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…mehr
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.
1 Detecting Block GI/M/1 and Block M/G/1 Matrices from Model Specifications.- 2 On Cyclic Reduction Applied to a Class of Toeplitz-like Matrices Arising in Queueing Problems.- 3 A Markov Modulated, Nearly Completely Decomposable M/M/1 Queue.- 4 Preconditioned Krylov subspace methods for the numerical solution of Markov chains.- 5 A Parallel Block Projection Method of the Cimmino Type for Finite Markov Chains.- 6 Iterative Methods for Queueing Models with Batch Arrivals.- 7 Transient Colutions of Markov Processes by Krylov Subspaces.- 8 Exact Methods for the Transient Analysis of Nonhomogeneous Continuous Time Markov Chains.- 9 Time-Dependent behavior of Redundant Systems with Deterministic Repair.- 10 What is Fundamental for Markov Chains: First Passage Times, Fundamental Matrices, and Group Generalized Inverses.- 11 Immediate Events in Markov Chains.- 12 Compositional Markovian Modelling Using A Process Algebra.- 13 Equivalence Relations for Stochastic Automata Networks.- 14 Graphs and Stochastic Automata Networks.- 15 Analyzing Sample Path Data from Markov Chain Sampling Experiments.- 16 Resource Sharing Models with State-Dependent Arrivais of Batches.- 17 Implementable Policies: Discounted Cost Case.- 18 Two Bounding Schemes for the Steady-State Solution of Markov Chains.- 19 The Power-Series Algorithm for Markovian Queueing Networks.- 20 Discrete-Time Markovian Stochastic Petri Nets.- 21 Concurrent Generalized Petri Nets.- 22 Exploiting Isomorphisms and Special Structures in the Analysis of Markov Regenerative Stochastic Petri Nets.- 23 Numerical solution of large finite Markov chains by algebraic multigrid techniques.- 24 On the Utility of the Multi-Level Algorithm for the Solution of Nearly Completely Decomposable Markov Chains.- 25 A Computationally Efficient Algorithm for Characterizing the Superposition of Multiple Heterogeneous Interrupted Bernoulli Processes.- 26 Generalized Folding Algorithm for Transient Analysis of Finite QBD Processes and its Queueing Applications.- 27 Efficient Solutions for a Class of Non-Markovian Models.- 28 Markovian Arrival and Service Communication Systems: Spectral Expansions, Separability and Kronecker-Product Forms.- 29 Empirical Comparison of Uniformization Methods for Continuous-Time Markov Chains.- 30 Numerical Methods for M/G/1 Type Queues.- 31 Closing the Gap between Classical and Tensor Based Iteration Techniques.- 32 Adaptive Relaxation for the Steady-State Analysis of Markov Chains.- 33 State Space Decomposition for Large Markov Chains.- 34 Aggregation/Disaggregation Method on Parallel Computer.- 35 Parallel Implementation of the GTH Algorithm for Markov Chains.- 36 A Parallel Implementation of the Block-GTH algorithm.- 37 Approximate Computation of Sojourn Time Distribution in Open Queueing Networks.
1 Detecting Block GI/M/1 and Block M/G/1 Matrices from Model Specifications.- 2 On Cyclic Reduction Applied to a Class of Toeplitz-like Matrices Arising in Queueing Problems.- 3 A Markov Modulated, Nearly Completely Decomposable M/M/1 Queue.- 4 Preconditioned Krylov subspace methods for the numerical solution of Markov chains.- 5 A Parallel Block Projection Method of the Cimmino Type for Finite Markov Chains.- 6 Iterative Methods for Queueing Models with Batch Arrivals.- 7 Transient Colutions of Markov Processes by Krylov Subspaces.- 8 Exact Methods for the Transient Analysis of Nonhomogeneous Continuous Time Markov Chains.- 9 Time-Dependent behavior of Redundant Systems with Deterministic Repair.- 10 What is Fundamental for Markov Chains: First Passage Times, Fundamental Matrices, and Group Generalized Inverses.- 11 Immediate Events in Markov Chains.- 12 Compositional Markovian Modelling Using A Process Algebra.- 13 Equivalence Relations for Stochastic Automata Networks.- 14 Graphs and Stochastic Automata Networks.- 15 Analyzing Sample Path Data from Markov Chain Sampling Experiments.- 16 Resource Sharing Models with State-Dependent Arrivais of Batches.- 17 Implementable Policies: Discounted Cost Case.- 18 Two Bounding Schemes for the Steady-State Solution of Markov Chains.- 19 The Power-Series Algorithm for Markovian Queueing Networks.- 20 Discrete-Time Markovian Stochastic Petri Nets.- 21 Concurrent Generalized Petri Nets.- 22 Exploiting Isomorphisms and Special Structures in the Analysis of Markov Regenerative Stochastic Petri Nets.- 23 Numerical solution of large finite Markov chains by algebraic multigrid techniques.- 24 On the Utility of the Multi-Level Algorithm for the Solution of Nearly Completely Decomposable Markov Chains.- 25 A Computationally Efficient Algorithm for Characterizing the Superposition of Multiple Heterogeneous Interrupted Bernoulli Processes.- 26 Generalized Folding Algorithm for Transient Analysis of Finite QBD Processes and its Queueing Applications.- 27 Efficient Solutions for a Class of Non-Markovian Models.- 28 Markovian Arrival and Service Communication Systems: Spectral Expansions, Separability and Kronecker-Product Forms.- 29 Empirical Comparison of Uniformization Methods for Continuous-Time Markov Chains.- 30 Numerical Methods for M/G/1 Type Queues.- 31 Closing the Gap between Classical and Tensor Based Iteration Techniques.- 32 Adaptive Relaxation for the Steady-State Analysis of Markov Chains.- 33 State Space Decomposition for Large Markov Chains.- 34 Aggregation/Disaggregation Method on Parallel Computer.- 35 Parallel Implementation of the GTH Algorithm for Markov Chains.- 36 A Parallel Implementation of the Block-GTH algorithm.- 37 Approximate Computation of Sojourn Time Distribution in Open Queueing Networks.
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