The multi-agent pickup and delivery (MAPD) problem, in which multiple agents iteratively carry materials without collisions, has received significant attention. However, many conventional MAPD algorithms assume a specifically designed grid-like environment, such as an automated warehouse. Therefore, they have many pickup and delivery locations where agents can stay for a lengthy period, as well as plentiful detours to avoid collisions owing to the freedom of movement in a grid. By contrast, because a maze-like environment such as a search-and-rescue or construction site has fewer pickup/delivery locations and their numbers may be unbalanced, many agents concentrate on such locations resulting in inefficient operations, often becoming stuck or deadlocked. Thus, to improve the transportation efficiency even in a maze-like restricted environment, we propose a deadlock avoidance method, called standby-based deadlock avoidance (SBDA). SBDA uses standby nodes determined in real-time using the articulation-point-finding algorithm, and the agent is guaranteed to stay there for a finite amount of time. We demonstrated that our proposed method outperforms a conventional approach. We also analyzed how the parameters used for selecting standby nodes affect the performance.