Delay-Limited Computation Offloading for MEC-Assisted Mobile Blockchain Networks

The proof-of-work (PoW) mining process requires a large amount of intensive computing, which leads to some plights such as heavy equipment and fixed access nodes in traditional blockchain networks. A novel mobile blockchain network with the help of a mobile edge computing (MEC) server is presented, where all mobile users participate in the PoW mining process. The traditional Bitcoin network adjusts the target difficulty value to ensure a stable block time. However, for MEC-assisted mobile blockchain networks, the adjusted difficulty value needs to be broadcast to all mobile users, which results in expensive communication costs. To maintain a stable block time of mobile blockchain networks, we formulate the delay-limited computation offloading strategy of the PoW-based mining task as a non-cooperative game that maximizes an individual revenue in the MEC-assisted mobile blockchain network. Specifically, the non-cooperative game problem can be divided into multiple sub-game optimization problems to obtain final solutions for all users. We analyze the sub-game optimization problem and prove the existence of Nash equilibrium (NE) of the non-cooperative game. Moreover, we design an alternating iterative algorithm based on the continuous relaxation and greedy rounding (CRGR) to achieve the NE of this game. Given the sub-optimal delay-limited computation offloading results, we also derive the optimal transmit power for an individual user within the maximum mining delay range. From the analytical results, we can see that the proposed CRGR-based alternating iterative algorithm can efficiently attain the sub-optimal delay-limited computation offloading strategies of all mobile users in the polynomial time. The individual transmit power increases accordingly with the delay-limited computation offloading strategies of all users. Numerical results demonstrate that the proposed CRGR-based alternating iterative algorithm has fast convergence and good stability.