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Excursion-based universal approximations for the Erlang-A queue in steady-state, Mathematics of Operations Research


We re-visit many-server approximations for the well-studied Erlang-A queue. This is a system with a single pool of i.i.d. servers that serve one class of i.i.d. impatient customers. Arrivals follow a Poisson process and service times are exponentially distributed as are the customers' patience times. We propose a diffusion approximation which applies simultaneously to all existing many-server heavy-traffic regimes: QED, ED, QD and NDS. We prove that the approximation provides accurate estimates for a broad family of steady-state metrics. Our approach is ``metric-free'' in that we do not use the specific formulas for the steady-state distribution of the Erlang-A queue. Rather, we study the excursions of the underlying Birth-and-Death process and relate these to properly defined excursions of the corresponding diffusion process. Regenerative-process and martingale arguments, together with derivative bounds for solutions to certain ODEs, allow us to control the accuracy of the approximation. We demonstrate the appeal of universal approximation by studying two staffing optimization problems of practical interest.




Itai Gurvich, J Huang, Avishai Mandelbaum

Date Published



Gurvich, Itai, J Huang, and Avishai Mandelbaum. 2014. Excursion-based universal approximations for the Erlang-A queue in steady-state. Mathematics of Operations Research. 39(2): 325-373.


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