There is a high demand that aggregating Home Energy Management System (HEMS) as demand response service. Aggregation scheme is divided into the centralized and decentralized approach. On the one hand, in a centralized fashion, a controller manages all device. On the other hand, in a decentralized fashion, a local controller manages own devices and exchanges information for achieving the global optimum. Our previous work has proposed decentralized HEMS aggregation with Alternating Direction Method of Multipliers (ADMM) to address scalability and privacy issue. The main idea of this method is that we decompose the large-scale aggregated scheduling problem into individual HEMS scheduling problem by introducing local upper limit which stands for the maximum purchasable electricity from an electrical grid. This article reports that we extend the previous decentralized HEM method to asynchronous fashion in order to improve convergence time efficiency from the practical implementation perspective. We propose the waiting ratio which represents the minimum HEMS number for updating the next local upper limit. We also evaluate the algorithm processing time with changing waiting ratio and the number of households. As a result, it is confirmed that though the result shows 53% of acceleration at the most accompanied by barely 2% increase cost, the asynchronous process does not always accelerate the processing time. It may be reasonable to suppose that the degree of acceleration is decreased, as the degree of asynchrony increases, because iteration number until fulfilling converging criteria is increased.