|
|
|
L2-Decay rate for non-ergodic Jackson network |
Huihui CHENG1,Yonghua MAO2,*( ) |
1. School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450045, China
2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China |
|
|
|
|
Abstract We establish the additive theorem of L2-decay rate for multidimensional Markov process with independent marginal processes. Using this and the decomposition method, we obtain explicit upper and lower bounds for decay rate of non-ergodic Jackson network. In some cases, we get the exact decay rate.
|
| Keywords
L2-Decay rate
additive theorem
decomposition method
Jackson network
|
|
Corresponding Author(s):
Yonghua MAO
|
|
Issue Date: 26 August 2014
|
|
| 1 |
Chen M F. Equivalence of exponential ergodicity and L2-exponential convergence for Markov chains. Stochastic Process Appl, 2000, 87(2): 281-297
doi: 10.1016/S0304-4149(99)00114-3
|
| 2 |
Chen M F. Explicit bounds of the first eigenvalues. Sci China Ser A, 2000, 43: 1051-1059
doi: 10.1007/BF02898239
|
| 3 |
Chen M F. From Markov Chains to Non-equilibrium Particle Systems. Singapore: World Scientific, 2004
|
| 4 |
Chen M F. Speed of stability for birth-death processes. Front Math China, 2010, 5(3): 379-515
doi: 10.1007/s11464-010-0068-7
|
| 5 |
Chen M F, Mao Y H. An Introduction to Stochastic Processes. Beijing: Higher Education Press, 2007 (in Cinese)
|
| 6 |
van Doorn E A. Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process. Adv Appl Probab, 1985, 17(3): 514-530
doi: 10.2307/1427118
|
| 7 |
Goodman J M, Massey W A. The non-ergodic Jackson network. J Appl Probab, 1984, 21: 860-869
doi: 10.2307/3213702
|
| 8 |
Jackson J R. Networks of waiting lines. Oper Res, 1957, 5: 518-521
doi: 10.1287/opre.5.4.518
|
| 9 |
Jackson J R. Jobshop-like queuing systems. Manag Sci, 1963, 10: 131-142
doi: 10.1287/mnsc.10.1.131
|
| 10 |
Jerrum M, Son J B, Tetali P, Vigoda E. Elementary bounds on Poincaré and log-Sobolev constant for decomposable Markov chains. Ann Appl Probab, 2004, 14: 1741-1765
doi: 10.1214/105051604000000639
|
| 11 |
Kelbert M Ya, Kontsevich M L, Rybko A N. On Jackson networks on countable graphs. Veroyatn Primen, 1988, 33: 379-382
|
| 12 |
Mao Y H. Nash inequalities for Markov processes in dimension on<?Pub Caret?>e. Acta Math Sin (Engl Ser), 2002, 18(1): 147-156
doi: 10.1007/s101140100128
|
| 13 |
Mao Y H. General Sobolev type inequalities for symmetric forms. J Math Anal Appl, 2008, 33: 1092-1099
doi: 10.1016/j.jmaa.2007.06.004
|
| 14 |
Mao Y H. Lp Poincaré inequality for general symmetric forms. Acta Math Sin (Engl Ser), 2009, 25: 2055-2064
doi: 10.1007/s10114-009-8205-5
|
| 15 |
Mao Y H, Ouyang S X. Strong ergodicity and uniform decay for Markov processes. Math Appl (Wuhan), 2006, 19(3): 580-586
|
| 16 |
Mao Y H, Xia L H. Spectral gap for jump processes by decomposition method. Front Math China, 2009, 4(2): 335-348
doi: 10.1007/s11464-009-0015-7
|
| 17 |
Mao Y H, Xia L H. The specrtal gap for quasi-birth and death processes. Acta Math Sin (Engl Ser), 2012, 28(5): 1075-1090
doi: 10.1007/s10114-011-9034-x
|
| 18 |
Mao Y H, Xia L H. Spectral gap for open Jackson networks. 2012, Preprint
|
| 19 |
Meyn S, Tweedie R L. Markov Chains and Stochastic Stability. London: Springer-Verlag, 1993
doi: 10.1007/978-1-4471-3267-7
|
| 20 |
Wang F Y. Functional inequalities for the decay of sub-Markov semigroups. Potential Anal, 2003, 18: 1-23
doi: 10.1023/A:1020535718522
|
| 21 |
Wang F Y. Functional Inequalities, Markov Semigroups and Spectral Theory. Beijing: Science Press, 2005
|
| 22 |
Yau S T, Schoen R. Lectures on Differential Geometry. Beijing: Higher Education Press, 2004 (in Chinese)
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
