What role does a cigarette play in the story contents of a dead mans pocket?

To me, the purpose of the cigarette in this story is to
show us in a very graphic way how little time elapses in the
story.

As the story begins, Tom lights a cigarette and puts
in the ashtray as Clare leaves for the movie.  After Tom goes through his ordeal out on
the ledge, he gets back into the apartment and finds that his cigarette is still
burning.  That shows he has not been out on the ledge that
long.

That helps emphasize the fact that his perspective is
affected by how much danger he was in.  He feels like it's been a long time but his
cigarette is still burning.