## Numerical Solution of Markov ChainsPapers presented at a workshop held January 1990 (location unspecified) cover just about all aspects of solving Markov models numerically. There are papers on matrix generation techniques and generalized stochastic Petri nets; the computation of stationary distributions, including aggregation/disagg |

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### Contents

A TwentyFive Year | 1 |

STEVEN BERSON Computer Science Department University of Califor | 11 |

Markov Chain Analyzer A Software Package | 37 |

A Survey of AggregationDisaggregation in Large Markov | 63 |

An Exact AggregationDisaggregation Algorithm | 89 |

On the Sensitivity of Nearly Uncoupled Markov Chains | 105 |

Sensitivity Analysis Ergodicity Coefficients and RankOne | 121 |

Iterative Methods for Determining Derivatives of Stationary | 131 |

A Splitting Technique for Markov Chain Transient Solution | 373 |

First Passage Times in Nearly Decomposable Markov Chains | 401 |

Evaluating Bounds on SteadyState Availability of Repairable | 435 |

Projection Methods for the Numerical Solution of Markov | 455 |

The Biconjugate Gradient Method for Obtaining the Steady | 473 |

Computing the Stationary Distribution Vector of an Irreducible | 491 |

A Numerical | 511 |

The Most Likely Steady State for Large Numbers of Stochastic | 529 |

The Joint Distribution of Arrivals and Departures | 147 |

Queuing Systems Having PhaseDependent Arrival | 161 |

A Generalized Recursive Technique for Finite Markov | 203 |

Some Markov Chain Problems in the Evaluation | 239 |

A Stochastic Model for a Computer Communication Network | 261 |

Numerical Comparison of the Replacement Process | 287 |

Analysis of a Loss System with Mutual Overflow in a Markovian | 303 |

Computing Conditional Distributions of Queuing Network | 329 |

Finding Transient Solutions in Markovian Event Systems | 357 |

Combinatorial Optimization Markov Chains and Stochastic | 543 |

Solution of Large GSPN Models | 565 |

On Bounds for Token Probabilities in a Class of Generalized | 597 |

The Importance of Bias Terms for Error Bounds | 617 |

Numerical Solution of Markov Reward Models Using Laguerre | 645 |

Experimental Results on MatrixAnalytical Solution | 659 |

Software to Formulate and Solve Markov Chains | 675 |

A Software Package for Queuing Models | 691 |

### Common terms and phrases

aggregation algorithm analysis application approach approximation arrival assume balance equations block bucket buffer called components condition consider convergence corresponding decomposable decomposition defined denote determine diagonal disaggregation eigenvalues eigenvectors elements ergodic evaluated example exponential exponentially distributed Figure finite Markov frame function Gauss-Seidel given GSPN IFFO initial input irreducible iterative methods left eigenvector linear macrostate mandatory set MARCA Markov chain Markov process Markovian matrix geometric messages null values null vector object types obtained Operations Res packets parameters partition performance perturbation Petri nets phase Poisson process probability distribution probability vector problem procedure processor protocols queue queuing networks r-partition random recursive computation Schweitzer Section server slots solution solving stationary distribution stationary distribution vector stationary probability steady-state probability step Stewart stochastic complement stochastic matrix structure subnet subroutine Sumita techniques Theorem throughput timeout period tion transform transient transition probability matrix truncation zero