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.


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Queueing Systems

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Academic Units
Industrial Engineering and Operations Research
Published Here
September 19, 2017