Publication: Optimal control and performance analysis of an M-X/M/1 queue with batches of negative customers
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2004-04
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EDP Sciences
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We consider a Markov decision process for an MX/M/1 queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different thresholds. Exact and asymptotic results concerning the computation of the stationary distribution of the model are also derived.
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J.R. Artalejo, G-networks: A versatile approach for work removal in queueing networks. Eur. J. Oper. Res. 126 (2000) 233-249.
D. Bertsekas, Dynamic Programming, Deterministic and Stochastic Models. Prentice-Hall, Englewood Cliffs, New Jersey (1987).
R.K. Deb, Optimal control of bulk queues with compound Poisson arrivals and batch service. Opsearch 21 (1984) 227-245.
R.K. Deb and R.F. Serfozo, Optimal control of batch service queues. Adv. Appl. Prob. 5 (1973) 340-361.
X. Chao, M.Miyazawa andM. Pinedo, Queueing Networks: Customers, Signals and Product Form Solutions. Wiley, Chichester (1999).
A. Economou, On the control of a compound immigration process through total catastrophes. Eur. J. Oper. Res. 147 (2003) 522-529.
A. Federgruen and H.C. Tijms, Computation of the stationary distribution of the queue size in an M/G/1 queueing system with variable service rate. J. Appl. Prob. 17 (1980) 515-522.
E. Gelenbe, Random neural networks with negative and positive signals and product-form solutions. Neural Comput. 1 (1989) 502-510.
E. Gelenbe, Product-form queueing networks with negative and positive customers. J. Appl. Prob. 28 (1991) 656-663.
E. Gelenbe, G-networks with signals and batch removal. Probab. Eng. Inf. Sci. 7 (1993) 335-342.
E. Gelenbe, P. Glynn and K. Sigman, Queues with negative arrivals. J. Appl. Prob. 28 (1991) 245-250.
E. Gelenbe and R. Schassberger, Stability of product form G-networks. Probab. Eng. Inf. Sci. 6 (1992) 271-276.
E. Gelenbe and G. Pujolle, Introduction to Queueing Networks. Wiley, Chichester (1998).
P.G. Harrison and E. Pitel, The M/G/1 queue with negative customers. Adv. Appl. Prob. 28 (1996) 540-566.
O. Hernandez-Lerma and J. Lasserre, Discrete-time Markov Control Processes. Springer, New York (1996).
E.G. Kyriakidis, Optimal control of a truncated general immigration process through total catastrophes. J. Appl. Prob. 36 (1999) 461-472.
E.G. Kyriakidis, Characterization of the optimal policy for the control of a simple immigration process through total catastrophes. Oper. Res. Letters 24 (1999) 245-248.
T. Nishigaya, K. Mukumoto and A. Fukuda, An M/G/1 system with set-up time for server replacement. Transactions of the Institute of Electronics, Information and Communication Engineers J74-A-10 (1991) 1586-1593.
S. Nishimura and Y. Jiang, An M/G/1 vacation model with two service modes. Prob. Eng. Inform. Sci. 9 (1994) 355-374.
R.D. Nobel and H.C. Tijms, Optimal control of an MX/G/1 queue with two service modes. Eur. J. Oper. Res. 113 (1999) 610-619.
M. Puterman, Markov Decision Processes. Wiley, New York (1994).
S.M. Ross, Applied Probability Models with Optimization Applications. Holden-Day Inc., San Francisco (1970).
S.M. Ross, Introduction to Stochastic Dynamic Programming. Academic Press, New York (1983).
L.I. Sennott, Stochastic Dynamic Programming and the Control of Queueing Systems. Wiley, New York (1999).
L.I. Sennott, P.A. Humblet and R.L. Tweedie, Mean drifts and the non-ergodicity of Markov chains. Oper. Res. 31 (1983) 783-789.
R. Serfozo, An equivalence between continuous and discrete time Markov decision processes. Oper. Res. 27 (1979) 616-620.
D. Stoyan, Comparison Methods for Queues and Other Stochastic Models. Wiley, Chichester (1983).
J. Teghem, Control of the service process in a queueing system. Eur. J. Oper. Res. 23 (1986) 141-158.
H.C. Tijms, A First Course in Stochastic Models. Wiley, Chichester (2003).
W.S. Yang, J.D. Kim and K.C. Chae, Analysis of M/G/1 stochastic clearing systems. Stochastic Anal. Appl. 20 (2002) 1083-1100.