With the growing number of distributed energy resources, the number of agents partaking in an electricity market is also bound to increase, which highlights the need of a scalable algorithm to clear the market. The interest towards distributed economic dispatch algorithms has grown in the last years as they were found to be scalable, unlike their centralized counterpart. However, these algorithms rely on communication between computational agents during the resolution of the problem. In the case where those computational agents are located far away from each other, the resolution may be impacted by the various hazards that can occur in the communication network. The asynchronous resolution of the algorithm provides a solution to the large variations in communication delays as it allows the agents to carry on with their computation despite not having received every messages from their market partners. This paper focuses on a peer-to-peer market clearing algorithm based on the alternating direction method of multipliers (ADMM) and its asynchronous version. Two communication delay models are introduced in order to study the effect of communication on the convergence of the synchronous and asynchronous versions of the algorithm. In a 110 agent testcase study, we show that the asynchronous resolution can speed up convergence by 40%, while also being more robust to delay variations.