Simulation and numerical solution of stochastic Petri nets with discrete and continuous timing

We introduce a novel stochastic Petri net formalism where discrete and continuous phase-type firing delays can appear in the same model. By capturing deterministic and generally random behavior in discrete or continuous time, as appropriate, the formalism affords higher modeling fidelity and efficiencies to use in practice. We formally specify the underlying stochastic process as a general state space Markov chain and show that it is regenerative, thus amenable to renewal theory techniques to obtain steady-state solutions. We present two steady-state analysis methods depending on the class of problem: one using exact numerical techniques, the other using simulation. Although regenerative structures that ease steady-state analysis exist in general, a noteworthy problem class arises when discrete-time transitions are synchronized. In this case, the underlying process is semi-regenerative and we can employ Markov renewal theory to formulate exact and efficient numerical solutions for the stationary distribution. We propose a solution method that shows promise in terms of time and space efficiency. Also noteworthy are the computational tradeoffs when analyzing the embedded versus the subordinate Markov chains that are hidden within the original process. In the absence of simplifying assumptions, we propose an efficient regenerative simulation method that identifies hidden regenerative structures within continuous state spaces. The new formalism and solution methods are demonstrated with two applications

TRANSIENT ANALYSIS OF A PREEMPTIVE RESUME M/D/l/2/2 THROUGH PETRI NETS

Stochastic Petri Nets (SPN) are usually designed to support exponential distributions only, with the consequence that their modelling power is restricted to Markovian systems. In recent years, some attempts have appeared in the literature aimed to define SPN models with generally distributed firing times. A particular subclass, called Deterministic and Stochastic Petri Nets (DSPN), combines into a single model both exponential and deterministic transitions. The available DSPN implementations require simplifying assumptions which limit the applicability of the model to preemptive repeat different service mechanisms only. The present paper discusses a semantical generalization of the DSPNs by including preemptive mechanisms of resume type. This generalization is crucial in connection with fault tolerant systems, where the work performed before the interruption should not be lost. By means of this new approach, the transient analysis of a M/D/1/2/2 queue (with 2 customers, 1 server, exponential thinking and deterministic service time) is fully examined under different preemptive resume policies

Petri Nets with Discrete Phase Type Timing: A Bridge Between Stochastic and Functional Analysis

Abstract The addition of timing specification in Petri Nets (PN) has followed two main lines: intervals for functional analysis or stochastic durations for performance and dependability analysis. The present paper proposes a novel technique to analyze time or stochastic PN models based on discretization. This technique can be seen as a bridge between the world of functional analysis and the world of stochastic analysis. The proposed discretization technique is based on the definition of a new construct called Discrete Phase Type Timing - DPT that can represent a discrete cumulative density function (cdf) over a finite support (or a deterministic cdf) as well as an interval with non-deterministic choice (or a deterministic duration). In both views, a preemption policy can be assigned and a strong (the transition must fire when the interval expires) or a weak (the transition can fire when the interval expires) firing semantics. The paper introduces the DPT construct and shows how the expanded state space can be built up resorting to a compositional approach based on Kronecker algebra. With this technique a functional model can be quantified by adding probability measures over the firing intervals without modifying the (compositional) structure of the PN model

Extended Abstracts: PMCCS3: Third International Workshop on Performability Modeling of Computer and Communication Systems

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Automatic phased mission system reliability model generation

There are many methods for modelling the reliability of systems based on component failure data. This task becomes more complex as systems increase in size, or undertake missions that comprise multiple discrete modes of operation, or phases. Existing techniques require certain levels of expertise in the model generation and calculation processes, meaning that risk and reliability assessments of systems can often be expensive and time-consuming. This is exacerbated as system complexity increases. This thesis presents a novel method which generates reliability models for phasedmission systems, based on Petri nets, from simple input files. The process has been automated with a piece of software designed for engineers with little or no experience in the field of risk and reliability. The software can generate models for both repairable and non-repairable systems, allowing redundant components and maintenance cycles to be included in the model. Further, the software includes a simulator for the generated models. This allows a user with simple input files to perform automatic model generation and simulation with a single piece of software, yielding detailed failure data on components, phases, missions and the overall system. A system can also be simulated across multiple consecutive missions. To assess performance, the software is compared with an analytical approach and found to match within 5% in both the repairable and non-repairable cases. The software documented in this thesis could serve as an aid to engineers designing new systems to validate the reliability of the system. This would not require specialist consultants or additional software, ensuring that the analysis provides results in a timely and cost-effective manner

アドホックネットワークにおけるネットワーク生存性評価に関する研究

広島大学(Hiroshima University)博士(工学)Doctor of Engineeringdoctora