Averaging in Markov models with fast Markov switches and applications to queueing models

Annals of Operations Research

Volumn 112, Issue 1-4, 2002, Pages 63-82

  Anisimov, V V ^a  

^a GLAXOSMITHKLINE   (United Kingdom)

Author keywords

Averaging principle; Markov process; Queueing system; Random environment; Stationary distribution; Switching process

Indexed keywords

EID: 0036430924     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1023/A:1020924920565     Document Type: Conference Paper

References (22)

1. V.V. Anisimov, Applications of limit theorems for switching processes, Cybernetics 14(6) (1978) 917-929.
2. V.V. Anisimov, Estimates for deviations of transient characteristics of nonhomogeneous Markov processes, Ukrainian Mathematical Journal 40(6) (1988) 588-592.
3. V.V. Anisimov, Switching processes: Averaging principle, diffusion approximation and applications, Acta Applicandae Mathematicae 40 (1995) 95-141.
4. V.V. Anisimov, Asymptotic analysis of stochastic models of hierarchic structure and applications in queueing models, in: Advances in Matrix Analytic Methods for Stochastic Models, eds. A.S. Alfa and S.R. Chakravarthy (Notable Publ. Inc., USA, 1998) pp. 237-259.
5. V.V. Anisimov, Asymptotic analysis of reliability for switching systems in light and heavy traffic conditions, in: Recent Advances in Reliability Theory: Methodology, Practice and Inference, eds. N. Limnios and M. Nikulin (Birkhäuser, Boston, 2000) pp. 119-133.
6. V.V. Anisimov, Diffusion approximation in overloaded switching queueing models, Queueing Systems 40 (2002) 141-180.
7. V.V. Anisimov and J.R. Artalejo, Analysis of Markov multiserver retrial queues with negative arrivals, Queueing Systems 39(2/3) (2001) 157-182.
8. P. Billingsley, Convergence of Probability Measures (Wiley, New York, 1968).
9. A. Bobbio and K.S. Trivedi, An aggregation technique for the transient analysis of stiff Markov chains, IEEE Transactions on Computers 35(9) (1986) 803-814.
10. G. Bolch, S. Greiner, H. de Meer and K.S. Trivedi, Queueing Networks and Markov Chains (Wiley, New York, 1998).
11. P.J. Courtois, Decomposability: Queueing and Computer Systems Applications (Academic Press, New York, 1977).
12. J.L. Doob, Stochastic Processes (Wiley, New York, 1953).
13. S.N. Ethier and T.G. Kurtz, Markov Processes, Characterization and Convergence (Wiley, New York, 1986).
14. H.J. Kushner, Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems (Birkhäuser, Boston, 1990).
15. D.M. Lucantoni, G.L. Choudhury and W. Whitt, The transient BMAP/G/1 queue, Comm. Statist. Stochastic Models 10(1) (1994) 145-182.
16. D.M. Lucantoni and M. Neuts, Some steady-state distributions for the MAP/SM/1 queue, Comm. Statist. Stochastic Models 10(3) (1994) 575-598.
17. M. Neuts, Matrix-Geometric Solutions in Stochastic Models (John Hopkins University Press, Baltimore, MD, 1981).
18. M. Pinsky, Random evolutions, in: Lecture Notes in Mathematics, Vol. 451 (Springer, New York, 1975) pp. 89-100.
19. V. Ramaswami, The generality of quasi Birth-and-Death processes, in: Advances in Matrix Analytic Methods for Stochastic Models, eds. A.S. Alfa and S.R. Chakravarthy (Notable Publ. Inc., USA, 1998) pp. 93-113.
20. A.V. Skorokhod, Limit theorems for random processes, Theory Probab. Appl. 1 (1956) 289-319.
21. A.V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations (Amer. Math. Soc., Providence, RI, 1989).
22. R.J. Williams, On the approximation of queueing networks in heavy traffic, in: Stochastic Networks. Theory and Applications, eds. F.P. Kelly, S. Zachary and I. Zieding (Oxford Univ. Press, 1996) pp. 35-56.