Calculating Cumulative Operational Time Distributions of Repairable Computer Systems
IEEE Transactions on Computers - The MIT Press scientific computation series
Analysis of a composite performance reliability measure for fault-tolerant systems
Journal of the ACM (JACM)
Transient analysis of acyclic markov chains
Performance Evaluation
Combinatorial theory and statistical design
Combinatorial theory and statistical design
Evaluation of Performability for Degradable Computer Systems
IEEE Transactions on Computers
Performability Analysis: Measures, an Algorithm, and a Case Study
IEEE Transactions on Computers - Fault-Tolerant Computing
Journal of the ACM (JACM)
On Evaluating the Cumulative Performance Distribution of Fault-Tolerant Computer Systems
IEEE Transactions on Computers
State space exploration in Markov models
SIGMETRICS '92/PERFORMANCE '92 Proceedings of the 1992 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Calculating transient distributions of cumulative reward
Proceedings of the 1995 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
A Unified Framework for the Performability Evaluation of Fault-Tolerant Computer Systems
IEEE Transactions on Computers
Closed-Form Solutions of Performability
IEEE Transactions on Computers
Markovian models for performance and dependability evaluation
Lectures on formal methods and performance analysis
Model-Based Evaluation: From Dependability to Security
IEEE Transactions on Dependable and Secure Computing
Providing evidence of likely being on time: counterexample generation for CTMC model checking
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
The ins and outs of the probabilistic model checker MRMC
Performance Evaluation
A New General-Purpose Method for the Computation of the Interval Availability Distribution
INFORMS Journal on Computing
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Markov reward models are an important formalism by which to obtain dependability and performability measures of computer systems and networks. In this context, it is particularly important to determine the probability distribution function of the reward accumulated during a finite interval. The interval may correspond to the mission period in a mission-critical system, the time between scheduled maintenances, or a warranty period. In such models, changes in state correspond to changes in system structure (due to faults and repairs), and the reward structure depends on the measure of interest. For example, the reward rates may represent a productivity rate while in that state, if performability is considered, or the binary values zero and one, if interval availability is of interest. We present a new methodology to calculate the distribution of reward accumulated over a finite interval. In particular, we derive recursive expressions for the distribution of reward accumulated given that a particular sequence of state changes occurs during the interval, and we explore paths one at a time. The expressions for conditional accumulated reward are new and are numerically stable. In addition, by exploring paths individually, we avoid the memory growth problems experienced when applying previous approaches to large models. The utility of the methodology is illustrated via application to a realistic fault-tolerant multiprocessor model with over half a million states.