S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. These de Docteur Ingegneur, CNAM, Paris, 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... However, in the reliability area stochastic modelling is more appropriate, and therefore we will consider in the sequel only TPN in which the timing mechanism is stochastic; we will refer to this class of models as Stochastic PN (SPN) SPN were initially proposed in two doctoral thesis [36, 35]. In these models, interpreting PN as Condition Event nets, time was naturally associated with activities that induce state changes, hence with the delay incurred before firing transitions. Although other possibilities have been explored, the choice of associating time with PN transitions is the ....

....a time continuous homogeneous Markov chain with state space isomorphic to the reachability graph of the PN. This case will be considered in details in the following sections. Extensions to cover the case of generally distributed transition firing times have been considered in a number of papers [36, 21, 4, 23, 26, 5]. Releasing the memoryless property of the exponential distribution, in order to univocally associate to each execution sequence the concept of SPN execution policy needs to be introduced 18 [4, 5] The execution policy consists of two parts: the way in which a transition is selected to fire ....

S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. Technical report, These de Docteur Ingegneur, CNAM, Paris, 1980.

.... ring may be forced when the maximum time expires (strong ring semantics) or ring may be not mandatory when the maximum time expires (weak ring semantics) Analysis of TPN models involves the search for reachable conditions through the exploration of ring zones [4,22] Since the initial work in [20,19], SPN have found a sound theoretical base and consolidated applications when the ring time assigned to timed transitions is an exponentially distributed random variable, so that the evolution of the system throughout its reachability graph is mapped into a continuous time Markov chain (CTMC) A ....

S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. Technical report, These de Docteur Ingegneur, CNAM, Paris, 1980.

.... may be forced when the maximum time expires (strong ring semantics) or ring may be not mandatory when the maximum time expires (weak ring semantics) Analysis of TPN models involves the search for reachable conditions through the exploration of ring zones [4,22] Since the initial work in [20,19], SPN have found a sound theoretical base and consolidated applications when the ring time assigned to timed transitions is an exponentially distributed random variable, so that the evolution of the system throughout its reachability graph is mapped into a continuous time Markov chain (CTMC) A ....

S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. Technical report, These de Docteur Ingegneur, CNAM, Paris, 1980.

.... PNPM. This series was initiated in Torino (Italy) in 1985, then moved to the USA, Japan, Australia and France. The sevents edition was held in Saint Malo (France) in 1997. The most common assumption, in the literature, is to assign to the PN transitions an exponentially distributed firing time [88, 89, 95], so that the resulting marking process is a Continuous Time Markov Chain (CTMC) Almost all the PN based tools are based on this assumption. In principle, simple and tractable equations can be derived for both transient and steadystate analysis of CTMCs. But practical limitations arise from the ....

....fl k associated with the PN transitions are exponentially distributed, and the execution policy is not pri, the dynamic behavior of the PN is mapped into a CTMC, with state space isomorphic to the reachability graph of the untimed PN. This restriction is the most popular in the literature [95, 88, 89, 54] and is usually referred to simply as SPN. A number of tools are built on this assumption [28, 39, 46, 81] In order to completely specify the model, the set = 1 ; 2 ; nt ) of the n t firing rates assigned to the n t transitions should be given in addition. A usual convention, in the ....

S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. These de Docteur Ingegneur, CNAM, Paris, 1980.

.... a simulative solution has been investigated in [29] With the aim of providing a modeler s representation able to automatically generate an analytical representation, various restrictions of the general GDT SPN model have been discussed in the literature [16, 9] The semimarkov SPN, studied in [38, 5], seems of little practical interest since the ring of any transition forces a resetting of all the other transitions. A semimarkov SPN more suited for applications has been discussed in [23] In this de nition, the transitions are partitioned into three classes: exclusive, competitive and ....

....is the most popular in the literature [37, 24, 2] and a number of tools are built on this assumption [13, 18, 20, 34] 3.2 Semi Markov SPN When all the PN transitions are assigned a resampling policy the marking process becomes a semi Markov process. This restriction has been studied in [38, 5] but is of little interest in applications where it is dicult to imagine a situation where the ring of any transition of the PN has the e ect of forcing a resampling to all the other transitions. A more consistent and interesting semi Markov SPN model has been discussed in [23] In this de ....

S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. Technical report, These de Docteur Ingegneur, CNAM, Paris, 1980.

.... PNPM. This series was initiated in Torino (Italy) in 1985, then moved to the USA, Japan, Australia and France. The sevents edition was held in Saint Malo (France) in 1997. The most common assumption, in the literature, is to assign to the PN transitions an exponentially distributed ring time [94, 95, 101], so that the resulting marking process is a Continuous Time Markov Chain (CTMC) Almost all the PN based tools are based on this assumption. In principle, simple and tractable equations can be derived for both transient and steadystate analysis of CTMCs. But practical limitations arise from the ....

....variables k associated with the PN transitions are exponentially distributed, and the execution policy is not pri, the dynamic behavior of the PN is mapped into a CTMC, with state space isomorphic to the reachability graph of the untimed PN. This restriction is the most popular in the literature [101, 94, 95, 60] and is usually referred to simply as SPN. A number of tools are built on this assumption [33, 44, 51, 87] In order to completely specify the model, the set = 1 ; 2 ; nt ) of the n t ring rates assigned to the n t transitions should be given in addition. A usual convention, in ....

S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. These de Docteur Ingegneur, CNAM, Paris, 1980.

....measurement of availability is usually rather impractical. In order to evaluate the availability of safety critical systems, formal modeling methods and tools were sucessfully used in the past, e.g. 2] These include Boolean Methods (e.g. 3] and [4] and State Space Based Methods (e.g. [5, 6, 7, 8, 9]) In this paper we will apply Markov Chains generated by Generalized Stochastic Petri Nets (GSPN) to assess the availability of a typical CPCI system. The paper is structured as follows: Section 2 introduces the CompactPCI standard and a typical low cost high availability CPCI system used for ....

S. Natkin. Les Reseaux de Petri Stochastique et leur Application a L'evaluation des Systems Informatiques. PhD thesis, CNAM Paris, France, 1980.

....because systems were being modelled to see what states they could attain, rather than probably would attain a sort of quantum mechanical superposition. Other variants have taken the other, probabilistic approach and attempted to assign probabilities to the arcs (stochastic Petri nets [natk80, moll81, ajmo84, ajmo87, ajmo89] In Petri s original work, places could only hold a single token, so transitions would be disabled if any of their output places already contained a token; thus, it only made sense to allow a single directed arc from a particular place to a particular ....

S. Natkin. Les reseaux de Petri stochastiques et leur application `a l"evaluation des syst`emes informatiques. Th`ese de Docteur Ingegneur, CNAM, Paris, France, 1980.

....and the analysis of special net classes [5] Since PNs do not have any notion of time, temporal specifications were incorporated emphasising those concepts which support a Markovian analysis of the time augmented net. Two well known representatives of this class are Stochastic Petri nets (SPNs; [15, 14]) where transitions have to fire after an exponentially distributed delay (timed transitions) and Generalized Stochastic Petri nets (GSPNs; 2] which additionally incorporate transitions firing immediately after being enabled (immediate transitions) Here firing of immediate transitions has ....

S. Natkin. Les Reseaux de Petri Stochastiques et leur Application a l'Evaluation des Systemes Informatiques. PhD thesis, CNAM, Paris, 1980.

....the models described with the Petri net formalism. Among these first proposals are worth mentioning those due to Noe and Nutt [172] Ramchandany [175] Merlin and Farber [165] The idea of associating a random delay with the firing of the transitions was independently proposed by several authors [48, 169, 170, 184] and led to the definition of Stochastic Petri Nets (SPN) 117, 168] in which a Markov chain that is isomorphic to the state space of the net can be defined starting from the time specifications of the model. Alternative definitions of timed Petri nets associated with underlying stochastic ....

S. Natkin. Les Reseaux de Petri Stochastiques et leur Application a l'Evaluation des Systemes Informatiques. PhD thesis, CNAM, Paris, France, 1980. These de Docteur Ingegneur.

.... for measuring several performance and reliability indices of purely probabilistic systems (i.e. systems not containing nondeterministic choice) A popular approach to the construction of performance models relies on probabilistic extensions of Petri nets, such as the stochastic Petri nets of [26, 25, 30] and the generalized stochastic Petri nets (GSPNs) of [1] The transitions of a GSPN can either fire immediately, or fire with an exponential delay distribution. GSPNs can be translated into continuoustime Markov chains, thus enabling the performance analysis of the systems. Another approach to ....

S. Natkin. Les Reseaux de Petri Stochastiques et leur Application a l'Evaluation des Systemes Informatiques. PhD thesis, CNAM, Paris, 1980.

No context found.

S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. These de Docteur Ingegneur, CNAM, Paris, 1980.

No context found.

S. Natkin. Les Reseaux de Petri Stochastiques et leur Application a l'Evaluation des Systemes Informatiques. PhD thesis, CNAM, Paris, 1980.

No context found.

S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. Technical report, These de Docteur Ingegneur, CNAM, Paris, 1980.

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