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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.
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Optimal Pricing in a Single Server System
We study optimal pricing in a single server queue when the customers valuation of service depends on their waiting time. In particular, we consider a very general model, where the customer valuations are random and are sampled from a distribution that depends on the queue length. The goal of the service provider is to set dynamic state dependent prices in order to maximize its revenue, while also managing congestion. We model the problem as a Markov decision process and present structural results on the optimal policy. We also present an algorithm to find an approximate optimal policy. We further present a myopic policy that is easy to evaluate and present bounds on its performance. We finally illustrate the quality of our approximate solution and the myopic solution using numerical simulations.
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- PAR ID:
- 10516556
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- ACM Transactions on Modeling and Performance Evaluation of Computing Systems
- Volume:
- 8
- Issue:
- 4
- ISSN:
- 2376-3639
- Page Range / eLocation ID:
- 1 to 32
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3607252
