More specifically, how does Little's Law continue to hold, for example, for a single bank teller that takes 10 minutes to process a client, and the clients arrive at the rate of 20 per hour (i.e., one every 3 minutes). Won't the line keep increasing, leading to the nonexistence of a "steady state" number of requests in the system?
2026-03-25 16:03:13.1774454593
What does "stationary system" mean in the assumptions for Little's Law?
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In your case it seems the average service time is so great that the queue almost surely grows without limit, then this is not a stationary system and there is no long-term average number of customers in the queue and no average time that a customer spends in the system
So if Little's Law is something like "the long-term average number $L$ of customers in a stationary system is equal to the long-term average effective arrival rate $λ$ multiplied by the average time $W$ that a customer spends in the system" then you should say that the terms in Little's Law would be meaningless (or perhaps that $L$ and $W$ would be infinite) in your case