ACM Transactions on Computer Systems (TOCS)
Analytic Queueing Network Models for Parallel Processing of Task Systems
IEEE Transactions on Computers
Analysis of large stochastic petri net models
Analysis of large stochastic petri net models
Approximate performance models of polling systems using Stochastic Petri nets
IEEE INFOCOM '92 Proceedings of the eleventh annual joint conference of the IEEE computer and communications societies on One world through communications (Vol. 3)
Approximate analysis for heterogeneous multiprocessor systems with priority jobs
Performance Evaluation
A decomposition approach for stochastic reward net models
Performance Evaluation
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Journal of the ACM (JACM)
A hierarchial, combinatorial-Markov model of solving complex reliability models
ACM '86 Proceedings of 1986 ACM Fall joint computer conference
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
On the modeling of parallel access to shared data
Communications of the ACM
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Petri Net Theory and the Modeling of Systems
Petri Net Theory and the Modeling of Systems
SPNP: Stochastic Petri Net Package
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
Fixed Point Iteration in Availability Modeling
Proceedings of the 5th International GI/ITG/GMA Conference on Fault-Tolerant Computing Systems, Tests, Diagnosis, Fault Treatment
Iterative Decomposition and Aggregation of Labeled GSPNs
ICATPN '98 Proceedings of the 19th International Conference on Application and Theory of Petri Nets
Model-Based Evaluation: From Dependability to Security
IEEE Transactions on Dependable and Secure Computing
Performance analysis of multistage interconnection networks with a new high-level net model
Journal of Systems Architecture: the EUROMICRO Journal
Achieving and assuring high availability
ISAS'08 Proceedings of the 5th international conference on Service availability
Call admission control for reducing dropped calls in CDMA cellular systems
Computer Communications
A method for multiple channel recovery in TDMA wireless communications systems
Computer Communications
Modeling and performance analysis of large scale IaaS Clouds
Future Generation Computer Systems
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Stochastic Petri net models of large systems that are solved by generating the underlying Markov chain pose the problem of largeness of the state-space of the Markov chain. Hierarchical and iterative models of systems have been used extensively to solve this problem. A problem with models which use fixed-point iteration is the theoretical proof of existence, uniqueness, and convergence of the fixed-point equations, which still remains an "art." In this paper, we establish conditions, in terms of the net structure and the characteristics of the iterated variables, under which existence of a solution is guaranteed when fixed-point iteration is used in stochastic Petri nets. We use these conditions to establish the existence of a fixed point for a model of a priority scheduling system, at which tasks may arrive according to a Poisson process or due to spawning or conditional branching of other tasks in the system.