be used in exploration and surveillance missions. Yet, the complex and time-consuming calculations required for such applications, along with the limited resources available onboard UAVs, makes computation-offloading a promising feasible solution to mitigate these shortcomings. In this paper, we have addressed the computation-offloading decision making problem in order to accomplish intensive computational tasks within acceptable response time and reasonable energy consumption. We have proposed a novel sequential offloading game approach where the players make offloading decisions based on the available computation resources. Furthermore, we proved the existence of a Nash Equilibrium and designed an offloading algorithm that converged to reach this optimal point. Finally, we evaluated the efficiency of our proposed sequential game compared to other decision-making models in terms of global utility. Our model provides the best possible tradeoff between energy consumption and delay whilst achieving 19%, 53% and 71% better global utility on average compared to computing on: edge server, base station and drone respectively. REFERENCES [1] G. Pajares, “Overview and Current Status of Remote Sensing Applications Based on Unmanned Aerial Vehicles ( UAVs )“, Photogrammetric Engineering & Remote Sensing, Vol 81, I 4, April 2015, pp 281–329.
[2] L. Ma, M. Li, L. Tong, Y. Wang and L. Cheng, “Using unmanned aerial vehicle for remote sensing application”, 2013 21st International Conference on Geoinformatics, Kaifeng, 2013, pp. 1-5. [3] Mohammad Mozaffari, Walid Saad, Mehdi Bennis, Merouane Debbah, “Mobile Unmanned Aerial Vehicles (UAVs) for Energy-Efficient Internet of Things Communications“, Publication: eprint arXiv:1703.05401, 2017. [4] N. Hossein Motlagh, T. Taleb and O. Arouk, “Low-Altitude Unmanned Aerial Vehicles-Based Internet of Things Services: Comprehensive Survey and Future Perspectives”, in IEEE Internet of Things Journal, vol. 3, no. 6, pp. 899922, Dec. 2016. [5] C. Luo, J. Nightingale, E. Asemota and C. Grecos, “A UAV-Cloud System for Disaster Sensing Applications”, 2015 IEEE 81st Vehicular Technology Conference (VTC Spring), 2015, pp. 1-5. [6] A. Mtibaa, K. A. Harras, K. Habak, M. Ammar and E. W. Zegura, “Towards Mobile Opportunistic Computing”, 2015 IEEE 8th International Conference on Cloud Computing, New York City, NY, 2015, pp. 1111-1114. [7] A. Ahmed and E. Ahmed, “A Survey on Mobile Edge Computing,“ 10th IEEE International Conference on Intelligent Systems and Control, (ISCO 2016), no. JANUARY, 2016. [8] M. T. Beck, M. Werner, S. Feld, and T. Schimper, “Mobile Edge Computing : A Taxonomy,“ in The Sixth International Conference on Advances in Future Internet (AFIN 2014), 2014, no. c, pp. 48–54. [9] Y. Jararweh, L. Tawalbeh, F. Ababneh and F. Dosari, “Resource Efficient Mobile Computing Using Cloudlet Infrastructure”, 2013 IEEE 9th International Conference on Mobile Ad-hoc and Sensor Networks, 2013, pp. 373-377. [10] M. A. Messous, S. M. Senouci and H. Sedjelmaci, , “Computation Offloading Game for an UAV Network in Mobile Edge Computing”, 2017 IEEE International Conference on Communications, Paris, 2017. [11] C. Zhu, X. Wang, and Z. Liu, “Commercial UAV Positioning Use Case,“ IEEE Document: IEEE 802.11- 15/0907r1. Huawei Technologies. 07-Jul-2015. [12] J. Chen, K.-F. Tong, and J. Wang, “A triple band arc-shaped slot patch antenna for UAV GPS/Wi-Fi applications,“ in 2013 International Symposium on Antennas Propagation (ISAP), 2013, vol. 01, pp. 367–370. [13] C. m Cheng, P. h Hsiao, H. T. Kung, and D. Vlah, “Performance Measurement of 802.11a Wireless Links from UAV to Ground Nodes with Various Antenna Orientations“, 15th International Conference on Computer Communications and Networks (ICCCN), 2006, pp. 303–308. [14] Theodore Rappaport. 2001. Wireless Communications: Principles and Practice (2nd ed.). Prentice Hall PTR, Upper Saddle River, NJ, USA. [15] M. Attia, H. Sedjelmaci, SM. Senouci and E. Aglzim, "Game Model to Optimally Combine Electric Vehicles with Green and Non-Green Sources into an End-to-End Smart Grid Architecture", Journal of Networking and Computer Applications,Vol 72, 2016,pp 1-13. [16] J.Li, G. Kendall, R.John, “Computing nash equilibria and evolutionarily stable states of evolutionary games”, IEEE Transactions on Evolutionary Computation, Vol 20, Issue 3, 2015. [17] X. Chen, “Decentralized Computation Offloading Game For Mobile Cloud Computing”,IEEE Transactions on Parallel and Distributed Systems, vol. 26, no. 4, pp. 974–983, 2015.. [18] X. Chen, L. Jiao, W. Li, and X. Fu, “Efficient multi-user computation offloading for mobile-edge cloud computing,” IEEE/ACM Trans. Netw., vol. 24, no. 5, pp. 2795–2808, Oct 2016. [19] D. Huang, P. Wang, and D. Niyato, “A dynamic offloading algorithm for mobile computing,” IEEE Transactions on Wireless Communications, vol. 11, no. 6, pp. 1991–1995, 2012. [20] M. Deng, H. Tian, and X. Lyu, “Adaptive sequential offloading game for multi-cell Mobile Edge Computing,” 2016 23rd Int. Conf. Telecommun. ICT 2016, pp. 0–4, 2016. [21] H. W. Kuhn. ”Extensive games and the problem of information.” Contributions to the Theory of Games. Annals of Mathematical Studies, volume 28. Princeton University Press, 1953 [22] M. Deng, H. Tian and X. Lyu, "Adaptive sequential offloading game for multi-cell Mobile Edge Computing," 2016 23rd International Conference on Telecommunications (ICT), 2016, pp. 1-5. [23] J. Lee, Y. Yi, S. Chong and Y. Jin, "Economics of WiFi offloading: Trading delay for cellular capacity," 2013 Proceedings IEEE INFOCOM, Turin, 2013, pp. 3309-3314. [24] Hanjin Park, Y. Jin, Jooho Yoon and Y. Yi, "On the economic effects of user-oriented delayed Wi-Fi offloading," 2014 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), 2014, pp. 436-443. [25] H. Park, Y. Jin, J. Yoon and Y. Yi, "On the Economic Effects of UserOriented Delayed Wi-Fi Offloading," in IEEE Transactions on Wireless Communications, vol. 15, no. 4, pp. 2684-2697, April 2016. [26] S.Kim, "Nested Game based Computation Offloading Scheme for Mobile Cloud IoT Systems", EURASIP Journal on Wireless Communications and Networking 2015.
