This paper addresses the critical challenge of optimizing resource allocation for task offloading in blockchain-enabled mobile edge computing (MEC), aiming to minimize the total energy consumption within wireless networks equipped with edge servers (ESs). We propose a novel joint resource allocation framework that integrates task offloading and blockchain processes within MEC, formulating it as a mixed-integer nonlinear programming (MINLP) problem. The solution assigns mobile terminals (MTs) to ESs and optimally allocates computational resources at ESs for both task computation and block generation. To manage the complexity of this optimization, we employ a two-stage dual decomposition approach. Initially, the problem is separated into subproblems for MEC and blockchain functionalities. These subproblems are further decomposed across ESs and MTs, enabling us to derive analytical solutions for optimal computational frequency allocation for both task offloading and blockchain operations. Leveraging these insights, we develop two low-complexity algorithms, which utilizes a greedy assignment strategy for MTs to ESs, and optimally allocates computational frequencies within the MEC and blockchain components. Performance evaluation results demonstrate the effectiveness of these algorithms, achieving significant reductions in total energy consumption while maximizing the efficiency of communication and computational resources. The approach also contributes to reducing network outage probability. This work presents a promising framework for developing resource-efficient blockchain-enabled MEC systems, positioning it as a scalable solution for future wireless networks.
