14 Queueing Theory

Queues form wherever customers arrive at random and service takes time: at bank counters, hospital clinics, toll gates, telephone exchanges, computer servers. Adding servers costs money; waiting costs customers’ time and the provider’s goodwill. Queueing theory, begun by Erlang in 1909 for the Copenhagen telephone exchange, predicts the lengths of queues and the times spent waiting from the arrival rate, the service rate and the number of servers, and so allows the trade-off to be made. Its most striking lesson is that queues grow without bound as the load approaches capacity: a system that is busy \(95\%\) of the time is not \(5\%\) from trouble, it is in it.

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