Asymptotic distribution of the queue length in a queueing system (Q1083771)

A single-server queueing system is considered that has a finite source of calls. The possibility is examined of approximating the normalized queue length by a diffusion process in the case of heavy load. A theorem is formulated and proved on the convergence of a sequence of stationary distributions of processes describing the queue length dynamics to the stationary distribution of a limit process when the source of calls increases infinitely. An example of design of a specific system is presented.