Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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.  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;  require that t n ?? and t n =o(n 1/2?? ) as n?? for some ?>0.
['Guodong Pang', 'Ward Whitt']
I am writing a research paper on a idea Heavy-traffic extreme value limits for Erlang delay models
[{"from": "human", "value": "I am writing a research paper on a idea Heavy-traffic extreme value limits for Erlang delay models"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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.  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;  require that t n ?? and t n =o(n 1/2?? ) as n?? for some ?>0."}]