Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider $$GI/Ph/n+M$$ G I / P h / n + M parallel-server systems with a renewal arrival process, a phase-type service time distribution, $$n$$ n homogenous servers, and an exponential patience time distribution with positive rate.  show that in the Halfin---Whitt regime, the sequence of stationary distributions corresponding to the normalized state processes is tight. As a consequence,  establish an interchange of heavy-traffic and steady-state limits for $$GI/Ph/n+M$$ G I / P h / n + M queues.
['Jim Dai', 'A. B. Dieker', 'Xuefeng Gao']
I am writing a research paper on a idea Validity of heavy-traffic steady-state approximations in many-server queues with abandonment
[{"from": "human", "value": "I am writing a research paper on a idea Validity of heavy-traffic steady-state approximations in many-server queues with abandonment"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider $$GI/Ph/n+M$$ G I / P h / n + M parallel-server systems with a renewal arrival process, a phase-type service time distribution, $$n$$ n homogenous servers, and an exponential patience time distribution with positive rate.  show that in the Halfin---Whitt regime, the sequence of stationary distributions corresponding to the normalized state processes is tight. As a consequence,  establish an interchange of heavy-traffic and steady-state limits for $$GI/Ph/n+M$$ G I / P h / n + M queues."}]