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It is a study of queues. A typical example is one that may be found in banks. Customers arrive at intervals that are determined by some probability distribution function. There are then two possible queueing scenarios: one in which there is a single queue which feeds into several cashiers or a system where there are multiple queues: one for each cashier. When a customer reaches a cashier, it takes the cashier an amount of time to serve him or her. This time also has a probability distribution function - different from the one governing arrival times.

The theory studies the optimum queueing scenario, time spent by customers in queues rather than being served, the optimum number of cashiers. The bank must find the best trade-off between the cost of employing more cashiers and the irritation of their customers.

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Q: What is a queuing system theory?
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