Queuing theory is the study of how systems cope with a variable demand for service. Queuing problems occur when the service doesn't match the level of demand, for example when a supermarket doesn't have enough cashiers on a busy morning. In IT, queuing problems crop up when requests reach a system faster than it can process them.
In queuing theory, problems occur when there's too much service as well as too little. A store that schedules four cashiers for a shift and sees three of them standing idle has a queuing problem, for instance. Queuing problems occur in many situations: When cars wait to get onto the freeway; when patients sit too long in the doctor's waiting room; or when many callers ask the police for assistance at once.
Queues in IT
In a computer network, queuing problems may involve the router and the transmissions it receives: If the traffic is more than the router can process efficiently, packets back up just like customers in a checkout line. If the computer runs multiple operations that demand more service from the central processor unit than it can provide efficiently, that's another type of queuing problem; if a database receives more calls for information than it can handle, that also creates a queue.
The goal of queuing theory is to develop formulas that predict the amount of service needed to eliminate queues without the service sitting idle a lot of the time. The first step is to develop a model for the system in question. All queuing models include a representation of the service -- cashiers or the router, for instance -- and the probable demands on the service at any given time. The level of demand varies not only with the number of requests for service but how long each request takes to process.
Queuing theory involves a number of calculations. One of the simpler ones is Little's Theory, which states that the number of customers on hand at a given time depends on the rate at which they arrive, multiplied by the time it takes to process them. If a network bottleneck causes a router to take twice as long forwarding data packets but the packets still arrive at the same rate, the number of data packets the router deals with at one time is now double. That often causes a backlog until someone resolves the problem or the arrival rate slows.