Computations with Markov Chains: Proceedings of the 2nd International Workshop on the Numerical Solution of Markov Chains

✍ Scribed by Steven Bersonl, Richard Muntz (auth.), William J. Stewart (eds.)

• Publisher: Springer US
• Year: 1995
• Tongue: English
• Leaves: 604
• Edition: 1
• Category: Library

✦ Synopsis

Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more.
An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.

✦ Table of Contents

Front Matter....Pages i-xvi
Detecting Block GI/M/1 and Block M/G/1 Matrices from Model Specifications....Pages 1-19
On Cyclic Reduction Applied to a Class of Toeplitz-Like Matrices Arising in Queueing Problems....Pages 21-38
A Markov Modulated, Nearly Completely Decomposable M/M/1 Queue....Pages 39-48
Preconditioned Krylov Subspace Methods for the Numerical Solution of Markov Chains....Pages 49-64
A Parallel Block Projection Method of the Cimmino Type for Finite Markov Chains....Pages 65-80
Iterative Methods for Queueing Models with Batch Arrivals....Pages 81-93
Transient Solutions of Markov Processes by Krylov Subspaces....Pages 95-119
Exact Methods for the Transient Analysis of Nonhomogeneous Continuous Time Markov Chains....Pages 121-133
Time-Dependent Behavior of Redundant Systems with Deterministic Repair....Pages 135-150
What is Fundamental for Markov Chains: First Passage Times, Fundamental Matrices, and Group Generalized Inverses....Pages 151-161
Immediate Events in Markov Chains....Pages 163-176
Compositional Markovian Modelling Using a Process Algebra....Pages 177-196
Equivalence Relations for Stochastic Automata Networks....Pages 197-215
Graphs and Stochastic Automata Networks....Pages 217-235
Analyzing Sample Path Data from Markov Chain Sampling Experiments....Pages 237-253
Resource-Sharing Models with State-Dependent Arrivals of Batches....Pages 255-282
Implementable Policies: Discounted Cost Case....Pages 283-306
Two Bounding Schemes for the Steady-State Solution of Markov Chains....Pages 307-320
The Power-Series Algorithm for Markovian Queueing Networks....Pages 321-338
Discrete-Time Markovian Stochastic Petri Nets....Pages 339-358
Concurrent Generalized Petri Nets....Pages 359-382
Exploiting Isomorphisms and Special Structures in the Analysis of Markov Regenerative Stochastic Petri Nets....Pages 383-402
Numerical Solution of Large Finite Markov Chains by Algebraic Multigrid Techniques....Pages 403-424
On the Utility of the Multi-Level Algorithm for the Solution of Nearly Completely Decomposable Markov Chains....Pages 425-442
A Computationally Efficient Algorithm for Characterizing the Superposition of Multiple Heterogeneous interrupted Bernoulli Processes....Pages 443-462
Generalized Folding Algorithm for Transient Analysis of Finite QBD Processes and Its Queueing Applications....Pages 463-481
Efficient Solutions for a Class of Non-Markovian Models....Pages 483-506
Markovian Arrival and Service Communication Systems: Spectral Expansions, Separability and Kronecker-Product Forms....Pages 507-546
Empirical Comparison of Uniformization Methods for Continuous-Time Markov Chains....Pages 547-570
Numerical Methods For M/G/1 Type Queues....Pages 571-581
Closing the Gap Between Classical and Tensor Based Iteration Techniques....Pages 582-584
Adaptive Relaxation for the Steady-State Analysis of Markov Chains....Pages 585-586
State Space Decomposition for Large Markov Chains....Pages 587-590
Aggregation/Disaggregation Method on Parallel Computer....Pages 591-593
Parallel Implementation of the GTH Algorithm for Markov Chains....Pages 594-596
A Parallel Implementation of the Block-GTH Algorithm....Pages 597-598
Approximate Computation of Sojourn Time Distribution in Open Queueing Networks....Pages 599-600

✦ Subjects

Number Theory; Probability Theory and Stochastic Processes; Numeric Computing; Computational Mathematics and Numerical Analysis; Operation Research/Decision Theory; Processor Architectures