Approximation methods for stochastic petri nets

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists

PETRI NET BASED MODELING OF PARALLEL PROGRAMS EXECUTING ON DISTRIBUTED MEMORY MULTIPROCESSOR SYSTEMS

The development of parallel programs following the paradigm of communicating sequen- tial processes to be executed on distributed memory multiprocessor systems is addressed. The key issue in programming parallel machines today is to provide computerized tools supporting the development of efficient parallel software, i.e. software effectively har- nessing the power of parallel processing systems. The critical situations where a parallel programmer needs help is in expressing a parallel algorithm in a programming language, in getting a parallel program to work and in tuning it to get optimum performance (for example speedup). . We show that the Petri net formalism is higly suitable as a performance modeling technique for asynchronous parallel systems, by introducing a model taking care of the parallel program, parallel architecture and mapping influences on overall system perfor- mance. PRM -net (Program-Resource- Mapping) models comprise a Petri net model of the multiple flows of control in a parallel program, a Petri net model of the parallel hardware and the process-to-processor mapping information into a single integrated performance model. Automated analysis of PRM-net models addresses correctness and performance of parallel programs mapped to parallel hardware. Questions upon the correctness of parallel programs can be answered by investigating behavioural properties of Petri net programs like liveness, reachability, boundedness, mutualy exclusiveness etc. Peformance of parallel programs is usefully considered only in concern with a dedicated target hard- ware. For this reason it is essential to integrate multiprocessor hardware characteristics into the specification of a parallel program. The integration is done by assigning the concurrent processes to physical processing devices and communication patterns among parallel processes to communication media connecting processing elements yielding an in- tegrated, Petri net based performance model. Evaluation of the integrated model applies simulation and markovian analysis to derive expressions characterising the peformance of the program being developed. Synthesis and decomposition rules for hierarchical models naturally give raise to use PRM-net models for graphical, performance oriented parallel programming, support- ing top-down (stepwise refinement) as well as bottom-up development approaches. The graphical representation of Petri net programs visualizes phenomena like parallelism, syn- chronisation, communication, sequential and alternative execution. Modularity of pro- gram blocks aids reusability, prototyping is promoted by automated code generation on the basis of high level program specifications

Compositional Performance Modelling with the TIPPtool

Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations

Availability modeling and evaluation on high performance cluster computing systems

Cluster computing has been attracting more and more attention from both the industrial and the academic world for its enormous computing power, cost effective, and scalability. Beowulf type cluster, for example, is a typical High Performance Computing (HPC) cluster system. Availability, as a key attribute of the system, needs to be considered at the system design stage and monitored at mission time. Moreover, system monitoring is a must to help identify the defects and ensure the system\u27s availability requirement. In this study, novel solutions which provide availability modeling, model evaluation, and data analysis as a single framework have been investigated. Three key components in the investigation are availability modeling, model evaluation, and data analysis. The general availability concepts and modeling techniques are briefly reviewed. The system\u27s availability model is divided into submodels based upon their functionalities. Furthermore, an object oriented Markov model specification to facilitate availability modeling and runtime configuration has been developed. Numerical solutions for Markov models are examined, especially on the uniformization method. Alternative implementations of the method are discussed; particularly on analyzing the cost of an alternative solution for small state space model, and different ways for solving large sparse Markov models. The dissertation also presents a monitoring and data analysis framework, which is responsible for failure analysis and availability reconfiguration. In addition, the event logs provided from the Lawrence Livermore National Laboratory have been studied and applied to validate the proposed techniques