Stochastic Systems

Optimal Admission Control for Many-Server Systems with QED-Driven Revenues

Jaron Sanders, S. C. Borst, A. J. E. M. Janssen, and J. S. H. van Leeuwaarden

Full-text: Open access

Abstract

We consider Markovian many-server systems with admission control operating in a Quality-and-Efficiency-Driven (QED) regime, where the relative utilization approaches unity while the number of servers grows large, providing natural Economies-of-Scale. In order to determine the optimal admission control policy, we adopt a revenue maximization framework, and suppose that the revenue rate attains a maximum when no customers are waiting and no servers are idling. When the revenue function scales properly with the system size, we show that a nondegenerate optimization problem arises in the limit. Detailed analysis demonstrates that the revenue is maximized by nontrivial policies that bar customers from entering when the queue length exceeds a certain threshold of the order of the typical square-root level variation in the system occupancy. We identify a fundamental equation characterizing the optimal threshold, which we extensively leverage to provide broadly applicable upper/lower bounds for the optimal threshold, establish its monotonicity, and examine its asymptotic behavior, all for general revenue structures. For linear and exponential revenue structures, we present explicit expressions for the optimal threshold.

Article information

Source
Stoch. Syst., Volume 7, Number 2 (2017), 315-341.

Dates
Received: September 2015
Accepted: September 2017
First available in Project Euclid: 24 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.ssy/1519441216

Digital Object Identifier
doi:10.1287/stsy.2017.0004

Mathematical Reviews number (MathSciNet)
MR3741356

Zentralblatt MATH identifier
06849804

Subjects
Primary: 90B22: Queues and service [See also 60K25, 68M20] 60K25: Queueing theory [See also 68M20, 90B22] 93E03: Stochastic systems, general 65K10: Optimization and variational techniques [See also 49Mxx, 93B40] 34E05: Asymptotic expansions

Keywords
queueing Quality-and-Efficiency-Driven (QED) regime asymptotic analysis optimal control threshold control variational calculus

Rights
Creative Commons Attribution 4.0 International License.

Citation

Sanders, Jaron; Borst, S. C.; Janssen, A. J. E. M.; Leeuwaarden, J. S. H. van. Optimal Admission Control for Many-Server Systems with QED-Driven Revenues. Stoch. Syst. 7 (2017), no. 2, 315--341. doi:10.1287/stsy.2017.0004. https://projecteuclid.org/euclid.ssy/1519441216


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