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
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.
Publisher
Marcel Dekker Inc
270 Madison Avenue
New York, New York, 10016, USA
ISBN 0-8247-8405-7
Table of Contents
- Numerical Markov Queuing Analysis: A Twenty-Five Year Odyssey.
Victor L. Wallace ... 1
- A Methodology for the Specification and Generation of Markov
Models.
Steven Berson, Edmundo de Souza e Silva, and Richard R. Muntz
... 11
- MARCA: Markov Chain Analyzer, A Software Package for Markov
Modeling.
William J. Stewart ... 37
- A Survey of Aggregation-Disaggregation in Large Markov Chains.
Paul J. Schweitzer ... 63
- An Exact Aggreagtion-Disaggregation Algorithm for Mandatory
Set Decomposable Markov Chains.
Davis S. Kim and Robert L. Smith ... 89
- On the Sensitivity of Nearly Uncoupled Markov Chains.
G.W. Stewart ... 105
- Sensitivity Analysis, Ergodicity Coefficients, and Rank-One
Updates for Finite Markov Chains.
E. Seneta ... 121
- Iterative Methods for Determining Deriavatives of Staionary
Distributions of Finite Markov Chains.
Jose J. Cruz and Shaler Stidham, Jr. ... 131
- The Joint Distribution of Arrivals and Departures in
Quasi-Birth-and-Death Processes.
Marcel E. Neuts ... 147
- Queuing Systems Having Phase-Dependent Arrival and Service
Service Rates.
John N. Daigle and David M. Lucantoni ... 161
- A Generalized Recursive Technique for Finite Markov Processes.
Tao Yang, M.J.M. Posner, and J.G.C. Templeton ... 203
- A Theory of Statistical Multiplexing of Markovian Sources:
Spectral Expansions and Algorithms.
A.I. Elwalid, D. Mitra, and T.E. Stern ... 223
- Some Markov Chain Problems in the Evaluation of Multiple-Access
Protocols.
Jeffery E. Wieselthier and Anthony Ephremides ... 239
- A Stochastic Model for a Computer Communication Network Node
with Phase Type Timeout Periods.
S. Chakravarthy and K.V. Ravi ... 261
- Numerical Comparison of the Replacement Process Approach with
the Aggregation-Disaggregation Algorithm for Row-Continuous
Markov Chains.
Ushio Sumita and Maria Reiders
- Analysis of a Loss System with Mutual Overflow in a Markovian
Environment.
Udo R. Krieger ... 303
- Computing Conditional Distributions of Queing Network Matrices.
Pierre Semal and Pierre-Jacques Courtois ... 329
- Finding Transient Solutions in Markovian Event Systems Through
Randomization.
Winfried K. Grassmann ... 357
- A Splitting Technigue for Markov Chain Transient Solution.
Andrew Reibman ... 373
- Transient Solutions of Time-Inhomogeneous Markov Reward
Models with Discontinuous Rates.
Mark K. Smotherman ... 385
- First Passage Times in Nearly Decomposable Markov Chains.
Guy Latouche ... 401
- Bounds for Transient Characteristics of Large or Infinite
Markov Chains.
Pierre-Jacques Courtois and Pierre Semal ... 413
- Evaluating Bounds on Steady-State Availability of
Repairable Systems from Markov Models.
John C.S. Lui and Richard R. Muntz ... 435
- Projection Methods for the Numerical Solution of Markov
Chain Models.
Youcef Saad ... 455
- 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
- Computing the Staionary Distribution Vector of an Irreducible
Markoc Chain on a Shared-Memory Multiprocessor.
R.B. Mattingly and C.D. Meyer ... 491
- Steady-State Behavior of Interacting Queues: A Numerical
Approach.
A. Nakasis and A. Ephremides ... 511
- The Most Likely Staedy State for Large Numbers of Stochastic
Traveling Salesman.
Robert Geist and Robert Reynolds ... 529
- Combinatorial Optimization, Markov Chains, and Stochastic
Automata.
Eugene Shragowitz and Rung-Bin Lin ... 543
- Solution of Large GSPN Models.
Gianfranco Ciardo and Kishor S. Trivedi ... 565
- On Bounds for Token Probabilities in a Class of Generalized
Stochastic Petri Nets.
S.M.R. Islam and H.H. Ammar ... 597
- The Importance of Bias Terms for Error Bounds and Comparison
Results.
Nico M. van Dijk ... 617
POSTER PAPERS
- Numerical Solution of Markov Reward Models Using Laguerre
Functions.
S.M.R. Islam and H.H. Ammar ... 645
- The Analysis of a Manufacturing Unit by Sparse Matrix
Techniques.
Vincent A. Barker and Bo Friis Nielson ... 649
- Approximating the Stationary Distribution of an Infinite
Stochastic Matrix.
Daniel P. Heyman ...653
- Transient Analysis of the M(t)/M(t)1 Queue,
Ji Zhang and Edward J. Coyle ... 655
- Experimental Results on Matrix-Analytical Solution
Techniques: Extensions and Comparisons.
Levent Gun ... 659
- Lumpimg in Markov Reward Processes.
Victor F. Nicola ... 663
- Accelerated Convergence Through Extrapolation for the
Discounted Return in Markov Chains.
Jeffery L. Popyack ... 667
- Computing the Fundamental Matrix for a Reducible Markov
Chain.
Theodore J. Sheskin ... 671
SOFTWARE DEMONSTRATIONS
- MARKOV1: Software to Formulate and Solve Markov Chains
Thomas R. Bowe and William Dapkus ... 675
- Queuing Network Analysis Package-2 (QNAP2).
Kshemendra Paul ... 683
- MARCA: Markov Chain Analyzer.
William J. Stewart ... 687
- Q-Lib: A Software package for Queuing Models.
H.C. Tijms ... 691
- SPNP: The Stochastic Petri Net Package.
Gianfranco Ciardo, Jogesh Muppala, and Kishor S. Trivedi
... 693
- SHARPE: Symbolic Hierarchical Automated Reliability and
Performance Evaluator.
Robin A. Sahner and Kishor S. Trivedi ... 695
Index ... 697