Abstract
A BMAP/SM/1 queueing system with two operation modes, a Markov disaster flow, and a modified threshold control strategy is studied. The stationary state probability distribution of the imbedded Markov chain is determined. An algorithm for finding the optimal modified threshold control strategy for the system is designed.
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REFERENCES
Rykov, V.V., Upravlyaemye sistemy massovogo obsluzhivaniya (Queue Control Systems), Itogi Nauki Tekhn., 1975, vol. 10, pp. 43-153.
Fainberg, M.A. and Fainberg, E.A., Control in Queueing Systems, Zarubezh. Elektronika, 1975, no. 3, pp. 3-34.
Dudin, A.N., Optimal Control for a Mx/G/1 Queue with Two Operation Modes, Probab. Eng. Inf. Sci., 1997, vol. 11, pp. 225-265.
Dudin, A.N. and Nishimura, S., Optimal Control for a BMAP/G/1 Queue with Two Service Modes, Math. Probl. Eng., 1999, vol. 5, pp. 255-273.
Nobel, R., A Regenerative Approach to Analysis of an MX/G/1 Queue with Two Service Modes, Avtom. Vychisl. Tekh., 1998, no. 1, pp. 3-14.
Gelenbe, E., Product Form Networks with Negative and Positive Customers, J. Appl. Prob., 1991, vol. 28, pp. 655-663.
Artalejo, J., G-networks: A Versatile Approach for Work Removal in Queueing Networks, Eur. J. Oper. Res., 2000, vol. 126, pp. 233-249.
Dudin, A.N. and Nishimura, S., A BMAP/SM/1 Queueing System with Markovian Arrival of Disasters, J. Appl. Prob., 1999, vol. 36, no.3, pp. 868-881.
Dudin, A.N. and Karolik, A.V., A BMAP/SM/1 Queue with Markovian Input of Disasters and Non-Instantaneous Recovery, Performance Evaluat., 2001, vol. 45, pp. 19-32.
Jain, G. and Sigman, K., A Pollaczeck-Khinchine Formula for M/G/1 Queues with Disasters, J. Appl. Prob., 1996, vol. 33, pp. 1191-1200.
Lucantoni, D.M., New Results on the Single-Server Queue with a Batch Markovian Arrival Process, Commun. Stat. Stochastic Models, 1991, vol. 7, pp. 1-46.
Lucantoni, D.M. and Neuts, M.F., Some Steady-State Distributions for the BMAP/SM/1 Queue, Commun. Stat. Stochastic Models, 1994, vol. 10, pp. 575-598.
Bocharov, P.P., Pechinkin, A.V., and Phong, N.H., Stationary Probabilities of the States of a BMAP/G/1/r System with Repeated Customers and Priority Service for Primary Customers, Avtom. Telemekh., 2000, no. 8, pp. 68-78.
Bocharov, P.P., Phong, N.H., and Hak, T., Analysis of a MAP2/G2/1/r Queueing System with Relative Priority and Queue-Length Dependent Service, Vestn. Ross. Univ. Druzhby Narodov, 1999, no. 1, pp. 92-109.
Bocharov, P.P. and Phong, N.H., Analysis of a MAP2/G2/1/r Queueing System with Absolute Priority, Avtom. Telemekh., 1997, no. 11, pp. 102-117.
Kolyadenkova, L.G., Pechinkin, A.V., and Trishechkin, S.P., A MAP2/G2/1/r System with Absolute Priority and Common Queue, Vestn. Ross. Univ. Druzhby Narodov, 2000, no. 1, pp. 72-90.
Bocharov, P.P., Analysis of a Finite Queue with Markov Input Flow Dependent on the State of the System and Arbitrary Service, Avtom. Telemekh., 1995, no. 12, pp. 60-70.
Bocharov, P.P., Analysis of a MAP/G/1/r Queueing System of Finite Buffer, Vestn. Ross. Univ. Druzhby Narodov, 1995, no. 1, pp. 52-67.
Bocharov, P.P. and Phong, N.H., Analysis of a MAP2/G2/1/r Queueing System with Relative Priority, Vestn. Ross. Univ. Druzhby Narodov, Prikl. Mat. Inf., 1996, no. 2, pp. 67-84.
Pechinkin, A.V., A Queueing System with Markov Input Flow and Random Selection of a Customer from the Queue, Avtom. Telemekh., 2000, no. 9, pp. 90-96.
Bocharov, P.P. and Pechinkin, A.V., Teoriya massovogo obsluzhivaniya (Queueing Theory), Moscow: Ross. Univ. Druzhby Narodov, 1995.
Neuts, M.F., Structured Stochastic Matrices of M/G/1 Type and Their Applications, New York: Marcel Dekker, 1989.
Tijms, H., 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.
Graham, A., Kronecker Products and Matrix Calculus with Applications, Chichester: Ellis Horwood, 1981.
Gail, H.R., Hantler, S.L., and Taylor, B.A., Spectral Analysis of M/G/1 and G=M=1 Type Markov Chains, Adv. Appl. Probab., 1991, vol. 28, pp. 114-165.
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, Queueing Syst., 1995, vol. 20, pp. 321-339.
Skorokhod, A.V., Teoriya veroyatnostei i sluchainykh protsessov (Theory of Probability and Random Processes), Kiev: Vysshaya Shkola, 1980.
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Semenova, O.V. An Optimal Threshold Control for a BMAP/SM/1 System with Map Disaster Flow. Automation and Remote Control 64, 1442–1454 (2003). https://doi.org/10.1023/A:1026099919088
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DOI: https://doi.org/10.1023/A:1026099919088