2009 Articles
Heavy-traffic extreme-value limits for Erlang delay models
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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Also Published In
- Title
- Queueing Systems
- DOI
- https://doi.org/10.1007/s11134-009-9132-y
More About This Work
- Academic Units
- Industrial Engineering and Operations Research
- Published Here
- September 19, 2017