Limit Theorems in the Theory of Queues. I

In the paper limit theorems describing the work of a queuing system with one server are considered in the general case. In § 1 the probabilities of large values of the waiting time are studied. The absence of the explicit form of the distributions does not prevent here the detailed study of the asymptotic expressions for the required probabilities. § 2 contains the refinement of the limit theorems obtained earlier in [2]–[5] and describes the work of the system under the condition of heavy traffic.