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Title: Many-Server Heavy-Traffic Limits for Queueing Systems with Perfectly Correlated Service and Patience Times
We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting in queue. Under the usual many-server diffusion scaling, we show that the system is asymptotically equivalent to a system with no abandonment. In particular, the limit is the Halfin-Whitt diffusion for the [Formula: see text] queue when the traffic intensity approaches its critical value 1 from below, and is otherwise a transient diffusion, despite the fact that the prelimit is positive recurrent. To obtain a refined measure of the congestion due to the correlation, we characterize a lower-order fluid (LOF) limit for the case in which the diffusion limit is transient, demonstrating that the queue in this case scales like [Formula: see text]. Under both the diffusion and LOF scalings, we show that the stationary distributions converge weakly to the time-limiting behavior of the corresponding process limit. Funding: This work was supported by the National Natural Science Foundation of China [Grant 72188101] and the Division of Civil, Mechanical and Manufacturing Innovation [Grants 1763100 and 2006350].  more » « less
Award ID(s):
2006350
PAR ID:
10464193
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Mathematics of Operations Research
Volume:
48
Issue:
2
ISSN:
0364-765X
Page Range / eLocation ID:
1119 to 1157
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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