Pigeonhole Principle - Age of Empires

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This diagram represents a system that simulates the construction mechanics of structures such as castles, wonders, and bombard towers in a game setting akin to Age of Empires. The construction process is modeled by allocating villagers to different building tasks, thus affecting the overall construction time based on the number of villagers assigned. Each villager contributes to reducing the remaining construction time by 20 seconds on each simulation step, showcasing the impact of resource management and allocation on construction efficiency. This system utilizes various nodes like sources to initiate building processes, pools to store and track the number of villagers and the buildings under construction, and registers to calculate remaining construction times based on villagers allocated and predefined construction durations.

Key simulation elements include gates to allocate villagers to specific construction tasks and state connections that adjust construction progress or redirect resources based on conditions like the remaining construction time reaching zero. Drains are used to signify the completion of constructions, permanently removing resources from the construction process. This setup highlights the strategic element of resource allocation in real-time strategy games, where the player must efficiently manage a pool of workers (villagers) to optimize construction times and achieve game objectives.