Journal of applied mathematics & informatics

  • 제5권2호
  • /
  • Pages.403-426
  • /
  • 1998
  • /
  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

AN ALGORITHMIC APPROACH TO THE MARKOV CHAIN WITH TRANSITION PROBABILITY MATRIX OF UPPER BLOCK-HESSENBERG FORM

  • Shin, Yang-Woo (Department of Statistics Changwon National University) ;
  • Pearce, C.E.M. (Department of Applied mathematics University of Adelaide)
  • 발행 : 1998.06.01

⟨ 이전 논문 다음 논문 ⟩

초록

We present an algorithm to find an approximation for the stationary distribution for the general ergodic spatially-inhomogeneous block-partitioned upper Hessenberg form. Our approximation makes use of an associated upper block-Hessenberg matrix which is spa-tially homogeneous except for a finite number of blocks. We treat the MAP/G/1 retrial queue and the retrial queue with two types of customer as specific instances and give some numerical examples. The numerical results suggest that our method is superior to the ordinary finite-truncation method.

키워드

참고문헌

  1. Stochastic Models v.11 no.3 Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes L.Bright;P.G.Taylor
  2. Mathematical and Computer Modeling Single server retrial queues with priority calls B.D.Choi;Y.Chang
  3. Stochastic Models v.11 Matrix analytic methods for M/PH/1 retrial queues J.E.Diamond;A.S.Alfa
  4. Retrial Queues G.I.Falin;J.G.C.Templeton
  5. Stoch. Proc. and Appl. v.24 Monotone infinite stochastic matrices and their augmented truncations D.Gibson;E.Seneta
  6. J. Appl. Prob. v.24 Augmented truncations of infinite stochastic matrices D.Gibson;E.Seneta
  7. J. Appl. Prob. v.27 Equilibrium distribution of block-structured Markov chains with repeating rows W.K.Grassman;D.P.Heyman
  8. ORSA J. on Computing v.5 Computation of steady-state probabilities for infinite-state Markov chains with repeating rows W.K.Grassman;D.P.Heyman
  9. Stochastic Models v.5 no.4 Experimental results on matrix-analytical solution techniques-extensions and comparisons L.Gun
  10. J. Appl. Prob. v.28 Approximating the stationary distribution of an infinite stochastic matrix D.P.Heyman
  11. Queueing Systems v.10 Using state reduction for computing steady state vectors in Markov chains of M/G/1 type E.P.C.Kao
  12. Naval Res. Log. Quart v.31 Finite Markov chain models skip-free in one direction G.Latouche;P.A.Jacobs;D.P.Gaver
  13. IEEE J. Select. Areas Commun. v.9 An efficient solution method for Markov models of ATM links with loss priorities J.Y.Le Boudec
  14. Technical report, TUNS The steady state distribution of the PH/M/1 retrial queue H.Li;T.Yang
  15. Adv. Appl. Prob. v.22 A single-server queue with server vacations and a class of non-renewal arrival processes D.M.Lucantoni;K.S.Meier Hellstern;M.F.Neuts
  16. Stochastic Models v.1 Efficient algorithms for solving the nonlinear matrix equations arising in phase type queues D.M.Lucantoni;V.Ramaswami
  17. Matrix-geometric solutions in stochastic models, an algorithmic approach M.F.Neuts
  18. Structured Stochastic Matrrices of M/G/1 Type and Their Applications M.F.Neuts
  19. Queueing Systems v.7 Numerical investigation of a multiserver retrial model M.F.Neuts;B.M.Rao
  20. Adv. Appl. Prob. v.21 Extended continued fractions recurrence relations and two-dimensional Markov processes C.E.M.Pearce
  21. Stochastic Models v.4 A stable recursion for the steady state vector in Markov chains of M/G/1 type V.Ramaswami
  22. SIAM Review v.30 Nonlinear matrix equations in applied probability-solution techniques and an open problems V.Ramaswami
  23. Non-negative matrices and Markov chains(2nd ed.) E.Seneta
  24. J. Australian Math. Soc. Series B. The BMAP/G/1 vacation queue with queuelength dependent vacation schedule Y.W.Shin;C.E.M.Pearce
  25. Adv. Appl. Prob. v.12 Approximation of the invariant probability measure of an infinite stochastic matrix D.Wolf
  26. INFOR Stationary probabilities of Markov chains with upper Hessenberg transition matrices Y.Q.Zhao;S.Li
  27. Adv. Appl. Prob. v.30 Infinite block-structured transition matrices and their properties Y.Q.Zhao;W.Li;W.J.Braun
  28. J. Appl. Prob. v.33 The censored Markov chain and the best augmentation Y.Q.Zhao;D.Liu