Heavy-traffic extreme value limits for Erlang delay models |
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Authors: | Guodong Pang Ward Whitt |
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Institution: | 1. IEOR Department, Columbia University, New York, USA
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Abstract: | 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 quality-and-efficiency-driven (QED) and ED many-server heavy-traffic limiting regimes as n and t increase to infinity together appropriately; we require that t n →∞ and t n =o(n 1/2?ε ) as n→∞ for some ε>0. |
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