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OPTIMAL ADMISSION AND ROUTING WITH CONGESTION-SENSITIVE CUSTOMER CLASSES

Published online by Cambridge University Press:  01 March 2021

Ayse Aslan Open the ORCID record for Ayse Aslan [Opens in a new window]
Ayse Aslan*
Affiliation:
Department of Operations, University of Groningen, Groningen 9747 AD, The Netherlands E-mail: [email protected]
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Abstract

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This paper considers optimal admission and routing control in multi-class service systems in which customers can either receive quality regular service which is subject to congestion or can receive congestion-free but less desirable service at an alternative service station, which we call the self-service station. We formulate the problem within the Markov decision process framework and focus on characterizing the structure of dynamic optimal policies which maximize the expected long-run rewards. For this, value function and sample path arguments are used. The congestion sensitivity of customers is modeled with class-independent holding costs at the regular service station. The results show how the admission rewards of customer classes affect their priorities at the regular and self-service stations. We explore that the priority for regular service may not only depend on regular service admission rewards of classes but also on the difference between regular and self-service admission rewards. We show that optimal policies have monotonicity properties, regarding the optimal decisions of individual customer classes such that they divide the state space into three connected regions per class.

Keywords

admission controlcongestionMarkov decision processesrevenue managementrouting control
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 3 , July 2022 , pp. 774 - 798
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

References

Ata, B. & Peng, X. (2020). An optimal callback policy for general arrival processes: a pathwise analysis. Operations Research 68: 327–347.Google Scholar
Atar, R. & Lev-Ari, A. (2018). Optimizing buffer size for the retrial queue: two state space collapse results in heavy traffic. Queueing Systems 90: 225–255.CrossRefGoogle Scholar
Atar, R., Mandelbaum, A., & Shaikhet, G. (2009). Simplified control problems for multiclass many-server queueing systems. Mathematics of Operations Research 34: 795–812.CrossRefGoogle Scholar
Bassamboo, A., Harrison, J.M., & Zeevi, A. (2005). Dynamic routing and admission control in high-volume service systems: asymptotic analysis via multi-scale fluid limits. Queueing Systems 51: 249–285.CrossRefGoogle Scholar
Bertsimas, D. & Chryssikou, T. (1999). Bounds and policies for dynamic routing in loss networks. Operations Research 47: 379–394.CrossRefGoogle Scholar
Chong, K.C., Henderson, S.G., & Lewis, M.E. (2018). Two-class routing with admission control and strict priorities. Probability in the Engineering and Informational Sciences 32: 163–178.CrossRefGoogle Scholar
Dai, J.G. & Tezcan, T. (2008). Optimal control of parallel server systems with many servers in heavy traffic. Queueing Systems 59: 95–134.CrossRefGoogle Scholar
Fan-Orzechowski, X. & Feinberg, E.A. (2006). Optimality of randomized trunk reservation for a problem with a single constraint. Advances in Applied Probability 38: 199–220.CrossRefGoogle Scholar
Feinberg, E.A. & Reiman, M.I. (1994). Optimality of randomized trunk reservation. Probability in the Engineering and Informational Sciences 8: 463–489.CrossRefGoogle Scholar
Feinberg, E.A. & Yang, F. (2011). Optimality of trunk reservation for an M/M/K/N queue with several customer types and holding costs. Probability in the Engineering and Informational Sciences 25: 537–560.CrossRefGoogle Scholar
Frostig, E. & Levikson, B. (1999). Optimal routing of customers to two parallel heterogeneous servers: the case of IHR service times. Operations Research 47: 438–444.CrossRefGoogle Scholar
Hordijk, A. & Koole, G. (1992). On the assignment of customers to parallel queues. Probability in the Engineering and Informational Sciences 6: 495–511.CrossRefGoogle Scholar
Hunt, P.J. & Laws, C.N. (1997). Optimization via trunk reservation in single resource loss systems under heavy traffic. Annals of Applied Probability 7: 1058–1079.CrossRefGoogle Scholar
Key, P. (1990). Optimal control and trunk reservation in loss networks. Probability in the Engineering and Informational Sciences 4: 203–242.CrossRefGoogle Scholar
Knudsen, N.C. (1972). Individual and social optimization in a multiserver queue with a general cost-benefit structure. Econometrica 40: 515–528.CrossRefGoogle Scholar
Koçaǧa, Y.L. & Ward, A.R. (2010). Admission control for a multi-server queue with abandonment. Queueing Systems 65: 275–323.CrossRefGoogle Scholar
Koole, G. (2006). Monotonicity in Markov reward and decision chains: theory and applications. Foundation and Trends in Stochastic Systems 1: 1–76.CrossRefGoogle Scholar
Levi, R. & Radovanovic, A. (2010). Provably near-optimal LP-based policies for revenue management in systems with reusable resources. Operations Research 58: 503–507.CrossRefGoogle Scholar
Lin, W. & Kumar, P. (1984). Optimal control of a queueing system with two heterogeneous servers. IEEE Transactions on Automatic Control 29: 696–703.CrossRefGoogle Scholar
Lippman, S.A. (1975). Applying a new device in the optimization of exponential queuing systems. Operations Research 23: 687–710.CrossRefGoogle Scholar
Miller, B.L. (1969). A queueing reward system with several customer classes. Management Science 16: 234–245.CrossRefGoogle Scholar
Naor, P. (1969). The regulation of queue size by levying tolls. Econometrica 37: 15–24.CrossRefGoogle Scholar
Nobel, R.D. & Tijms, H.C. (2000). Optimal control of a queueing system with heterogeneous servers and setup costs. IEEE Transactions on Automatic Control 45: 780–784.CrossRefGoogle Scholar
Puterman, M.L. (1994). Markov decision processes: discrete stochastic dynamic programming. Hoboken, NJ: John Wiley and Sons.CrossRefGoogle Scholar
Rubinovitch, M. (1985). The slow server problem: a queue with stalling. Journal of Applied Probability 22: 879–892.CrossRefGoogle Scholar
Serfozo, R.F. (1979). Technical note: An equivalence between continuous and discrete time Markov decision processes. Operations Research 27: 616–620.CrossRefGoogle Scholar
Stidham, S. (1978). Socially and individually optimal control of arrivals to a GI/M/1 queue. Management Science 24: 1598–1610.CrossRefGoogle Scholar
Ward, A.R. & Armony, M. (2013). Blind fair routing in large-scale service systems with heterogeneous customers and servers. Operations Research 61: 228–243.CrossRefGoogle Scholar
Winston, W. (1977). Optimality of the shortest line discipline. Journal of Applied Probability 14: 181–189.CrossRefGoogle Scholar