Optimal multi-threshold control by the BMAP/SM/1 retrial system
A single server retrial system having several operation modes is considered. The modes are distinguished by the transition rate of the batch Markovian arrival process (BMAP), kernel of the semi-Markovian (SM) service process and the intensity of retrials. Stationary state distribution is calculated under the fixed value of the multi-threshold control strategy. Dependence of the cost criterion, which includes holding and operation cost, on the thresholds is derived. Numerical results illustrating the work of the computer procedure for calculation of the optimal values of thresholds are presented.
KeywordsBatch Markovian arrival process Controlled operation modes Cost criterion Optimal control
Unable to display preview. Download preview PDF.
- Chakravarthy S.R. (2001). “The batch Markovian arrival process: A review and future work.” in: Advances in Probability Theory and Stochastic Processes, eds. A. Krishnamoorthy, et al.(Notable Publications) pp. 21–39.Google Scholar
- Cinlar E. (1975). Introduction to Stochastic Processes (Prentice-Hall).Google Scholar
- Dudin A.N. and Klimenok V.I. (1999). “Multi-dimensional quasitoeplitz Markov chains.” Journal of Applied Mathematics and Stochastic Analysis 12, 393–415.Google Scholar
- Dudin A.N., Klimenok V.I., Klimenok I.A., et al. (2000). “Software “SIRIUS+” for evaluation and optimization of queues with the BMAP-input.” in: Advances in Matrix Analytic Methods for Stochastic Models, eds. G. Latouche and P. Taylor (Notable Publications, Inc., New Jersey) pp. 115–133.Google Scholar
- Kemeni J., Shell J. and Knapp A. (1966). “Van Nostrand, New York.” Denumerable Markov chains.Google Scholar
- Klimenok V.I. and Dudin A.N. (2003). “Application of censored Markov chains for calculating the stationary distribution of the multi-dimensional left-skip-free Markov chains.” Queues: flows, systems, networks 17, 121–128.Google Scholar
- Klimenok V.I. (2000). “About stationary distribution existence conditions in queueing sytems with the MAP and retrials.” Reports of Belarusian Academy of Science 39, 128–132 (in Russian).Google Scholar
- Lucantoni D.M. (1991). “New results on the single server queue with a batch markovian arrival process.” Communications in Statistics-Stochastic Models 7, 1–46.Google Scholar
- Neuts M.F. (1989). Structured Stochastic Matrices of M/G/1 type and their applications (Marcel Dekker).Google Scholar
- Tijms H.C. (1976). “On the optimality of a switch-over policy for controlling the queue size in an M/G/1 queue with variable service rate.” Lecture Notes in Computer Sciences 40, 736–742.Google Scholar