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Dynamic pricing and scheduling in a multi-class single-server queueing system

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Abstract

This paper investigates an optimal sequencing and dynamic pricing problem for a two-class queueing system. Using a Markov Decision Process based model, we obtain structural characterizations of optimal policies. In particular, it is shown that the optimal pricing policy depends on the entire queue length vector but some monotonicity results prevail as the composition of this vector changes. A numerical study finds that static pricing policies may have significant suboptimality but simple dynamic pricing policies perform well in most situations.

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References

  1. Aktaran-Kalayci, T., Ayhan, H.: Sensitivity of optimal prices to system parameters in a steady-state service facility. Cent. Eur. J. Oper. Res. 193, 120–128 (2009)

    Google Scholar 

  2. Baras, J.S., Ma, D.-J., Makowski, A.M.: K competing queues with geometric service requirements and linear costs: The μc-rule is always optimal. Syst. Control Lett. 6, 173–180 (1985)

    Article  Google Scholar 

  3. Buyukkoc, C., Varaiya, P., Walrand, J.: The rule revisited. Adv. Appl. Probab. 17, 237–238 (1985)

    Article  Google Scholar 

  4. Çil, E.B., Karaesmen, F., Örmeci, E.L.: Sensitivity analysis on a dynamic pricing problem of an m/m/c queueing system. In: Proceedings of the 12th IFAC Symposium on Information Control Problems in Manufacturing (2006)

    Google Scholar 

  5. Çil, E.B., Örmeci, E.L., Karaesmen, F.: Effects of system parameters on the optimal policy structure in a class of queueing control problems. Queueing Syst. 61, 273–304 (2009)

    Article  Google Scholar 

  6. Chen, H., Frank, M.Z.: State-dependent pricing with a queue. IIE Trans. 33, 847–860 (2001)

    Google Scholar 

  7. Gans, N., Savin, S.: Pricing and capacity rationing for rentals with uncertain durations. Manag. Sci. 53, 390–407 (2007)

    Article  Google Scholar 

  8. Gayon, J.P., Değirmenci, I.T., Karaesmen, F., Örmeci, E.L.: Dynamic pricing and replenishment in a production-inventory system with Markov modulated demand. Probab. Eng. Inf. Sci. 23, 205–230 (2009)

    Article  Google Scholar 

  9. Gross, D., Harris, C.M.: Fundamentals of Queueing Theory. Wiley-Interscience, New York (1998)

    Google Scholar 

  10. Hordijk, A., Koole, G.: On the optimality of lept and μc rules for parallel processors and dependent arrival processes. Adv. Appl. Probab. 25, 979–996 (1993)

    Article  Google Scholar 

  11. Koole, G.: Structural results for the control of queueing systems using event-based dynamic programming. Queueing Syst. 30, 323–339 (1998)

    Article  Google Scholar 

  12. Koole, G.: Monotonicity in Markov reward and decision chains: Theory and applications. Found. Trends Stoch. Syst. 1, 1–76 (2006)

    Article  Google Scholar 

  13. Li, L.: A stochastic theory of the firm. Math. Oper. Res. 13(3), 447–466 (1988)

    Article  Google Scholar 

  14. Low, D.W.: Optimal dynamic pricing policies for an m/m/s queue. Oper. Res. 22, 545–561 (1974)

    Article  Google Scholar 

  15. Low, D.W.: Optimal pricing for an unbounded queue. IBM J. Res. Dev. 18, 290–302 (1974)

    Article  Google Scholar 

  16. Maglaras, C.: Revenue management for a multiclass single-server queue via a fluid model analysis. Oper. Res. 54(5), 914 (2006)

    Article  Google Scholar 

  17. Naor, P.: The regulation of queue size by levying tolls. Econometrica 37, 15–24 (1969)

    Article  Google Scholar 

  18. Paschalidis, I., Tsitsiklis, J.N.: Congestion-dependent pricing of network services. IEEE/ACM Trans. Netw. 8, 171–184 (2000)

    Article  Google Scholar 

  19. Puterman, M.L.: Discrete Stochastic Dynamic Programming. Wiley, New York (1994)

    Google Scholar 

  20. Son, J.-D.: Optimal admission and pricing control problem with deterministic service times and sideline profit. Queueing Syst. 60, 71–85 (2008)

    Article  Google Scholar 

  21. Weber, R.R., Stidham, S.: Optimal control of service rates in network queues. Adv. Appl. Probab. 19, 202–218 (1987)

    Article  Google Scholar 

  22. Yoon, S.H., Lewis, M.E.: Optimal pricing and admission control in a queueing system with periodically varying parameters. Queueing Syst. 47, 177–199 (2004)

    Article  Google Scholar 

  23. Ziya, S., Ayhan, H., Foley, R.D.: Optimal prices for finite capacity queueing systems. Oper. Res. Lett. 34, 214–218 (2006)

    Article  Google Scholar 

  24. Ziya, S., Ayhan, H., Foley, R.D.: A note on optimal pricing for finite capacity queueing systems with multiple customer classes. Nav. Res. Logist. 55, 412–418 (2008)

    Article  Google Scholar 

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Correspondence to Fikri Karaesmen.

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Çil, E.B., Karaesmen, F. & Örmeci, E.L. Dynamic pricing and scheduling in a multi-class single-server queueing system. Queueing Syst 67, 305–331 (2011). https://doi.org/10.1007/s11134-011-9214-5

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  • DOI: https://doi.org/10.1007/s11134-011-9214-5

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