Abstract
Optimal hysteresis control strategies are designed for single-server queueing systems with waiting, batch Markov flow, semi-Markovian service, and two operation modes. Operation modes are changed not instantaneously and the failures of the server in idle states occur in a Markovian flow.
Similar content being viewed by others
REFERENCES
Neuts, M. and Lucantoni, D., Some Steady-State Distribution for the MAP=SM=1 Queue, Commun.Statistics-Stochastic Models, 1994, vol. 10, pp. 575–598.
Neuts, M., Structured Stochastic Matrices of M=G=1 Type and Their Applications, New York: Marcel Dekker, 1989.
Dudin, A.N. and Klimenok, V.I., Sistemy massovogo obsluzhivaniya s korrelirovannymi potokami (Queueing Systems with Correlated Flows), Minsk: Belarus. Gos. Univ., 2000.
Rykov, V.V., Controllable Queueing Systems, in Teoriya veroyatnostei.Matematicheskaya statistika.Teoreticheskaya kibernetika (Itogi nauki i tekhniki) (Probability Theory. Mathematical Statistics. Theoretical Cybernetics: Advances in Science and Technology), Moscow: VINITI, 1975, vol. 10, pp. 43–153.
Nobel, R.D., A Regenerative Approach to Analysis of M x =G=1 Queues with Two Service Modes, Avtom.Vychisl.Tekh., 1998, no. 1, pp. 3–14.
Dudin, A.N. and Nishimura, S., Optimal Control for a BMAP=G=1 Queue with Two Service Modes, Math.Probl.Eng., 1999, vol. 5, no. 3, pp. 397–420.
Dudin, A.N. and Nishimura, S., Optimal Hysteretic Control for a BMAP=SM=1=N Queue with Two Service Modes, Math.Probl.Eng., 2000, vol. 5, no. 5, pp. 255–273.
Lucantoni, D.M. New Results on the Single-Server Queue with a Batch Markovian Arrival Process, Commun.Statistics-Stochastic Models, 1991, vol. 7, no. 1, pp. 1–46.
Lu, F.V. and Serfozo, R.F., M=M=1 Queueing Decision Process with Monotone Hysteretic Optimal Policies, Oper.Res., 1984, vol. 32, pp. 1116–1129.
Rykov, V.V., Hysteresis in Controlled Queueing Systems, Vest.Ross.Univ.Druzhby Narodov, 1995, vol. 3, pp. 101–111.
Dudin, A.N. and Klimenok, V.I., Multidimensional Quasi-Toeplitz Markov Chains, J.Appl.Math.Stoch.Anal., 1999, vol. 12, no. 4, pp. 393–415.
Graham, A., Kronecker Products and Matrix Calculus with Aplications, Chichester: Ellis Horwood, 1981.
Bocharov, P.P. and Pechinkin, A.V., Teoriya massovogo obsluzhivaniya (Queueing Theory), Moscow: Ross. Univ. Druzhby Narodov, 1995.
Klimov, G.P., Stokhasticheskie sistemy obsluzhivaniya (Stochastic Queueing Systems), Moscow: Nauka, 1966.
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. 321–329.
Gail, H.R., Hantler, S.L., and Taylor, B.A., Spectral Analysis of M=G=1 and GI=M=1 Type Markov Chains, Adv.Appl.Prob., 1996, vol. 28, pp. 114–165.
Dudin, A.N., Optimal Control for a M x =G=1 Queue with Two Operation Modes, Prob.Eng.Inf.Sci., 1997, vol. 11, pp. 255–265.
Dudin, A.N., Optimal Multithreshold Control for a BMAP=G=1 Queue with N Service Modes, Queueing Syst., 1998, vol. 30, no. 3–4, pp. 273–287.
Skorokhod, A.V., Teoriya veroyatnostei i sluchainykh protsessov (Theory of Probability and Random Processes), Kiev: Vishcha Shkola, 1980.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dudin, A.N. Optimal Hysteresis Control for an Unreliable BMAP/SM/1 System with Two Operation Modes. Automation and Remote Control 63, 1585–1596 (2002). https://doi.org/10.1023/A:1020496612713
Issue Date:
DOI: https://doi.org/10.1023/A:1020496612713