From antiquity to the present, queues and delays have seemed to be phenomena human beings are always encountering with. Such events are assumed to be probabilistic and described by stochastic models in classical science. In fact, queueing theory, a great branch of probability theory, handles these problems. At the same time, relatively new theory of deterministic queuing systems, or network calculus, considers queues and delays as being deterministic and operates with regular bounds. The article presents a historical review, basic ideas and results of conventional queueing theory and its competitor, network calculus, highlighting the advantages of the latter for dealing with facilities of increased danger.