Transient diffusion approximation for some queuening systems.

There are many situations where information about the transient behaviour of computer systems is wanted. In this paper a diffusion approximation to the transient behaviour of some queueing systems is proposed. The solution of the forward diffusion equation on the real positive line with the elementary return barrier having almost general holding time distribution provides the approximation for the GI/G/1 queue. The solution of the diffusion equation in a finite region approximates the transient behaviour for the two-server cyclic system and gives approximations for the first overflow time in the GI/G/1/N system and for the maximum number of customers in the GI/G/1 system. Also the approximation for the busy period of the GI/G/1 system and of the two-server cyclic system are presented.