On the solution of GSPN reward models
Performance Evaluation
LAPACK's user's guide
On Open Synchronized Queuing Networks
International Workshop on Timed Petri Nets
A Necessary and Sufficient Saturation Condition for Open Synchronized Queueing Networks
PNPM '87 The Proceedings of the Second International Workshop on Petri Nets and Performance Models
SPNP: Stochastic Petri Net Package
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
SPN2MGM: Tool Support for Matrix-Geometric Stochastic Petri Nets
IPDS '96 Proceedings of the 2nd International Computer Performance and Dependability Symposium (IPDS '96)
Matrix-geometric solution of infinite stochastic Petri nets
IPDS '95 Proceedings of the International Computer Performance and Dependability Symposium on Computer Performance and Dependability Symposium
LAPACK Working Note 20: A Portable Linear Algebra Library For High-Performance Computers
LAPACK Working Note 20: A Portable Linear Algebra Library For High-Performance Computers
An analytical solution for a tandem queue with blocking
Queueing Systems: Theory and Applications
Spectral Expansion Solutions for Markov-Modulated Queues
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
FiFiQueues: Fixed-Point Analysis of Queueing Networks with Finite-Buffer Stations
TOOLS '00 Proceedings of the 11th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
TOOLS '98 Proceedings of the 10th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
The pseudo-self-similar traffic model: application and validation
Performance Evaluation - Dependable systems and networks-performance and dependability symposium (DSN-PDS) 2002: Selected papers
A new disk-based technique for solving the largeness problem of stochastic modeling formalisms
Journal of Systems and Software
CSL model checking algorithms for QBDs
Theoretical Computer Science
Journal of Computational and Applied Mathematics
A new performability model for queueing and FDL-related burst loss in optical switching nodes
Computer Communications
Generalized QBD processes, spectral expansion and performance modeling applications
Network performance engineering
Some new Markovian models for traffic and performance evaluation of telecommunication networks
Network performance engineering
Journal of Network and Computer Applications
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In this paper we investigate the efficiency of two solution approaches to infinite stochastic Petri nets: the matrix-geometric method and the spectral expansion method. We first informally present infinite stochastic Petri nets, after which we describe, using uniform notation, the matrix-geometric and the spectral expansion method. We put special emphasis on the numerical aspect of the solution procedures. Then, we investigate the suitability of these approaches to account for batch-movements of tokens. We then compare the two solution approaches when applied to a larger modelling study of a fault-tolerant computer system. It turns out that the spectral expansion method is favorable in all cases, especially when more heavily loaded systems are studied and when batch arrivals are incorporated in the model.To the best of our knowledge, this paper is the first to compare the spectral expansion method, as advocated by Mitrani and Chakka, with the Latouche-Ramaswami algorithm for the matrix-geometric case. Furthermore, our comparisons go well beyond the usual textbook cases, since we are able to generate, with the tool SPN2MGM, models that are much larger than those that have been assessed in the past.