1990 International Meeting on the
Numerical Solution of Markov Chains.
Raleigh, NC, USA.

Proceedings Published by Marcel Dekker Inc., NJ

``Numerical Solution of Markov Chains''

Edited by

William J. Stewart

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Proceedings of the 1st International Workshop on the Numerical Solution of Markov Chains is a collection of peer-reviewed articles presented at the Workshop on Numerical Solutions of Markov Chains which was held January 8 to January 10, 1990 in Raleigh, North Carolina. These papers provide an authoritative overview of the field, including coverage of recent developments, current status of ongoing research, and projections for future directions in the field.


Marcel Dekker Inc
270 Madison Avenue
New York, New York, 10016, USA
ISBN 0-8247-8405-7

Table of Contents

  1. Numerical Markov Queuing Analysis: A Twenty-Five Year Odyssey.
    Victor L. Wallace ... 1

  2. A Methodology for the Specification and Generation of Markov Models.
    Steven Berson, Edmundo de Souza e Silva, and Richard R. Muntz ... 11

  3. MARCA: Markov Chain Analyzer, A Software Package for Markov Modeling.
    William J. Stewart ... 37

  4. A Survey of Aggregation-Disaggregation in Large Markov Chains.
    Paul J. Schweitzer ... 63

  5. An Exact Aggreagtion-Disaggregation Algorithm for Mandatory Set Decomposable Markov Chains.
    Davis S. Kim and Robert L. Smith ... 89

  6. On the Sensitivity of Nearly Uncoupled Markov Chains.
    G.W. Stewart ... 105

  7. Sensitivity Analysis, Ergodicity Coefficients, and Rank-One Updates for Finite Markov Chains.
    E. Seneta ... 121

  8. Iterative Methods for Determining Deriavatives of Staionary Distributions of Finite Markov Chains.
    Jose J. Cruz and Shaler Stidham, Jr. ... 131

  9. The Joint Distribution of Arrivals and Departures in Quasi-Birth-and-Death Processes.
    Marcel E. Neuts ... 147

  10. Queuing Systems Having Phase-Dependent Arrival and Service Service Rates.
    John N. Daigle and David M. Lucantoni ... 161

  11. A Generalized Recursive Technique for Finite Markov Processes.
    Tao Yang, M.J.M. Posner, and J.G.C. Templeton ... 203

  12. A Theory of Statistical Multiplexing of Markovian Sources: Spectral Expansions and Algorithms.
    A.I. Elwalid, D. Mitra, and T.E. Stern ... 223

  13. Some Markov Chain Problems in the Evaluation of Multiple-Access Protocols.
    Jeffery E. Wieselthier and Anthony Ephremides ... 239

  14. A Stochastic Model for a Computer Communication Network Node with Phase Type Timeout Periods.
    S. Chakravarthy and K.V. Ravi ... 261

  15. Numerical Comparison of the Replacement Process Approach with the Aggregation-Disaggregation Algorithm for Row-Continuous Markov Chains.
    Ushio Sumita and Maria Reiders

  16. Analysis of a Loss System with Mutual Overflow in a Markovian Environment.
    Udo R. Krieger ... 303

  17. Computing Conditional Distributions of Queing Network Matrices.
    Pierre Semal and Pierre-Jacques Courtois ... 329

  18. Finding Transient Solutions in Markovian Event Systems Through Randomization.
    Winfried K. Grassmann ... 357

  19. A Splitting Technigue for Markov Chain Transient Solution.
    Andrew Reibman ... 373

  20. Transient Solutions of Time-Inhomogeneous Markov Reward Models with Discontinuous Rates.
    Mark K. Smotherman ... 385

  21. First Passage Times in Nearly Decomposable Markov Chains.
    Guy Latouche ... 401

  22. Bounds for Transient Characteristics of Large or Infinite Markov Chains.
    Pierre-Jacques Courtois and Pierre Semal ... 413

  23. Evaluating Bounds on Steady-State Availability of Repairable Systems from Markov Models.
    John C.S. Lui and Richard R. Muntz ... 435

  24. Projection Methods for the Numerical Solution of Markov Chain Models.
    Youcef Saad ... 455

  25. The Biconjugate Gradient Method for Obtaining the Steady- State Probablity Distributions of Markovian Multiechelon Repairable Item Inventory Systems.
    Donald Gross, Bingchang Gu, and Richard M. Soland ... 473

  26. Computing the Staionary Distribution Vector of an Irreducible Markoc Chain on a Shared-Memory Multiprocessor.
    R.B. Mattingly and C.D. Meyer ... 491

  27. Steady-State Behavior of Interacting Queues: A Numerical Approach.
    A. Nakasis and A. Ephremides ... 511

  28. The Most Likely Staedy State for Large Numbers of Stochastic Traveling Salesman.
    Robert Geist and Robert Reynolds ... 529

  29. Combinatorial Optimization, Markov Chains, and Stochastic Automata.
    Eugene Shragowitz and Rung-Bin Lin ... 543

  30. Solution of Large GSPN Models.
    Gianfranco Ciardo and Kishor S. Trivedi ... 565

  31. On Bounds for Token Probabilities in a Class of Generalized Stochastic Petri Nets.
    S.M.R. Islam and H.H. Ammar ... 597

  32. The Importance of Bias Terms for Error Bounds and Comparison Results.
    Nico M. van Dijk ... 617


  33. Numerical Solution of Markov Reward Models Using Laguerre Functions.
    S.M.R. Islam and H.H. Ammar ... 645
  34. The Analysis of a Manufacturing Unit by Sparse Matrix Techniques.
    Vincent A. Barker and Bo Friis Nielson ... 649
  35. Approximating the Stationary Distribution of an Infinite Stochastic Matrix.
    Daniel P. Heyman ...653
  36. Transient Analysis of the M(t)/M(t)1 Queue,
    Ji Zhang and Edward J. Coyle ... 655
  37. Experimental Results on Matrix-Analytical Solution Techniques: Extensions and Comparisons.
    Levent Gun ... 659
  38. Lumpimg in Markov Reward Processes.
    Victor F. Nicola ... 663
  39. Accelerated Convergence Through Extrapolation for the Discounted Return in Markov Chains.
    Jeffery L. Popyack ... 667
  40. Computing the Fundamental Matrix for a Reducible Markov Chain.
    Theodore J. Sheskin ... 671

  41. MARKOV1: Software to Formulate and Solve Markov Chains
    Thomas R. Bowe and William Dapkus ... 675
  42. Queuing Network Analysis Package-2 (QNAP2).
    Kshemendra Paul ... 683
  43. MARCA: Markov Chain Analyzer.
    William J. Stewart ... 687
  44. Q-Lib: A Software package for Queuing Models.
    H.C. Tijms ... 691
  45. SPNP: The Stochastic Petri Net Package.
    Gianfranco Ciardo, Jogesh Muppala, and Kishor S. Trivedi ... 693
  46. SHARPE: Symbolic Hierarchical Automated Reliability and Performance Evaluator.
    Robin A. Sahner and Kishor S. Trivedi ... 695
    Index ... 697

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