Asymptotic analysis of queueing systems with reneging: A survey of results for FIFO, single class models

In this paper, we survey results for the GI/GI/N+GIGI/GI/N+GI queueing model. Our focus is on finding situations in which simple performance measure approximations can be developed. To do this, we study the behavior of the GI/GI/N+GIGI/GI/N+GI queue in the conventional heavy traffic and Halfin–Whitt limit regimes, and we also discuss the overloaded regime in which there is a single server as well as the overloaded many-server regime.