Zaiming Liu | Wei Deng | Gang Chen
OPEN ACCESS
This paper analyses the optimal dynamic pricing and admission control policies to maximize the average benefit in a Markovian queue with negative customers. The negative customers, as a type of job cancellation signals, are frequently employed to solve the congestion problem in the production system. In our model, the manager proposes a price for positive customers, and decide whether or not to accept the arriving negative customers in any decision epoch. Treating the problem as a Markov decision process, the author derived the monotonicity of the optimal pricing policy, proved the optimal admission policy as a threshold policy, and verified the monotonicity of the threshold policy in system parameters. Finally, some numerical experiments were presented to depict the effect of system parameters on the optimal policy and average benefit.
Queueing system, Dynamic pricing, Admission control, Markov decision process, Negative customers.
1. E. Gelenbe, Product-form queueing networks with negative and positive customers, 1991, Journal of Applied Probability vol. 28, no. 3, pp. 656-663.
2. J.R. Artalejo, G-networks: A versatile approach for work removal in queueing networks, 2000, European Journal of Operational Research, vol. 126, no. 2, pp. 233-249.
3. C.S. Kim, V.I. Klimenok, D. Orlovskii, Multi-server queueing system with a batch Marconian arrival process and negative customers, 2006, Automation and Remote Control, vol.67, no.12, pp. 1958-1973.
4. I. Atencia, P. Moreno, A single-server g-queue in discrete-time with geometrical arrival and service process, 2005, Performance Evaluation, vol. 59, no.1, pp. 85-97.
5. A. Pechinkin, Markov queueing system with finite buffer and negative customers affecting the queue end, 2007, Automation and Remote Control, vol. 68, no. 6, pp. 1104-1117.
6. C.H. Wu, W.C. Chien, Y.T. Chuang, Y.C. Cheng, Multiple product admission control in semiconductor manufacturing systems with process queue time (PQT) constraints, 2016 Computers & Industrial Engineering vol. 99, pp. 347-363.
7. P.V. Laxmi, M. Soujanya, K. Jyothsna, An inventory model with negative customers and service interruptions, 2016, International Journal of Mathematics in Operational Research, vol. 9, no. 1, pp. 1-14.
8. M. Soujanya, et.al, Perishable inventory system with service interruptions, Retrial Demands and Negative Customers, 2015, Applied Mathematics and Computation, vol. 262, pp. 102-110.
9. B. E. C¸il, F. Karaesmen, E.L. Ormeci, Dynamic pricing and scheduling in a multi-class single-server queueing system, 2011, Queueing Systems, vol. 67, no. 4, pp. 305-331.
10. J.D. Son, Optimal admission and pricing control problem with deterministic service times and side line profit, 2008, Queueing Systems, vol. 60, no. 1-2, pp. 71-85.
11. D.W. Low, Optimal dynamic pricing policies for an m/m/s queue, 1974, Operations Research, vol. 22, no. 3, pp. 545-561.
12. S. Yoon, M.E. Lewis, Optimal pricing and admission control in a queueing system with periodically varying parameters, 2004, Queueing Systems, vol. 47, no. 3, pp. 177-199.
13. J, Gayon, I. Degirmenci, F. Karaesmen, E.L. Ormeci, Dynamic pricing and replenishment in a production/inventory system with Markov-modulated demand, 2004, Probability in Engineering and Informational Sciences.
14. B. Cil.E. E.L. O¨rmeci, F. Karaesmen, Effects of system parameters on the optimal policy structure in a class of queueing control problems, 2009, Queueing Systems, vol. 61, no. 4, pp. 273-304.
15. E.A. Feinberg, F. Yang, Optimal pricing for a GI/M/K/N with several customer types and holding costs, 2016, Queueing Systems, vol. 82, no. 1-2, pp. 103-120.
16. D.P. Heyman, Optimal operating policies for M/G/1 queuing systems, 1968, Operations Research, vol. 16, no. 2, pp. 362-382.
17. J.S. Stidham, Optimal control of admission to a queueing system, 1985, Automatic Control, IEEE Transactions on, vol. 30, no. 8, pp. 705-713.
18. J. Wu, Z. Liu, G. Yang, Analysis of the finite source MAP/PH/N retrial g-queue operating in a random environment, 2011, Applied Mathematical Modelling, vol. 35, no. 3, pp. 1184-1193.
19. G. Koole, Monotonicity in Markov reward and decision chains, 2007, Theory and applications.
20. K.Y. Lin, S.M. Ross, Optimal admission control for a single-server loss queue, 2004, Journal of Applied Probability, pp. 535-546.
21. M.L. Puterman, Markov decision processes: discrete stochastic dynamic programming, 2014, John Wiley & Sons.
22. H.C. Tijms, Stochastic models: An algorithmic approach, 1994, John Wiley & Sons.
23. Y. Aviv, A. Federgruen, The value iteration method for countable state Markov decision processes, 1999, Operations Research Letters, vol. 24, no. 5, pp. 223-234.
24. L.I. Sennott, Stochastic dynamic programming and the control of queueing systems, 2009, vol. 504, John Wiley & Sons.
25. S. Benjaafar, J. P. Gayon, S. Tepe, Optimal control of a production–inventory system with customer impatience, 2010, Operations Research Letters, vol. 38, no. 4, pp. 267-272.