When parents are moving from playpen time to roomtime (both forms of independent playtime ), they often have questions. Roomtime is essentially the same thing as independent playtime, just with larger boundaries (a room rather than a playpen).
On Becoming Babywise II says you will move to roomtime between 18-22 months (page 76). With both of my children, I moved much earlier. Brayden started roomtime around 14-15 months. Kaitlyn started it at 12 months. Exactly when you move your child to roomtime is up to you. Base it on the child's ability to handle the freedom.
Roomtime is a structured activity. Mom decides when it starts, not the child. If your child is the type to wander into his room and play on his own for 45 minutes, this is not roomtime. Roomtime is when mom decides that it is time for roomtime and the child willingly complies.
Roomtime is not a free-for-all. The child doesn't get to do whatever he wants to. If he is doing things in his room that you find inappropriate, you should stop it. What is inappropriate? That is up to you. You are the parent.
A common question I get is about a gate or shutting the door. I shut the door at first for roomtime. If you don't want the door shut, you can do a child safety gate. Once your child is able to handle the door being open, you can leave it open. He can handle it if he stays in his room with it open. Brayden (3.5) will happily play in his room with the door open, but still to this day he usually prefers it to be shut. Brayden and Kaitlyn have roomtime at the same time, and their rooms are right next to each other, so it is better for the doors to be shut. Then they don't have the temptation and distraction of playing with each other during this independent playtime. You want this to be a time when your child can "focus and play independently without having someone or something there to 'entertain' him" (On Becoming Toddlerwise, page 48).
Roomtime can be in a location other than the child's bedroom (Babywise II, page 76). Remember, it is just playpen time with extended boundaries, so it can be anywhere you deem appropriate.