Time is used as literary device in "A Rose for Emily" to help us understand Emily and the period in which she lived. Time does not move in a linear progression but rather appears as a patchwork of moments throughout Emily's life. Through this approach we gain insight into Emily's neurosis and feelings of abandonment.
The story begins at Emily's funeral feeding the readers' curiosity about this dead woman. Who was she and what happened to her? The story is presumably told through the townspeople and begins with recollections of when they tried to reinstate the taxes that Colonel Sartoris rescinded twenty years prior. Miss Emily refuses to give any legitimacy to the matter and demands they see the Colonel or look up the town records to resolve the matter. The initial impression we get of Emily is one of a stubborn woman who lives in her own world, perhaps one out of touch with reality.
Next the narrator goes further back to when Emily "vanquishes" the townspeople about the smell that is emitting from her house. We begin to sense something sinister about Miss Emily that maybe everything isn't so harmless and she is in fact delusional or worse. Her reality is the only one she is willing to accept.
The story jumps back again to when Emily's father dies. We find he was a domineering man who drove away all possible suitors for Emily, not because no one was good enough for her but out of fear of being left. He exhibited total control over her and refused anyone from taking her away from him. When he died, Emily denied he had passed and kept him for three days, perhaps, in her own way, exerting her control over him.
From here the story moves in linear sequence and we learn about Emily trying to relive her past when she was of prime age for suitors and her encounter with Homer Baron. You are aware of her stubborn tendencies when the federal postal service begins posting numbers on houses. Emily refuses to let them number her house because that is too modern. She is entrenched in her old ways and nothing will change her. The use of time in the story gains relevance when we hear about Homer and what happened to him. The three pieces in the beginning were a preface for the real story of their "courtship" and the murder. From the start we know Emily is stubborn and lives in her own reality. She has issues of abandonment from her father which probably was the motive behind the murder. The past is ever-present which is why, I believe, it was told simultaneously. The past affects the present.