Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T23:49:47.310Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal control for a BMAP/SM/1 queuewith MAP-inputof disasters and two operation modes

Published online by Cambridge University Press:  15 April 2004

Olga V. Semenova
Olga V. Semenova*
Affiliation:
Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4 F. Skorina Ave., 220050 Minsk 50, Belarus; semenovaov@bsu.by.
Get access

Abstract

A single-server queueing system with a batch Markovian arrivalprocess (BMAP) and MAP-input of disasters causing all customers toleave the system instantaneously is considered. The system has twooperation modes, which depend on the current queue length. Theembedded and arbitrary time stationary queue length distributionhas been derived and the optimal control threshold strategy hasbeen determined.

Keywords

Negative arrivalsBMAP/SM/1 queueMarkovianarrival process of disastersoperation modes.
Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 2: Advances in modelling of complex systems , April 2004 , pp. 153 - 171
Copyright
© EDP Sciences, 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

J. Artalejo, G-networks: A versatile approach for work removal in queueing networks. Eur. J. Oper. Res. 126 (2000) 233-249.
A. Chen and E. Renshaw, The M/M/1 queue with mass exodus and mass arrivals when empty. J. Appl. Prob. 34 (1997) 192-207.
Dudin, A.N., Optimal control for a Mx/G/1 queue with two operation modes. Prob. Eng. Inform. Sci. 11 (1997) 225-265. CrossRef
Dudin, A.N. and Nishimura, S., Optimal control for a BMAP/G/1 queue with two service modes. Math. Prob. Eng. 5 (1999) 255-273. CrossRef
Dudin, A.N. and Karolik, A.V., BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery. Perform. Eval. 45 (2001) 19-32. CrossRef
A.N. Dudin and S. Nishimura, A BMAP/SM/1 queueing system with Markovian arrival of disasters. J. Appl. Prob. 36 (1999) 868-881.
Dudin, A.N. and Nishimura, S., Embedded stationary distribution for the BMAP/SM/1/N queue with disasters, Queues: Flows Syst. Networks 14 (1998) 92-97.
Gail, H.R., Hantler, S.L., Sidi, M. and Taylor, B.A., Linear independence of root equations for M/G/1 type of Markov chains. Queue. Syst. 20 (1995) 321-339. CrossRef
H.R. Gail, S.L. Hantler and B.A. Taylor, Spectral analysis of M/G/1 and G/M/1 type Markov chains. Adv. Appl. Prob. 28 (1996) 114-165.
E. Gelenbe, Réseaux stochastiques ouverts avec clients négatifs et positifs, et réseaux neuronaux. C. R. Acad. Sci. Paris II 309 (1989) 979-982.
E. Gelenbe, Random neural networks with positive and negative signals and product form solution. Neural Comput. 1 (1989) 502-510.
E. Gelenbe, Réseaux neuronaux aléatoires stables. C. R. Acad. Sci. 310 (1990) 177-180.
E. Gelenbe, Stable random neural networks. Neural Comput. 2 (1990) 239-247.
E. Gelenbe, Queueing networks with negative and positive customers. J. Appl. Prob. 28 (1991) 655-663.
E. Gelenbe, P. Glynn and K. Sigman, Queues with negative arrivals. J. Appl. Prob. 28 (1991) 245-250.
E. Gelenbe and S. Tucci, Performances d'un systeme informatique dupliqué. C. R. Acad. Sci. Paris II 312 (1991) 27-30.
Gelenbe, E. and Schassberger, M., Stability of product form G-networks. Proba Eng. Inform. Sci. 6 (1992) 271-276. CrossRef
E. Gelenbe, G-networks with instantaneous customer movement. J. Appl. Prob. 30 (1993) 742-748.
Gelenbe, E., G-networks with signals and batch removal. Prob. Eng. Inform. Sci. 7 (1993) 335-342. CrossRef
E. Gelenbe, G-networks: An unifying model for queueing networks and neural networks. Ann. oper. Res. 48, (1994) 141-156.
Fourneau, J.M., Gelenbe, E. and Suros, R., G-networks with multiple classes of positive and negative customers. Theoret. Comput. Sci. 155 (1996) 141-156. CrossRef
E. Gelenbe and A. Labed, G-networks with multiple classes of signal and positive customers. Eur. J. Oper. Res. 108 (1998) 293-305.
A. Graham, Kronecker Products and Matrix Calculus with Applications. Ellis Horwood, Chichester, UK (1981).
P.G. Harrison and E. Pitel, The M/G/1 queue with negative customers. Adv. Appl. Prob. 28 (1996) 540-566.
G. Jain and K. Sigman, A Pollaczeck–Khinchine formula for M/G/1 queues with disasters. J. Appl. Prob. 33 (1996) 1191-1200.
D.M. Lucantoni, New results on the single server queue with a batch Markovian arrival processes. Stoch. Mod. 7 (1991) 1-46.
D.M. Lucantoni and M.F. Neuts, Some steady-state distributions for the BMAP/SM/1 queue. Stoch. Mod. 10 (1994) 575-598.
M.F. Neuts, Structured Stochastic Matrices of M/G/1 Type Applications. Marcel Dekker, New York (1989).
Nishimura, S. and Jiang, J., An M/G/1 vacation model with two service modes. Prob. Eng. Inform. Sci. 9 (1995) 355-374. CrossRef
Nobel, R.D., A regenerative approach for an MX/G/1 queue with two service modes. Automat. Control Comput. Sci. 32 (1998) 3-14.
R.D. Nobel and H. Tijms, Optimal control for a MX/G/1 queue with two service modes. Eur. J. Oper. Res. 113 (1999) 610-619.
X. Skorokhod, Probability Theory and Random Process. High School, Kiev (1980).
H. Tijms, On the optimality of a switch-over with exponential controlling the queue size in a M/G/1 queue with variable service rate. Lect. Notes Comput. Sci. (1976).