How long will it take for roaches in a suitcase to suffocate to death if I put 10 garbage bags over it?

My suitcase has a a roach problem, but I have important stuff in there that I don't want to spray poisonous chemicals in. So if I put the suitcase in a garbage bag and tie it tight and another on over that, and another one over that (10 times) and make it air tight, I'm wondering how long I should wait in order to guarantee that all roaches would definitely be dead from suffocation. A week? Months? A year? I don't want to wait months, but I would if It was the only way.