Diffusion Approximations for the GI/G/c/K queue

Although diffusion approximations are widely used for analyzing non-Markovian queueing systems, so far there are few results on the relationship between the approximation accuracy and a combination choice of two boundary conditions and two discretization for finite-capacity multi-server queuing systems. The finite-capacity system requires two boundary conditions at origin (x=0) and capacity limit (x=K). Taking account of this requirement, four types of diffusion approximations have been presented. We present accuracy comparisons among four types of diffusion approximations which differ from one another in the boundary conditions and the discretizations. We observe that the coefficient of variation of the inter-arrival time distribution is a key factor for choosing the appropriate combination of the boundary conditions and the discretizations.