It started with a problem.
Agner Krarup Erlang, a Danish mathematician working for the Copenhagen Telephone Company, published his first paper on telephone traffic and congestion in 1909. He sought to determine how many telephone circuits were needed to serve a given number of customers with an acceptable probability of a busy signal. His models described the relationship between arrival rate, service rate, and queue length — establishing the foundations of queuing theory. The unit for telephone traffic measurement, the Erlang, is named after him. His work was later generalized by mathematicians and applied to operations research across industries.
Historical sources below ↓Then something changed.
Queuing theory provided a mathematical basis for capacity planning. Before Erlang's models, service operations were planned by intuition or by observation — hiring more staff when queues grew long. After queuing theory, planners could calculate the relationship between capacity and waiting time: adding one more server reduces average wait time by a calculable amount; doubling capacity does not halve wait time in the same way for all utilization levels. The counterintuitive insight is that systems operating at high utilization develop disproportionately long queues — a server working at 90 percent capacity has a much longer expected queue than one at 80 percent. This shaped how call centers, hospitals, banks, and logistics systems were designed.
What a builder can learn.
Our interpretation: queuing theory shows that the relationship between capacity and wait time is not linear. At low utilization, adding more demand does not increase wait time much. Near full capacity, small increases in demand cause large increases in wait time. For a business builder, this means that the decision about how much capacity to maintain is not just a cost decision but a quality decision — and that running too close to capacity consistently produces poor customer experience even if no individual server is slacking.
A door still open.
A hypothesis worth testing: if a small service business measured its utilization rate — what fraction of its capacity was being used — during peak periods, would it find that it was operating near or above the threshold where wait time begins to increase disproportionately?
At what point during your busiest periods are you operating at a utilization level that makes your customers' wait time grow faster than your business is growing?
Follow the evidence.
History is sourced below. Business lessons are editorial interpretations; future possibilities are questions to test, not predictions.
Prepared from primary-source histories. First edition: 25 Sept 2026.