Many previous studies on discharging MEC calculations consider only one of a macro cell or a small cell as a choice for discharging. Previous research on computation offloading assumed that users offload to a MEC server located in a macro cell or in a small cell [6]. Each user can calculate his calculation task locally, transfer it to a small cell MEC server or transfer it to a macro cell MEC server.
In Section IV, we formulate the three-layer computational offloading game and find the potential function.
Related Work
Through the use of game theory, we will show that all users must make mutually satisfactory decisions without harming the utility of other users. For practice, we will use different communication schemes for small cell communication and macro cell communication. Because there is no standard way to find the probability function, much research dealing with probability games does not propose the probability function.
But we will introduce the potential function that perfectly shows the dynamics of our game.
System Model
System Environment
Communication Model
- Communication between a UE and the small cell base station 𝑠
- Communication between a UE and the macro cell base station 𝑚
Therefore, the decision profile of other users does not affect the uplink transmission rate to the small cell, and we can formulate the uplink transmission rate 𝑟𝑛𝑠 of user 𝑛 with 𝑎𝑛= 1 angle. Since the 5G uplink transmission scheme is similar to the LTE uplink transmission scheme, we can implement the LTE uplink scheme to calculate the data rate. In LTE, users acquire uplink resources according to eNodeB scheduling, where the resources are a multiple of Physical Resource Blocks (PRBs).
We assume that each user wants to complete their uplink transmission between the station 𝑚 within 1 ms, where 1 ms corresponds to the LTE transmission time interval (TTI). Hence, we can calculate the required amount of bandwidth 𝑊𝑛 by each user for completing the uplink transmission within 1 ms axis. Unlike the small cell uplink transmission, the channel bandwidth 𝑊𝑚 is shared with other users downloading to the macrocell MEC server.
Note that in (4), ∑𝑖≠𝑛𝑊𝑖⋅ 𝐼{𝑎𝑖=2} means the users who choose to download to the MEC macro cell server. Finally, we can calculate the uplink transmission rate of user 𝑛 who has selected a macro cell for offloading. 𝑊𝑛+ ∑𝑖≠𝑛𝑊𝑖⋅ 𝐼{𝑎𝑖=2}⋅ 𝑙𝑜𝑔2(1 + 𝑆𝑁𝑅𝑛𝑚) (5) Note that if too many mobile devices choose to offload to the MEC macrocell server, it leads to very low uplink speed.
Computation Model
- Local Computing
- Offloading to the small cell MEC server…
- Offloading to the macro cell MEC server
We denote by 𝑓𝑚 the computational power of the macrocell MEC server and by 𝑃𝑛𝑚 the transmission power from the mobile unit 𝑛 to the base station 𝑚. In this situation, users considering the macrocell MEC server should reconsider their decisions. 5), (8) and (16), we need to compare user 𝑛's local processing overhead and the macrocell offload overhead.
Then, some users may change their decision from offloading macro cells to local computing or offloading small cells. So users need to know information about how many users choose macro cell offloading. Users who have different decisions with the previous decision slot send decision change messages to the BS macro cell.
Other cases such as local calculation ⇄ macro cell download and small cell download ⇄ macro cell download can be formulated in the same way. Assume that the coverage of a small BS cell is 100 m and the coverage of a macro BS cell is 1 km. But we can notice that many users choose macro cell offloading to minimize their overall load rather than small cell offloading.
Game Formulation
Game Formulation as a strategic game
For user 𝑛, we need to define the set of strategies 𝑎𝑛∈ 𝒜𝑛≜ {0,1,2}, where 𝑎𝑛 = 0 means the local computing, 𝑎𝑛= 1 means transferring to the small cell MEC server and finally 𝑎𝑛= 2 means transfer to the macro cell MEC server. According to the definition [19], the strategy space 𝕊 is defined as the Cartesian products of all individual strategy sets, i.e. Using these definitions we can formulate each user's strategies and overhead functions taking into account the interaction with other users.
According to (8), (12) and (16), we can formulate 𝑍𝑛 which is the overhead function that interacts with other players as. According to the definition [18], a Nash equilibrium is a strategy profile such that if other users' strategies remain unchanged, no player will not change his current strategy. At a Nash equilibrium, no user can improve, so it is also called a stable operating point.
For these reasons, the goal of a given game is to prove the existence of Nash equilibrium and to find Nash equilibria.
Potential Game
- Local computing vs. Small cell offloading
- Local computing vs. Macro cell offloading
- Small cell offloading vs. Macro cell offloading
- Finding the potential function
- Proof
So we can claim that our game has a Nash equilibrium and can reach it in finite time if our game is a potential game. In order to design a potential function for our game, we need to consider the dynamics of our system model. By chasing the conditions when each user changes their decision, we can find the shape of our potential function.
As mentioned earlier, we need to understand the dynamics of our game in order to formulate the potential function. Using these relations, we can show that the three-layer computational offloading decision game is a potential game by constructing the potential function 𝜙 with a given decision profile 𝒂 as . Finally, if we can prove that our potential function shows the dynamics according to each user's decision change well, then we can say that our game is a potential game.
For case 2, we can use the same proof method for case 1. First, we should calculate the two potential outputs of the function when 𝑎𝑘 = 0 and 𝑎𝑘 = 2. When the user 𝑘 decides to unload the macro cells, it becomes the potential output of the function. In short, the three-level computational relief game is a regular potential game because the potential function can well represent the dynamics of the game. So we can claim that our game has a Nash equilibrium and will converge in finite time by the definition of an ordinal potential game.
Offloading Algorithm and Convergence Analysis
Three-tier computation offloading decision game algorithm
Through the communication model (i.e. Equation 4)), we explained that the interaction with other users takes place in the communication between mobile devices and the macro cell BS using a 4G/5G mobile network. Because the bandwidth of the cellular channel is limited, the bandwidth allocated to each user who wants to transfer to the macro cell MEC server is determined based on the number of users who select macro cell transfer. As the number of users offloading macro cells increases, the data rate allocated to each user should decrease, causing an increase in communication overhead.
To solve this problem, the BS macro cell transmits ∑ 𝑊𝑖⋅ 𝐼{𝑎𝑖=2} which is the aggregated value of bandwidth demand from users who choose macro cell offloading. Using this structure, users who want to download to the MEC server of the macro cell need to transmit 𝑊𝑛 which is the bandwidth request to the macro cell BS using the allocated uplink subframe. Then, the BS macro cell will select a user at random and transmit the approval message that allows the selected user's decision to be changed.
The selected user will change their decision and other users who are not selected keep their decision in the next decision slot. When the BS macro cell does not receive any "Change Decision" message from the uses through several slots, it will transmit the CONVERGENCE message which means that the users' decisions are in a Nash equilibrium state. Finding the appropriate game period considering the allocation of uplink/downlink resources for information exchange (i.e., 𝑊𝑛, ∑ 𝑊𝑖⋅ 𝐼{𝑎𝑖=2}, Decision Change, approval and CONVERGENCE) is our job of future between mobile and macro devices.
Convergence analysis
So we can use the absolute value to find the potential difference of local computing ⇄ small cell offloading as |𝑇𝑘(𝑠,𝑚)− 𝑇𝑘(𝑙,𝑚)|. Since the values 𝑃𝑚𝑎𝑥 and 𝑃𝑚𝑖𝑛 are a real number in practice, we need to use the ceiling function to find the correct 𝑀.
Simulation and Evaluation
Some users change their decisions from offloading macro cells to offloading small cells because the bandwidths allocated to those users decrease with the increase in the number of users offloading macro cells. But the 4 user game is converged on the 11th slot and the 8 user game is converged on the 17th slot. When we calculate 𝑀-values, the maximum amount of potential is related to the maximum value between 𝑊𝑇𝑚𝑎𝑥(𝑠,𝑚) , 𝑊𝑇𝑚𝑎𝑥(𝑙,𝑚) and (1 +1. 2𝑁) 𝑊𝑚𝑎𝑥2.
It means that when all users select small cell discharge, the potential function has the maximum amount of potential. The same circumstance can be observed for the 𝑃𝑚𝑖𝑛. For these reasons, the game converges faster than the calculated 𝑀-slot. To prove that our game is well suited for practical situations, consider the urgent situation such as a car accident.
Because the task processed at each decision slot is simple overhead computations, we can assume that the decision slot size is a few milliseconds (ie, 1 ms). According to the Korea Road Safety Act, the safety distance for the 50 km/h vehicle is 35m. Using the mentioned 𝑀 values (𝑀𝑁=4= 346 & 𝑀𝑁=8= 132), we can observe that a game requires hundreds of milliseconds for the convergence.
Conclusion
Ji, “Partitioning multi-user computing for delay-sensitive mobile cloud applications,” in IEEE Transactions on Computers , vol. Karakostas, "Energy-aware offloading for competing users on a shared communication channel," in IEEE Transactions on Mobile Computing, vol. Becvar, "Mobile Edge Computing: A Survey of Architecture and Computational Offloading," in IEEE Communications Surveys & Tutorials, vol.
Kim, "Energiedoeltreffende hulpbrontoewysing vir die aflaai van mobiele randberekenings," in IEEE Transactions on Wireless Communications, vol. Chen, "Decentralized Computation Offloading Game for Mobile Cloud Computing," in IEEE Transactions on Parallel and Distributed Systems, vol. Choi, "Competitive Partial Computation Offloading for Maximizing Energy Efficiency in Mobile Cloud Computing," in IEEE Access, vol.
Fu, "Efficient Multi-User Computation Offloading for Mobile-Edge Cloud Computing," i IEEE/ACM Transactions on Networking, vol. Cai, "Distributed Multiuser Computation Offloading for Cloudlet-Based Mobile Cloud Computing: A Game-Theoretic Machine Learning Approach," i IEEE Transactions on. Tang, "Computation Offloading and Resource Allocation in Wireless Cellular Networks With Mobile Edge Computing," i IEEE Transactions on Wireless Communications, vol.
