Two fluid approximations for multi-server queues with abandonments

Insight is provided into a previously developed M/M/s/r+M(n) approximation for the M/GI/s/r+GI queueing model by establishing fluid and diffusion limits for the approximating model. Fluid approximations for the two models are compared in the many-server efficiency-driven (overloaded) regime. The two fluid approximations do not coincide, but they are close.