Approximate Linear Programming for a Queueing Control Problem

39 Pages Posted: 25 Jan 2024

See all articles by Saied Samiedaluie

Saied Samiedaluie

University of Alberta - School of Business; University of Alberta - Department of Accounting, Operations & Information Systems

Rui Zhang

University of Colorado at Boulder

Dan Zhang

University of Colorado at Boulder

Abstract

Admission control for loss systems accessed by multiple customer classes is a classical queueing control problem with a wide variety of applications. When a server is available, the decision is whether to admit an arriving customer and collect a lump-sum revenue. The system can be modeled as a continuous-time infinite-horizon dynamic program but suffers from the curse of dimensionality when different customer classes have different service rates. We use approximate linear programming to solve the problem under three approximation architectures: affine, separable piecewise linear, and finite affine. The finite affine approximation is a recently proposed generalization of the affine approximation, which allows for non-stationary parameters. For both affine and finite affine approximations, we derive equivalent, but more compact, formulations that can be efficiently solved. We propose a column generation algorithm for the separable piecewise linear approximation. Our numerical results show that the finite affine approximation can obtain the tightest bounds for 75% of the instances among the three approximations. Especially, when the number of servers is large and/or the load on the system is high, the finite affine approximation always achieves the tightest bounds. Regarding policy performance, the finite affine approximation has the best performance on average compared to the other two approximations and the achievable performance region method (Bertsimas et al. 1994, Kumar and Kumar 1994). Furthermore, the finite affine approximation is 4 to 5 orders of magnitude faster than the achievable performance region method and the separable piecewise linear approximation for large-scale instances. Therefore, considering bounds, policy performance, and computational efficiency, the finite affine approximation emerges as a competitive approximation architecture for the class of problems studied here.

Keywords: Dynamic programming, Queues, Approximate Linear Programming, Admission control

Suggested Citation

Samiedaluie, Saied and Zhang, Rui and Zhang, Dan, Approximate Linear Programming for a Queueing Control Problem. Available at SSRN: https://ssrn.com/abstract=4706325 or http://dx.doi.org/10.2139/ssrn.4706325

Saied Samiedaluie

University of Alberta - School of Business ( email )

2-43 Business Building
Edmonton, Alberta T6G 2C7
Canada

University of Alberta - Department of Accounting, Operations & Information Systems ( email )

Edmonton, Alberta T6G 2R6
Canada

Rui Zhang (Contact Author)

University of Colorado at Boulder

256 UCB
Boulder, CO CO 80300-0256
United States

Dan Zhang

University of Colorado at Boulder ( email )

1070 Edinboro Drive
Boulder, CO CO 80309
United States

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