Academic Commons


Heavy-traffic extreme-value limits for Erlang delay models

Pang, Guodong; Whitt, Ward

We consider the maximum queue length and the maximum number of idle servers in the classical Erlang delay model and the generalization allowing customer abandonment – the M/M/n + M queue. We use strong approximations to show, under regularity conditions, that properly scaled versions of the maximum queue length and maximum number of idle servers over subintervals [0, t] in the delay models converge jointly to independent random variables with the Gumbel extreme- value distribution in the QED and ED many-server heavy-traffic limiting regimes as n and t increase to infinity together appropriately; we require that tn → ∞ and tn = o(n1/2−ε) as n → ∞ for some ε>0.


  • thumnail for PangWhittExtremesErlang061709.pdf PangWhittExtremesErlang061709.pdf application/pdf 205 KB Download File

Also Published In

Queueing Systems

More About This Work

Academic Units
Industrial Engineering and Operations Research
Published Here
September 19, 2017
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.