G. Ciardo, R. Zijal, Well-defined stochastic Petri nets, in: MASCOTS, 1996, pp. 278--284.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....also possible ( 21] refined in later sections of this paper) In this paper, we make several new contributions related to well specified, including the existence of an e#cient algorithm that works without any assumptions. Another approach has been through the use of the concept of well defined [22]. Well defined itself is a very strict condition and does not allow the expression of concurrent events. However, also defined in [22] is well defined with respect to a reward structure, which does allow ambiguity so long as it is not measured by the reward structure. This will be described ....

....including the existence of an e#cient algorithm that works without any assumptions. Another approach has been through the use of the concept of well defined [22] Well defined itself is a very strict condition and does not allow the expression of concurrent events. However, also defined in [22] is well defined with respect to a reward structure, which does allow ambiguity so long as it is not measured by the reward structure. This will be described formally and in greater detail in following sections. The authors propose an algorithm to check for a su#cient condition for a model to be ....

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G. Ciardo and R. Zijal, "Well-defined stochastic Petri nets," in Proc. 4th Int. Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS'96), San Jose, California, pp. 278--284, Feb. 1996.

....several other tests that may be performed at state generation time that are aimed at reducing the burden of specification and eliminating over specification, while still ensuring that the behavior of a GSPN is completely specified. One of these tests is based on the notion of a well defined GSPN [2]. A GSPN is well defined if the underlying stochastic process is completely described at every step, including all events that occur in zero time. A check that a model is well defined can be done when exploring the state space by an efficient algorithm that does not add to the asymptotic running ....

.... may be too restrictive, since some ambiguities do not change the behavior of the stochastic process in a measurable sense (for example, with respect to a reward structure) Therefore, a more relaxed definition called well defined with respect to a reward structure was defined and applied [2]. We discuss some of the details of this definition later. An efficient algorithm to detect whether a GSPN is well defined with respect to a reward structure has been given in [2] In parallel with the evolution of GSPNs, stochastic activity networks (SANs) 6, 7] have developed a technique to ....

[Article contains additional citation context not shown here]

G. Ciardo and R. Zijal. Well-defined stochastic Petri nets. In Proc. 4th International Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS'96), pages 278--284, San Jose, California, Feb. 1996.

....that define when a stochastic activity network s behavior is completely probabilistically specified. Since the time this material first appeared [15] further work has been done to develop algorithms that are tailored to specific reward variables [16] and are more e# cient [17] In addition, [18] presents a similar concept in the context of stochastic reward nets. These works present newer and more e#cient algorithms to determine whether a net is well specified; in contrast, this section focuses on the concept itself and how the structure of a SAN can be used to reduce the complexity of ....

G. Ciardo and R. Zijal, "Well-defined stochastic Petri nets," in Proceedings of the Fourth International Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS'96), San Jose, California, Feb. 1996, pp. 278--284.

....normal approximation, and most likely will not lead to improvements in model solution. However, the concept should prove useful in developing other approximations. The set M# can be determined by exploring all possible measure functions MF(m) with the requirement that the model be well defined [24]. Previously, it was mentioned that a measure is a mapping A model that is not well defined contains some nondeterminism. A measure could be defined on the portion of the model containing nondeterminism, but the solution of that measure cannot be computed. 20 from a sample path to a real ....

G. Ciardo and R. Zijal, "Well-defined stochastic Petri nets," in Proc. 4th International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems, 1996, pp. 278--284.

....the marking process M(t) is a right continuous, piecewise constant, continuous time, discrete state stochastic process whose state space is isomorphic to the reachability graph of the untimed PN. Intrigued semantic interpretations related to the possibility of contemporary firings are avoided [90, 69, 36, 43]. Given a marking in which more than one transition is enabled (with the same priority level if priority is used) the firing policy determines the transition that will fire next. Two possible alternatives have been discussed in [1] i) Under the race policy, the transition whose firing time ....

.... The drawback of this approach is, of course, the explosion of the state space that can be alleviated by resorting to the use Kronecker operators for matrices [63] 21 A very recent and interesting modification of the expansion technique, resorts to the use of discrete PH type random variables [36, 43], so that the continuous time marking process is approximated by an expanded discrete time Markov chain (DTMC) However, discrete random variables are not covered by the assumptions stated in Section 2, and their consideration is outside the scope of the present review. 7.1 Markov Regenerative ....

G. Ciardo and R. Zijal. Well-defined stochastic Petri nets. In Proceedings of the 4-th International Workshop on Modeling Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS'96), pages 278--284. IEEE Computer Society Press, 1996.

....the marking process M(t) is a rightcontinuous, piecewise constant, continuous time discrete state stochastic process whose state space is isomorphic to the reachability graph of the untimed PN. Intrigued semantic interpretations related to the possibility of contemporary firings are avoided [25, 20, 9, 12]. A formal definition of a class of Markov Regenerative Stochastic Petri Nets (MRSPN) has been presented in [7] Definition 2 A SPN is called a Markov Regenerative Stochastic Petri Net (MRSPN) if its marking process M(t) is a Markov Regenerative Process (MRGP) 2 . MRGPs [22] or Semi ....

G. Ciardo and R. Zijal. Well-defined stochastic Petri nets. In Proceedings of the 4-th International Workshop on Modeling Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS'96), pages 278--284. IEEE Computer Society Press, 1996.

....success flows F s ; makes that the execution must be considered for all different elements in F s . Hence, by repetition of execution for all success flows in F s , the execution rules are complete. There are important and intricate issues associated with whether an action model is well specified [3, 22]. In nonformal terms, an instance of an action model is well specified if all possible evolutions that follow from the execution rules result in the same set of reachable markings, with the same probabilities pm associated to them. It is beyond the scope of this paper to further discuss this ....

....the same probabilities pm associated to them. It is beyond the scope of this paper to further discuss this topic, but it implies that the user must take care in using dependency coefficients in a correct way, and must be aware of wellspecified issues familiar from nets with immediate transitions [3, 22]. 4. Path Based Solution Algorithm In action models we need to solve for the absorption probabilities of the sinks. We do this using on the fly or path based algorithms [2, 5, 27, 28] Compared to statespace generation approaches for Petri nets, on the fly algorithms combine generation of ....

G. Ciardo and R. Zijal. Well-defined stochastic Petri nets. In 4th International Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, pages 278--284, San Jose, CA, USA, Feb. 1996. IEEE, IEEE Computer Society Press.

....specified. Well specified ness is a necessary and sufficient condition for the probabilistic behavior of a SAN to be completely specified and for a unique state level reward model to exist. Previous work along these lines was done by Sanders [10] in 1988, and concurrently by Ciardo and Zijal [11], but both of these works considered a more limited reward structure. In this paper, we develop an algorithm to generate a state level representation from a SAN with a very general reward structure, which can capture information regarding sequences of instantaneous activities that can complete, ....

....that can occur when transitioning from one stable marking to another. This is necessary since multiple non quantified activity choices may occur without an intervening stable marking. Simpler algorithms exist when this is not case. See, for example, the algorithm presented by Ciardo and Zijal [11]. B State Level Representation The final step in obtaining a state level representation of a SAN is to construct a statelevel reward structure and corresponding stochastic process. Several types of stochastic processes can result from the SAN specification. Ciardo et al. 12] for example, ....

G. Ciardo and R. Zijal, "Well-defined stochastic Petri nets," in Proceedings 4th International Workshop on Modelling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS '96), (San Jose, CA, USA), pp. 278--284, Feb. 1996.

....case of time extended Petri nets with exponentially, deterministically, and expolynomially timed transitions without restrictions is referred to as SPNs, for convenience. ffl Discrete Time Approach: The temporal behavior of a discrete deterministic and stochastic Petri net (DDSPN) [14, 6] is characterized by its underlying discrete time scale. An exponentially distributed firing time is approximated by its discrete analog the geometric distribution (cf. Sec. 3.8) Deterministic firing times are represented by a special case of the geometric distribution. Immediate transitions ....

G. Ciardo and R. Zijal. Well-defined Stochastic Petri Nets. In Proc. 4th Int. Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS'96), pages 278--284, San Jose, CA, USA, Feb. 1996. IEEE Computer Society Press.

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G. Ciardo and R. Zijal. Well-defined Stochastic Petri Nets. In Proc. 4th Int. Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS'96), pages 278--284, San Jose, CA, USA, Feb. 1996. IEEE Computer Society Press.

....time distributions are specified by arbitrary finite absorbing DTMCs. It has been proven in [4] that the underlying stochastic process of a DTMSPN is a DTMC, provided that the modeler detects and resolves all conflicts and confusions manually, possibly a very difficult task. This drawback lead in [6] to the development of a new method for the automatic detection of conflicts and confusions applicable to all types of stochastic Petri nets. This approach is independent of structural PN properties and is solely based on the state space generation of a given model, so that only actually occurring ....

....approaches, which are based on necessary, not sufficient, conditions. Thus, structural tests can lead to an overspecification of a given model resulting in a more difficult correct interpretation of obtained results measures. The work presented in this paper combines the results of [13] 4] and [6], while removing the mentioned drawbacks of [13] and [4] We define discrete deterministic and stochastic Petri nets (DDSPNs) In DDSPNs, transitions can fire either in zero time or after a time delay specified by arbitrary finite absorbing DTMCs without any structural restriction. Firing time ....

[Article contains additional citation context not shown here]

G. Ciardo and R. Zijal. Well-defined Stochastic Petri Nets. In Proc. 4th Int. Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS'96), pp. 278--284, San Jose, CA, USA, Feb. 1996. IEEE Comp. Soc. Press.

No context found.

G. Ciardo, R. Zijal, Well-defined stochastic Petri nets, in: MASCOTS, 1996, pp. 278--284.

No context found.

G. Ciardo and R. Zijal. Well-defined stochastic Petri nets. In Proceedings of the 4-th International Workshop on Modeling Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS'96), pages 278--284. IEEE Computer Society Press, 1996.

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