Numerical Solution of Markov Chains

William J. Stewart (North Carolina State University, Raleigh)

• 1. Numerical Markov Queuing Analysis: A Twenty-Five Year Odyssey 2. A Methodology for the Specification and Generation of Markov Models 3. MARCA: Markov Chain Analyzer, A Software Package for Markov Modeling 4. A Survey of Aggregation-Disaggregation in Large Markov Chains 5. An Exact Aggregation-Disaggregation Algorithm for Mandatory Set Decomposable Markov Chains 6. On the Sensitivity of Nearly Uncoupled Markov Chains 7. Sensitivity Analysis, Ergodicity Coefficients, and Rank-One Updates for Finite Markov Chains 8. Iterative Methods for Determining Derivatives of Stationary Distributions of Finite Markov Chains 9. The Joint Distribution of Arrivals and Departures in Quasi-Birth-and-Death Processes 10. Queuing Systems Having Phase-Dependent Arrival and Service Rates 11. A Generalized Recursive Technique for Finite Markov Processes 12. A Theory of Statistical Multiplexing of Markovian Sources: Spectral Expansions and Algorithms 13. Some Markov Chain Problems in the Evaluation of Multiple-Access Protocols 14. A Stochastic Model for a Computer Communication Network Node with Phase Type Timeout Periods 15. Numerical Comparison of the Replacement Process Approach with the Aggregation-Disaggregation Algorithm for Row-Continuous Markov Chains 16. Analysis of a Loss System with Mutual Overflow in a Markovian Environment 17. Computing Conditional Distributions of Queuing Network Matrices 18. Finding Transient Solutions in Markovian Event Systems Through Randomization 19. A Splitting Technique for Markov Chain Transient Solution 20. Transient Solutions of Time-Inhomogeneous Markov Reward Models with Discontinuous Rates 21. First Passage Times in Nearly Decomposable Markov Chains 22. Bounds for Transient Characteristics of Large or Infinite Markov Chains 23. Evaluating Bounds on Steady-State Availability of Repairable Systems from Markov Models 24. Projection Methods for the Numerical Solution of Markov Chain Models 25. The Biconjugate Gradient Method for Obtaining the SteadyState Probability Distributions of Markovian Multiechelon Repairable Item Inventory Systems 26. Computing the Stationary Distribution Vector of an Irreducible Markov Chain on a Shared-Memory Multiprocessor 27. Steady-State Behavior of Interacting Queues: A Numerical Approach 28. The Most Likely Steady State for Large Numbers of Stochastic Traveling Salesmen 29. Combinatorial Optimization, Markov Chains, and Stochastic Automata 30. Solution of Large GSPN Models 31. On Bounds for Token Probabilities in a Class of Generalized Stochastic Petri Nets 32. The Importance of Bias Terms for Error Bounds and Comparison Results