B. Plateau, J.-M. Fourneau, K.H. Lee, PEPS: a package for solving complex Markov models of parallel systems, in: R. Puigjaner (Ed.), Proceedings of the Fourth International Conference Modelling Techniques and Tools, 1988, pp. 341--360.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....The last chapter contains conclusive remarks about the methods investigated. Observations and comments about methods, the SAN methodology and Markov chains based on our work are provided in the chapter. We included an appendix that describes how to incorporate new models into the Peps package[12], which is the software tool developed in France for solving SAN models in compact form, since we implemented our methods as an extension to Peps. Markov Chains In our attempt to understand the characteristics of natural and artificial phenomena, mathematical models of systems are developed. It ....

....a uniformly distributed probability vector as the initial approximation for all experiments. We ran all the experiments on SUN Sparcstation 4 s each with 32 megabytes (MB) of RAM. All the algorithms are implemented in C language and the new methods are incorporated into the software package PEPS [12]. Regardless of its size, each problem produced a smaller number of iterations in either the backward or the forward approach; we present results of the better approach. We experimented with three problems. The first two, resource sharing and three queues, are explained in [5] The third one, the ....

[Article contains additional citation context not shown here]

Plateau, B., Fourneau, J. M., and K.-H. Lee, "PEPS: A package for solving complex Markov models of parallel systems," in: Modeling Techniques and Tools for Computer Performance Evaluation, R. Puigjaner and D. Potier, eds., Spain, September 1988, 291--305.

....graph first. Another line of research is concerned with building SPNs in a structured way, basically by synchronising subnets via common transitions, which is an instance of the Kronecker approach described below. Stochastic automata networks (SAN) developed in the 1980ies and 1990ies [82 85], consist of several stochastic automata, basically CTMCs whose transitions are labelled with event names, which run in parallel and may perform certain synchronising events together. Thus, the SAN formalism is truly structured, since it allows the user to specify an overall model as a collection ....

B. Plateau, J.-M. Fourneau, and K.-H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In Proc. of the 4th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, pages 341-- 360, Palma (Mallorca), September 1988.

....to the matrix while in this form. As with our approach, storage requirements for the matrix are relatively small, but ingenious techniques must be developed to minimise the time overhead required for numerical solution. Tools which support Kronecker based methods include APNN [BBK98] PEPS [PFL88] and SMART [CM97] In particular, SMART incorporates matrix diagrams [CM99] a data structure developed as an ecient implementation of the Kronecker techniques. The matrix diagram approach has much in common with the hybrid method we present in this paper. In particular, both methods use a ....

B. Plateau, J. Fourneau, and K. Lee. PEPS: A package for solving complex Markov models of parallel systems. In Modelling Techniques and Tools for Computer Performance Evaluation, 2, 1988. 17

....matrices. Specially designed algorithms are able to take advantage of this expression and find the steady state solution in terms of the expression, avoiding the construction of the complete matrix. This general approach has been pioneered by Plateau and others with Stochastic Automata Networks [53, 54, 58]. In [12] Buchholz identifies the relationship between the parallel composition operator in the SPA language, MPA, and tensor algebra expressions for the underlying Markov process. He shows how an expression for the complete model can be constructed in terms of smaller matrices representing the ....

B. Plateau, J.M. Fourneau, and K.H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In Proc. of the 4th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, 1988.

....the faster than relation developed for a subset of TCCS in [50] An alternative compositional approach to the solution of Markov processes is the use of tensor algebra to express the generator matrix of a process. This approach has been proposed by Plateau et al. . for Stochastic Automata Networks [51], Donatelli for Superposed Stochastic Automata and Superposed GSPN [16, 17] and Buchholz for queueing networks and SPN [7] This is based on a restricted form 13 of interaction between subsystems within the system. Similar approaches for SPA models have been proposed [10, 54] 6 Implementing ....

B. Plateau, J-M. Fourneau, and K-H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In R. Puigjaner, editor, Proc. of 4th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, pages 341--360. Plenum Press, 1988.

....the potential, state space) Then one can avoid having to store the full size matrix by storing the component matrices instead and reformulating steady state probability calculation in terms of the component matrices. Existing implementation work in this area includes Petri net tools such as [16, 39]. In this paper we adapt and extend the ideas of [4, 2] in order to represent concurrent probabilistic systems in terms of MTBDDs. The differences with the corresponding work in numerical analysis of Markov chains are: we allow nondeterminism as well as probability; we work with probability ....

B. Plateau, J. M. Fourneau, and K. H. Lee. PEPS: a package for solving complex Markov models of parallel systems. In R. Puigjaner and D. Potier, editors, Modelling techniques and tools for computer performance evaluation, Spain, September 1988.

....potential, state space) Then one can avoid having to store the full size matrix by storing the component matrices instead and reformulating steady state probability calculation in terms of the component matrices. Existing implementation work in this area includes tools such as SMART [11] and PEPS [27]. In this paper we adapt and extend the ideas of [3, 2] in order to represent concurrent probabilistic systems in terms of MTBDDs. The di erences with the corresponding work in numerical analysis of Markov chains are: we allow nondeterminism as well as probability; we work with probability ....

B. Plateau, J. M. Fourneau, and K. H. Lee. PEPS: a package for solving complex Markov models of parallel systems. In R. Puigjaner and D. Potier, editors, Modelling techniques and tools for computer performance evaluation, 1988.

....from UltraSAN all tools rely on flat and uncoloured nets. As far as the authors know there exists presently one other tool which supports Markov chain analysis based on a tensor representation of the generator matrix, namely the tool PEPS for the analysis of stochastic automata networks (SANs) [21]. However, SANs are completely different from the model class introduced here since they specify stochastic automata which communicate via synchronised transitions, rather than by asynchronous exchange of entities. There is also work going on to transfer the results for SANs in the GSPN area ....

B. Plateau, J.M. Forneau, K.H. Lee. PEPS: A package for solving complex Markov models of parallel systems. In R. Puigjaner (ed.), Proc. of the 4th Int. Conf. on Modelling Tools and Techniques for Comp. Perf. Eval., Plenum Publishers (1988).

....The only remaining memory constraint is the storage of the iteration vector(s) However, these approaches based on Kronecker operators still su#er from important limitations, which we now address. 4.1. Implementations based on T . In the first implementations that appeared in the literature [1, 15, 16, 18], a vector # # IR n K 1 is used to store #. In it, only the entries corresponding to states i [1,K] #T are actually used, while the remaining entries, corresponding to potential but not reachable states, are always zero. All Kronecker operations are performed ignoring the distinction ....

B. Plateau, J.-M. Fourneau, and K. H. Lee, PEPS: a package for solving complex Markov models of parallel systems, in Proc. 4th Int. Conf. Modelling Techniques and Tools, R. Puigjaner, ed., 1988, pp. 341--360.

....while the two referred elements provide guidelines throughout the project. 1 Introduction Many powerful modeling tools have been proposed or developed, yet, their use in practice has been very limited. Despite their inherent merits, performance modeling tools (e.g. QNAP2 [1] RESQME [2] and PEPS [3]) reliability modeling tools (e.g. SURF 2 [4] HARP [5] and SAVE [6] and performability modeling tools (e.g. SHARPE [7] SPNP [8] UltraSAN [9] DSPNexpress [10] and TimeNET [11] still have limited penetration in industrial environments 1 . One possible method of encouraging, indeed ....

B. Plateau, J.-M. Fourneau, K.-H. Lee, "PEPS: A Package for Solving Complex Markov Models of Parallel Systems", in: Modeling Techniques and Tools for Computer Performance Evaluation, Editors: D. Potier, R. Puigjaner, pp.291--305, 1990.

....and acceptance of such systems. Markovian models are widely used for the modelling of parallelism because they are amenable to numerical analysis. For their specification such different modelling paradigms as queueing networks, stochastic Petri nets and stochastic automata can be used. Tools exist [1, 2] which support the generation of high level models which are then translated into an underlying continuous time Markov chain. The solution of the Markov chain yields probability values from which performance and reliability measures of the modelled system can be derived. Steady state analysis is ....

....very easily without affecting the specification of other components, resulting in a great flexibility. Among published approaches to structured modelling, the following are of particular relevance: In the work of Plateau et al. stochastic automata networks are used for model specification [5, 2]. Information on the interdependence between automata is given by synchronizing events and functional rates (rates dependent on the global state) It is shown that the generator matrix of the overall model can be described by a tensor expression involving only small submodel matrices. The ....

B. Plateau, J.-M. Fourneau, and K.-H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In Proceedings of the 4th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, pages 341--360, Palma (Mallorca), September 1988.

No context found.

B. Plateau, J.-M. Fourneau, K.H. Lee, PEPS: a package for solving complex Markov models of parallel systems, in: R. Puigjaner (Ed.), Proceedings of the Fourth International Conference Modelling Techniques and Tools, 1988, pp. 341--360.

No context found.

B.Plateau, J.M.Fourneau, K.Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In: R.Puigjaner, D.Potier, eds. Modelling Techniques and Tools for Computer Performance Evaluation, 1988.

No context found.

B. Plateau, J.M. Fourneau and K.H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In R. Puigjaner, D. Potier, Eds., Modelling Techniques and Tools for Computer Performance Evaluation, Spain, September 1988.

....the description of complex customers exchange behaviors among queues. Other characteristics not shown in this paper could be incorporated to the proposed method. For example, complex fork and join behaviors (splitting and assembling customers) could be easily modeled by the synchronized events [8]. In all cases described in Section 4, the synchronized events were used to associate the departure of a customer in one queue to the arrival into another one, establishing an one to one relationship. Fork and join procedures may correspond to the association of the departure from n queues with ....

J.M.Fourneau, B.Plateau. PEPS: a package for solving complex Markov models of parallel systems. In: Proceedings of the Fourth International Conference on Modelling Techniques and Tools for Computer Performance Evaluation. Palma, Spain, 1988.

....in non decreasing size. ffl Then take the automata that are neither functional nor arguments and rank them last, in any order. INRIA Numerical Issues for Stochastic Automata Networks. 13 4 Some Small Examples All numerical experiments were conducted using the software package PEPS, version 3. 0 [23]. This version of PEPS is implemented in C . Only the non diagonal elements of the descriptor are handled by this algorithm. The diagonal elements of the descriptor are pre calculated once and stored in a vector. The vector matrix multiplication includes a dot product with the diagonal entries. ....

B. Plateau, J.M. Fourneau and K.H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In R. Puigjaner, D. Potier, Eds., Modelling Techniques and Tools for Computer Performance Evaluation, Spain, September 1988.

No context found.

B. Plateau, J.M. Fourneau and K.H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In R. Puigjaner, D. Potier, Eds., Modelling Techniques and Tools for Computer Performance Evaluation, Spain, September 1988.

No context found.

B. Plateau, J.M. Fourneau and K.H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In R. Puigjaner, D. Potier, Eds., Modelling Techniques and Tools for Computer Performance Evaluation, Spain, September 1988. RR n2939 38 Brigitte Plateau and William J. Stewart

No context found.

B. Plateau, PEPS: A package for solving complex Markov models of parallel systems, in R. Puigjaner and D. Potier, eds., Modelling Techniques and Tools for Computer Performance Evaluation, Plenum Press, New York, 1990, pp. 291-306. 17

No context found.

B. Plateau, J. M. Fourneau, and K. H. Lee. PEPS: a package for solving complex Markov models of parallel systems. In R. Puigjaner and D. Potier, editors, Modelling techniques and tools for computer performance evaluation, 1988.

No context found.

Plateau B. PEPS: A package for solving complex Markov models of parallel systems. In Puigjaner R, Potier D, eds. Modelling Techniques and Tools for Computer Performance Evaluation 1990; Plenum Press: New York, 291-306.

No context found.

B. Plateau, J.-M. Fourneau, and K.-H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In Proceedings of the 4th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, pages 341--360, Palma (Mallorca), September 1988.

No context found.

B. Plateau, J.-M. Fourneau, and K.-H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In Proceedings of the 4th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, pages 341--360, Palma (Mallorca), September 1988.

No context found.

B. Plateau, J.M. Fourneau and K.H. Lee, #Peps: A package for solving complex Markov models of parallel systems," in Proc. 4th Int. Conf. on Mod Techn. and Tools for Comp. Perf. Eval.,Palma, Sept. 1988, pp. 341#360.

No context found.

B. Plateau. PEPS: A package for solving complex Markov models of parallel systems. In R. Puigjaner and D. Poiter, editors, Modeling techniques and tools for computer performance evaluation, pages 291--306. Plenum Press, New York and London, 1990.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC