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This is classic open-loop queuing theory with Poisson arrivals. Nothing really works like that. There's always a "rejection rate", where people leave the line before being serviced. Or, in networking, the connection times out. Or, for a shopping site or a real store, you get an "abandoned cart". In real life, this has a lot to do with how many sales you lose.

In the early days of the Internet, people were trying to analyze datagram networks as open-loop systems with Poisson arrivals. That's because everybody read Kleinrock back then. His thesis was on Western Union Plan 55-A, which was Sendmail made out of telephone relays and paper tape punches feeding paper tape readers as buffers. A mail system behaves much more like an open loop system - people don't mail less as the mail propagation time goes up. That was the wrong model for IP messages, because TCP connections add a closed loop system on top of IP.

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