"There Will Come Soft Rains" is largely set up in a chronological pattern; the events start at the beginning of one day and end 24 hours later. Attention is distributed to various times throughout the day that correspond either to predetermined events, such as breakfast or playtime, and random ones, which the house must adapt to. Some of these events are merely descriptive, while others, especially the unanticipated ones, are established in a problem-solution organizational pattern.
Problem-solution instances include the bird that lands on the window, the dog that enters the house and dies, and especially the fire that eventually destroys the house. Indeed the entire story could almost be treated as two separate stories and organizational patterns; the lead-up to the outbreak of the fire tells us almost everything we need to know about the house, its "personality" and capabilities, so that its reaction to the fire doesn't come as much of a surprise. The portion of the story dealing with the fire also establishes the first real conflict and objective; the house seeks to put out the fire, to solve the problem, whereas the majority of the chronological events that took place throughout the day had no objective other than performing a preprogrammed action.
So, the predominate organizational style is a chronological sequence, with underlying problem-solution events.