Subexponential Asymptotics of the Stationary Distributions of GI/G/1-Type Markov Chains

REFERENCES

• Asmussen , S. Applied Probability and Queues, , 2nd ed. ; Springer : New York , 2003 .
   Google Scholar
• Asmussen , S. ; Foss , S. ; Korshunov , D. Asymptotics for sums of random variables with local subexponential behavior . J. Theoret. Probab. 2003 , 16 , 489 – 518 .
   Web of Science ®Google Scholar
• Asumussen , S. ; Henriksen , L.F. ; Klüppelberg , C. Large claims approximations for risk processes in a Markovian environment . Stochastic Processes and Their Applications 1994 , 54 , 29 – 43 .
   Web of Science ®Google Scholar
• Asmussen , S. ; Møller , J.R. Tail asymptotics for M/G/1 type queueing processes with subexponential increments . Queueing Systems 1999 , 33 , 153 – 176 .
   Web of Science ®Google Scholar
• Bingham , N.H. ; Goldie , C.M. ; Teugels , J.L. Regular Variation ; Cambridge University Press : New York , 1989 .
   Google Scholar
• Bremaud , P. Markov Chains, Gibbs Fields, Monte Carlo Simulation and Queues ; Springer : New York , 1999 .
   Google Scholar
• Chistyakov , V.P. A theorem on sums of independent positive random variables and its applications to branching random processes . Theor. Probab. Appl. 1964 , 9 , 640 – 648 .
   Google Scholar
• Chover , J. ; Ney , P. ; Wainger , S. Functions of probability measures . J. Anal. Math. 1973 , 26 , 255 – 302 .
   Web of Science ®Google Scholar
• Embrechts , P. ; Klüppelberg , C. ; Mikosch , T. Modelling Extremal Events for Insurance and Finance ; Springer : Berlin , 1997 .
   Google Scholar
• Grassmann , W.K. ; Heyman , D.P. Equilibrium distribution of block-structured Markov chains with repeating rows . J. Appl. Probab. 1990 , 27 , 557 – 576 .
   Web of Science ®Google Scholar
• Horn , R.A. ; Johnson , C.R. Matrix Analysis ; Cambridge University Press : New York , 1990 .
   Google Scholar
• Jelenković , P.R. ; Lazar , A.A. Subexponential asymptotics of a Markov-modulated random walk with queueing applications . J. Appl. Probab. 1998 , 35 , 325 – 347 .
   Web of Science ®Google Scholar
• Kim , B. ; Kim , J. A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains . Eur. J. Oper. Res. 2012 , 220 , 132 – 134 .
   Web of Science ®Google Scholar
• Kimura , T. ; Daikoku , K. ; Masuyama , H. ; Takahashi , Y. Light-tailed asymptotics of stationary tail probability vectors of Markov chains of M/G/1 type . Stoch. Model. 2010 , 26 , 505 – 548 .
   Web of Science ®Google Scholar
• Kimura , T. ; Daikoku , K. ; Masuyama , H. ; Takahashi , Y. Light-tailed asymptotics of stationary tail probability vectors of Markov chains of M/G/1 type. arXiv:1110.4457.
   Google Scholar
• Klüppelberg , C. Subexponential distributions and integrated tails . J. Appl. Probab. 1988 , 25 , 132 – 141 .
   Web of Science ®Google Scholar
• Li , Q.-L. ; Zhao , Y.Q. Heavy-tailed asymptotics of stationary probability vectors of Markov chains of GI/G/1 type . Adv. Appl. Probab. 2005 , 37 , 482 – 509 .
   Web of Science ®Google Scholar
• Li , Q.-L. ; Zhao , Y.Q. Light-tailed asymptotics of stationary probability vectors of Markov chains of GI/G/1 type . Adv. Appl. Probab. 2005 , 37 , 1075 – 1093 .
   Web of Science ®Google Scholar
• Masuyama , H. Subexponential asymptotics of the stationary distributions of M/G/1-type Markov chains . Eur. J. Oper. Res. 2011 , 213 , 509 – 516 .
   Web of Science ®Google Scholar
• Pitman , E.J.G. Subexponential distribution functions. J. Aust. Math. Soc. Ser. A 1980, 29, 337–347.
   Google Scholar
• Shin , Y.W. BMAP/G/1 queue with correlated arrivals of customers and disasters . Oper. Res. Lett. 2004 , 32 , 364 – 373 .
   Web of Science ®Google Scholar
• Sigman , K. Appendix: A primer on heavy-tailed distributions . Queueing Systems 1999 , 33 , 261 – 275 .
   Web of Science ®Google Scholar
• Takine , T. Geometric and subexponential asymptotics of Markov chains of M/G/1 type . Math. Oper. Res. 2004 , 29 , 624 – 648 .
   Web of Science ®Google Scholar
• Wilf , H.S. Generating Functionology, , 2nd ed. ; Academic Press : Boston , 1994 .
   Google Scholar
• Zhao , Y.Q. ; Li , W. ; Braun , W.J. Infinite block-structured transition matrices and their properties . Adv. Appl. Probab. 1998 , 30 , 365 – 384 .
   Web of Science ®Google Scholar
• Zhao , Y.Q. ; Li , W. ; Alfa , A.S. Duality results for block-structured transition matrices . J. Appl. Probab. 1999 , 36 , 1045 – 1057 .
   Web of Science ®Google Scholar
• Zhao , Y.Q. ; Li , W. ; Braun , W.J. Censoring, factorizations, and spectral analysis for transition matrices with block-repeating entries . Meth. Comput. Appl. Probab. 2003 , 5 , 35 – 58 .
   Web of Science ®Google Scholar