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Title: Learning-Based Optimal Admission Control in a Single-Server Queuing System
We consider a long-term average profit–maximizing admission control problem in an M/M/1 queuing system with unknown service and arrival rates. With a fixed reward collected upon service completion and a cost per unit of time enforced on customers waiting in the queue, a dispatcher decides upon arrivals whether to admit the arriving customer or not based on the full history of observations of the queue length of the system. Naor [Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24] shows that, if all the parameters of the model are known, then it is optimal to use a static threshold policy: admit if the queue length is less than a predetermined threshold and otherwise not. We propose a learning-based dispatching algorithm and characterize its regret with respect to optimal dispatch policies for the full-information model of Naor [Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24]. We show that the algorithm achieves an O(1) regret when all optimal thresholds with full information are nonzero and achieves an [Formula: see text] regret for any specified [Formula: see text] in the case that an optimal threshold with full information is 0 (i.e., an optimal policy is to reject all arrivals), where N is the number of arrivals.  more » « less
Award ID(s):
2006305
PAR ID:
10535934
Author(s) / Creator(s):
; ;
Publisher / Repository:
INFORMS
Date Published:
Journal Name:
Stochastic Systems
Volume:
14
Issue:
1
ISSN:
1946-5238
Page Range / eLocation ID:
69 to 107
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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