Heindl, A. and German, R. (1997). A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs. In 7th International Workshop on Petri Nets and PerformanceModels, pages 60-- 69, Saint Malo, France. IEEE, IEEE Computer Society Press.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....around = 1 (max 1 = 0:300283 at = 0:945027) where the throughput with pri preemption policy vanishes. 17 N t 7 Figure 7: Transmission channel with failures 6. 3 Noisy transmission channel As a second example, we consider a noisy transmission channel that served as an example in [14] as well with di erent preemption policy. The NMPSN model of the channel is depicted in Figure 7. The data to be transmitted arrives to the channel from a Markovian source. The source is the superposition of N switched Poisson processes (SPP) Transitions t 1 and t 2 model the jumps between the ....

A. Heindl and R. German. A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs. In 7-th International Conference on Petri Nets and Performance Models - PNPM97, pages 60-69. IEEE Computer Society, 1997.

....with a(t) i.e. M(t) a(t) is a Markov process over the state space R Theta IR, where R is the set of reachable tangible markings and IR is the set of 4 non negative real numbers. The joint process can be analyzed by the method of supplementary variables [10] This approach was followed in [13,11,16] to analyze Stochastic Petri Nets with only prd MEM transitions. 3 Analysis of MRSPNs with prd type transitions The method of supplementary variable has been applied to MRSPNs in which, in each (tangible) marking, at most one enabled transition can have nonexponential distribution with prd ....

....scheme that conserves the sum of probabilities this correction is not necessary) going back to step 2 or start with the next time instant (n 1)d. An improved numerical procedure, based on the same approach, but with an adaptively varying interval length (d) has been recently described in [16]. The steady state behavior of the considered class of MRSPN can be easily obtained, based on the above set of equations, by setting the time derivatives to 0 [12] Lindemann proposed an effective numerical method to evaluate the steady state probabilities of DSPN based on Markov renewal theory ....

A. Heindl and R. German. A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs. In 7-th International Conference on Petri Nets and Performance Models - PNPM97, pages 60--69. IEEE Computer Society, 1997.

....transforms. While this numerical method is certainly of theoretical interest, it is not suitable for transient analysis of large DSPNs. More recently, German et al. developed a numerical method for transient analysis of DSPNs based on the method of supplementary variables (see e.g. [5,10]) Using the same approach in a recent paper, Telek and Horvath developed state equations for transient analysis of Markov regenerative stochastic Petri nets in which timed transitions keep their remaining firing times in case their firing process gets preempted for subsequent resumption instead ....

....the transient analysis of quite large DSPN with deterministic transitions concurrently enabled. Furthermore, for DSPNs without concurrent deterministic transitions, the GSSMC approach is three orders of magnitude faster than the previously known method based on the supplementary variables approach [5,10]. In particular, for a DSPN as considered in [10] the GSSMC approach requires a couple of minutes whereas the refined implementation of the supplementary variables approach requires more than 100 hours of CPU time. This considerable gain in computational efficiency over the approach based on ....

[Article contains additional citation context not shown here]

A. Heindl, R. German, A fourth order algorithm with automatic step size control for the transient analysis of DSPNs, in: Proc. 7th Int. Workshop on Petri Nets and Performance Models, Saint Malo, France, 1997, pp. 60--69.

....with a(t) i.e. M(t) a(t) is a Markov process over the state space R IR, where R is the set of reachable tangible markings and IR is the set of 4 non negative real numbers. The joint process can be analyzed by the method of supplementary variables [10] This approach was followed in [13,11,16] to analyze Stochastic Petri Nets with only prd MEM transitions. 3 Analysis of MRSPNs with prd type transitions 3.1 Application of the method of supplementary variables The method of supplementary variable has been applied to MRSPNs in which, in each (tangible) marking, at most one enabled ....

....scheme that conserves the sum of probabilities this correction is not necessary) going back to step 2 or start with the next time instant (n 1)d. An improved numerical procedure, based on the same approach, but with an adaptively varying interval length (d) has been recently described in [16]. The steady state behavior of the considered class of MRSPN can be easily obtained, based on the above set of equations, by setting the time derivatives to 0 [12] Lindemann proposed an e#ective numerical method to evaluate the steady state probabilities of DSPN based on Markov renewal theory ....

A. Heindl and R. German. A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs. In 7-th International Conference on Petri Nets and Performance Models - PNPM97, pages 60--69. IEEE Computer Society, 1997.

....method has been, up to now, applied to prd execution policies only and with mutually exclusive general transitions. The steady state solution has been proposed by German and Lindemann in [56, 83, 84] while the possibility of applying the methodology to the transient analysis has been explored in [55, 67]. A comparison of numerical methods for the transient analysis of MRGPs applying the Markov regenerative theory and the method of the supplementary variables has been presented in [57] The third line of research, aimed at affording the solution of non Markovian SPN, is based on the expansion of ....

....variable a(t) i.e. M(t) a(t) is a Markov process over the state space R 0 Theta IR [47] where R 0 is the set of reachable tangible markings and IR is the set of non negative real numbers. The joint process can be analyzed by the method of supplementary variables [47] as shown in [56, 55, 67]. Following the concept and the notations of [55] the solution approach is briefly summarized. Let T G be the set of non exponential timed transitions. The tangible state space R 0 is partitioned into #T G 1 disjoint subsets. R E 0 is the set of states in which no general transition is ....

[Article contains additional citation context not shown here]

A. Heindl and R. German. A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs. In 7-th International Conference on Petri Nets and Performance Models - PNPM97, pages 60--69. IEEE Computer Society, 1997.

....method has been, up to now, applied to prd execution policies only and with mutually exclusive general transitions. The steady state solution has been proposed by German and Lindemann in [62, 89, 90] while the possibility of applying the methodology to the transient analysis has been explored in [61, 73]. 21 A comparison of numerical methods for the transient analysis of MRGPs applying the Markov regenerative theory and the method of the supplementary variables has been presented in [63] The third line of research, aimed at a ording the solution of non Markovian SPN, is based on the expansion ....

....supplementary variable a(t) i.e. M(t) a(t) is a Markov process over the state space R 0 IR [52] where R 0 is the set of reachable tangible markings and IR is the set of non negative real numbers. The joint process can be analyzed by the method of supplementary variables [52] as shown in [62, 61, 73]. Following the concept and the notations of [61] the solution approach is brie y summarized. Let T G be the set of non exponential timed transitions. The tangible state space R 0 is partitioned into #T G 1 disjoint subsets. R E 0 is the set of states in which no general transition is ....

[Article contains additional citation context not shown here]

A. Heindl and R. German. A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs. In 7-th International Conference on Petri Nets and Performance Models - PNPM97, pages 60-69. IEEE Computer Society, 1997.

....with a(t) i.e. M(t) a(t) is a Markov process over the state space R 0 IR, where R 0 is the set of reachable tangible markings and IR is the set of non negative real numbers. The joint process can be analyzed by the method of supplementary variables [10] This approach was followed in [12, 11, 14] to analyse of Stochastic Petri Nets with only prd MEM transitions. 3. Method of supplementary variables for prd type transitions The method of supplementary variable has been applied to MRSPNs in which, in each (tangible) marking, at most one enabled transition can have non exponential ....

....boundary conditions (4) 5. Check the precision (the sum of the state probabilities) and go back to step 2 or start with the next time instant (n 1)d. An improved numerical procedure, based on the same approach, but with an adaptively varying interval length (d) has been recently described in [14]. The steady state behaviour of the considered class of MRSPN can be easily obtained, based on the above set of equations, by setting the time derivatives to 0. Lindemann proposed an effective numerical method to evaluate the steady state probabilities of DSPN based on this approach [15, 16] 4. ....

A. Heindl and R. German. A fourth-order algorithm with automatic step size control for the transient analysis of DSPNs. In PNPM'97, pages 60--69, St Malo, France, June 1997. IEEE CS Press.

....algorithms form the first step in evaluating the potential of uniformization for numerical solution of non homogeneous Markov processes. With the gained understanding of how to apply uniformization best, the next step is to compare it to rival methods (typically differential equation solvers [Heindl and German, 1997, Stoer and Bulirsch, 1980] with regard to speed, accuracy and memory use. This comparison needs not be limited to non homogeneous Markov chains, but may also include some types of non Markovian models, using the hazard rate of delay distributions as time dependent transition rate [Nicola et ....

Heindl, A. and German, R. (1997). A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs. In 7th International Workshop on Petri Nets and Performance Models, pages 60-- 69, Saint Malo, France. IEEE, IEEE Computer Society Press.

....stochastic process [5] They introduced a numerical method for transient analysis of such DSPNs based on numerical inversion of Laplace Stieltjes transforms. More recently, German et al. developed a numerical method for transient analysis of DSPNs based on the approach of supplementary variables [10]. Using the same approach, Telek and Horvath developed state equations for transient analysis of Markov regenerative stochastic Petri nets in which timed transitions keep their remaining firing times in case their firing process gets preempted for subsequent resumption instead of discarding them ....

....analysis less than 5 minutes of CPU time. Furthermore, we showed in [15] that DSPNexpress 2000 performs transient analysis of DSPNs without concurrent deterministic transitions in a few minutes of CPU time (i.e. three orders of magnitude less computational effort than the previously known method [10]) To outreach from stochastic Petri net modeling to system specification languages used in industrial projects, DSPNexpress 2000 contains filters to the widely known commercial design packages StateMate TM and Together TM. Thus, the numerical solvers of DSPNexpress can also be utilized for ....

A. Heindl and R. German, A Fourth Order Algorithm with Automatic Step Size Control for the Transient Analysis of DSPNs, IEEE Trans. Softw. Engin., 25, 194-206, 1999.

....transforms. While this numerical method is certainly of theoretical interest, it is not suitable for transient analysis of large DSPNs. More recently, German et al. developed a numerical method for transient analysis of DSPNs based on the method of supplementary variables (see e.g. 5] [10]) Using the same approach in a recent paper, Telek and Horvath developed state equations for transient analysis of Markov regenerative stochastic Petri nets in which timed transitions keep their remaining firing times in case their firing process gets preempted for subsequent resumption instead ....

....analysis of quite large DSPN with deterministic transitions concurrently enabled. Furthermore, for DSPNs without concurrent deterministic transitions, the GSSMC approach is three orders of magnitude faster than the previously known method 2based on the supplementary variables approach [5] [10]. In particular, for a DSPN as considered in [10] the GSSMC approach requires a couple of minutes whereas the refined implementation of the supplementary variables approach requires more than 100 hours of CPU time. This considerable gain in computational efficiency over the approach based on ....

[Article contains additional citation context not shown here]

A. Heindl and R. German, A Fourth Order Algorithm with Automatic Step Size Control for the Transient Analysis of DSPNs, Proc. 7 th Int. Workshop on Petri Nets and Performance Models, Saint Malo, France, 60-69, 1996

....stochastic process [5] They introduced a numerical method for transient analysis of such DSPNs based on numerical inversion of Laplace Stieltjes transforms. More recently, German et al. developed a numerical method for transient analysis of DSPNs based on the approach of supplementary variables [7]. While these methods are certainly of theoretical interest, they are both not suitable for application in practical dependability modeling projects. The remainder of this paper is organized as follows. Section 2 describes the software architecture of DSPNexpress 2.000. The graphical interface of ....

....nonzero elements of the transition kernel versus model size and, thus, provides further evidence along this line. In these experiments, the number of discretization steps employed in the numerical quadrature is M = 10. A DSPN of an MMPP D 1 K queue with failure and repair was already considered in [7] and a computational effort of 100 hours of CPU was reported. Figures 3 and 4 show 0,5 1 1,5 2,4 3 3,4 3,9 4,4 4,9 2 0 1 2 3 4 5 6 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Model size MBytes Figure 4. Memory requirements versus size 6,3 7,7 8,5 9,5 9,8 10,1 ....

[Article contains additional citation context not shown here]

A. Heindl and R. German, A Fourth Order Algorithm with Automatic Step Size Control for the Transient Analysis of DSPNs, Proc. 7 th Int. Workshop on Petri Nets and Performance Models, Saint Malo, France, 60-69, 1996.

....analysis less than 5 minutes of CPU time. Furthermore, we showed that DSPNexpress 2000 performs transient analysis of DSPNs without concurrent deterministic transitions in a few minutes of CPU time; i.e. three orders of magnitude less computational effort than the previously known method [3]. The remainder of this paper is organized as follows. Section 2 outlines the innovative features of DSPNexpress 2000. Furthermore, the graphical user interface and the organization of the numerical solvers are explained in detail. In Section 3, the mapping of UML system specification onto ....

R. German and A. Heindl, A Fourth Order Algorithm with Automatic Step Size Control for the Transient Analysis of DSPNs, IEEE Trans. Softw. Engin., 25, 194-206, 1999.

....algorithms form the first step in evaluating the potential of uniformization for numerical solution of non homogeneous Markov processes. With the gained understanding of how to apply uniformization best, the next step is to compare it to rival methods (typically differential equation solvers [Heindl and German 1997, Stoer and Bulirsch 1980] with regard to speed, accuracy and memory use. This comparison needs not be limited to non homogeneous Markov chains, but may also include some types of non Markovian models, using the hazard rate of delay distributions as time dependent transition rate [Nicola et al. ....

Heindl, A. and German, R. (1997). A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs. In 7th International Workshop on Petri Nets and Performance Models, pages 60-- 69, Saint Malo, France. IEEE, IEEE Computer Society Press.

.... Pi G (0; 0) G (0) R, where ffi (x) denotes the Dirac impulse. The firing frequencies and the state probabilities of S G are given by the integrals: t) X g2G Z 1 0 p g (t; x)Rf g (x) dx; 4) G (t) X g2G Z 1 0 p g (t; x) F g (x) dx Pi G (t; 0) 5) See [7, 11, 13, 19] for the analysis of the equations in time domain. 3.2 Transient Analysis in Laplace Domain An expression for the state probabilities can be derived in Laplace domain. In the following first a solution of the PDE system is obtained and inserted into the integrals. Then the sum of the ODE system ....

A. Heindl and R. German. A fourth order algorithm with automatic stepsize control for the transient analysis of DSPNs. IEEE Trans. Softw. Engin., 25:194--206, 1999.

....timing is also required for more realistic models. For the stationary and transient analysis of models incorporating non exponential timing, researchers have pursued the exact approaches based on Markov renewal theory (e.g. 3, 4, 21] and on the method of supplementary variables (e.g. [11, 12, 15]) However, both approaches usually require that at most one non exponential activity is enabled in each state of the state space. If this limitation is violated, phase type representations of the concurrently enabled non exponential activities may render the model accessible to efficient analysis ....

A. Heindl, R. German. A Fourth-Order Algorithm with Automatic Stepsize Control for the Transient Analysis of DSPNs. Proc. 7th Int. Workshop on Petri Nets and Performance Models, pp. 60--69, St. Malo, France, 1997.

No context found.

Heindl, A. and German, R. (1997). A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs. In 7th International Workshop on Petri Nets and PerformanceModels, pages 60-- 69, Saint Malo, France. IEEE, IEEE Computer Society Press.

No context found.

A. Heindl and R. German. A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs. In 7-th International Conference on Petri Nets and Performance Models - PNPM97, pages 60--69. IEEE Computer Society, 1997.

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