The One with Joeys Sandwich

Joey is up for Sandwich from his favorite sandwich store, which has n counters and ith counter can support queue of Ai people. Every queue counter takes constant time 1 min for handling front customer. As we know Joey loves sandwich and he doesn’t like to wait as well, so what he does is; he joins queue of first counter and waits for one minute and after a minute if he doesn't reach the first p