CIARDO, G. and TRIVEDI, K. S., A Decomposition Approach for Stochastic Reward Net Models, in: Performance Evaluation, vol. 18, pp. 37-59, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... for the special class of decision free processes [74] Another such approach, based on the exploitation of the structure of a special class of process algebraic models, is described in [7] Approximate decomposition based analysis for nearly independent GSPN structures is considered in [27, 30]. 2.2 Modular model representations Queueing models, stochastic Petri nets and the tool specific modelling languages mentioned above do not offer the possibility of composing an overall model from components which can be specified in isolation. Such a composition, however, is a highly desirable ....

G. Ciardo and K.S. Trivedi. A decomposition approach for stochastic reward net models. Performance Evaluation, 18(1):37--59, July 1993.

....algorithm. Nevertheless, in practice, constant factors must be su#ciently small. In this chapter, we evaluate the performance implications of the use of the Mobius statelevel AFI for two examples taken from the literature: the Flexible Manufacturing System (FMS) described by Ciardo et al. [14] and a parallel communication protocol (Courier protocol) designed by Woodside and Li [42] We also compare the e#ciency of di#erent methods of accessing the elements of the generator matrix, i.e. the column, allEdges, and submatrix iterators. We consider the two AFI implementations discussed in ....

....bank size, and instruction re ordering. So far, we conclude that the overhead is overweighted by platform specific and compiler specific e#ects; that it is su#ciently limited to retain the same time complexity; and that the constant factors are almost always less than 2. 4. 1 Example Models In [14], FMS is described to illustrate the benefits of an approximate analysis technique based on decomposition. The model has been used in many papers as a benchmark model for CTMC analysis (e.g. 9, 43] For simplicity, we consider a variant in which transitions have marking independent incidence ....

G. Ciardo and K. S. Trivedi. A decomposition approach for stochastic reward net models. Performance Evaluation, 18(1):37--59, 1993.

....and space consuming solution trajectory, while the performance measures of interest are shown to be very accurate, as compared to the overall solution. Our structural decomposition and serial solution bears resemblance with the (fixed point) decomposition approach proposed by Ciardo and Trivedi [5]. We do, however, not require a fixed point iteration; a one way pass through the submodels is sufficient, i.e. the import graph (terminology from [5] is acyclic. Secondly, the way we propose to interrelate the submodels is very much tailored towards the specific application. In this paper we ....

.... Our structural decomposition and serial solution bears resemblance with the (fixed point) decomposition approach proposed by Ciardo and Trivedi [5] We do, however, not require a fixed point iteration; a one way pass through the submodels is sufficient, i.e. the import graph (terminology from [5]) is acyclic. Secondly, the way we propose to interrelate the submodels is very much tailored towards the specific application. In this paper we use the SPN formalism as proposed by Ciardo et al. as supported by their package SPNP [4] The employed terminology therefore also refers to the class ....

G. Ciardo, K.S. Trivedi, "A Decomposition Approach for Stochastic Reward Net Models", Performance Evaluation 18, pp.37--59, 1993.

....a connected model. A connected model is an ordered set of reward models and their corresponding solution methods in which input parameters to some of the models depend on the results of other models in the set. This is useful for modeling using decompositional approaches, such as that used in [31]. In those cases, the model of interest is a set of reward models with dependencies expressed through results, where the overall model may be solved through a system of nonlinear equations (if a solution exists) B. Tool description The Mobius tool is our implementation of the Mobius framework. ....

G. Ciardo and K. S. Trivedi, "A decomposition approach for stochastic reward net models," Performance Evaluation, vol. 18, pp. 37--59, 1993.

....of the form Ax = b: 1) We have in mind applications where the matrix A in (1) is singular and the linear system is consistent. These include certain stochastic processes, queuing models [18] Markov chains [26] 29] as well as performance evaluation of computer and other critical systems [9], 33] where Petri Nets play an important role in the models [1] 10] In the methods we study for the solution of (1) the variables (and equations) are permuted and partitioned into r groups, i.e. Px = x 1 ; x 2 ; x r ] x i 2 R n i , i = 1; r, and r i=1 n i ....

Gianfranco Ciardo and Kishor S. Trivedi. A decomposition approach for stochastic reward net models. Performance Evaluation, 18:37--59, 1993.

....conducive to reward model solutions. Based on this reward mapping enabled intermediate model, we take our final step to specify reward structures in the composite base model, which is built on three stochastic activity network (SAN) 4] reward models. As with behavioral decomposition methods (see [5, 6], for example) and hierarchical composition techniques (see [7, 8] for example) the objective of this model translation approach is to avoid dealing with a model that is too complex to allow derivation of a closed form solution. The difference between those previously developed techniques and ....

G. Ciardo and K. S. Trivedi, "A decomposition approach for stochastic reward net models," Performance Evaluation, vol. 18, no. 1, pp. 37--59, 1993.

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G. Ciardo and K. S. Trivedi. A decomposition approach for stochastic reward net models. Perf. Eval., 18(1):37-59, 1993.

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G. Ciardo and K.S. Trivedi. A decomposition approach for stochastic reward net models. Performance Evaluation, 18:37--59, 1993.

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G. Ciardo and K. S. Trivedi. A decomposition approach for stochastic reward net models. Perf. Eval., 18(1):37--59, 1993.

....are dedicated to the application while it runs, but application communication trac may contend with that of other applications. For the purposes of comparison with our earlier approach, we will study a model of a Flexible Manufacturing System, illustrated in Figure 6, originally discussed in [3]. A key parameter to this model is the number of tokens k initially placed in places P1, P2, and P3; increasingly larger statespaces are generated by increasing k. This Petri net has timed transitions (white boxes) and immediate transitions (black boxes) The state space generator eliminates ....

G. Ciardo and K. Trivedi. A decomposition approach for stochastic reward net models. Performance Evaluation, 18(1):37-59, 1993.

....evaluate the proposed approximation approach on a set of experiments. Two small examples are considered initially to observe the e ect of synchronization, a fork and join model and a juggling server model, followed by two classical Petri net models: a Kanban [10] and a exible manufacturing system [12]. All experiments were performed on a Pentium II 400Mhz machine, with 384Mbytes of RAM, with the Linux operating system, and without the use of virtual memory. The exact results used to evaluate our approximation were obtained with SMART [9] In each case, we report the relative error in ....

....seven xed point iterations. An exact solution is possible only for N up to 5: for the cases in which the comparison is possible the relative error on the throughput of transitions is always less than 1 . 6.4 A flexible manufacturing system (FMS) Fig. 9 depicts a Petri net of a FMS system [12] with three machines (places M1 , M2 , and M3 ) Four types of parts are present, and are modeled by the four places P1 , P2 , P3 , and P12 : only the rst three are initialized with N tokens, since parts of the last type come from the combination of parts of type 1 and 2. Also in this case the ....

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G. Ciardo and K. S. Trivedi. A decomposition approach for stochastic reward net models. Perf. Eval., 18(1):37-59, 1993.

....that the host has an up to date copy. Both the quorum gathering process and the mechanism by which hosts not included into the quorum for a write request become out of date require to move a marking dependent number of tokens. As an ordinary P T net was used, the resulting model is quite complex. [12] models the productivity of a exible manufacturing system with CTMCbased stochastic reward nets. When nished parts are ready to leave the factory, they are gathered in a place, from where they are removed periodically, in bulk. This behavior closely re ects reality, where the means used for ....

G. Ciardo and K. S. Trivedi. A decomposition approach for stochastic reward net models. Perf. Eval., 18:37-59, 1993.

....It is composed of four instances of essentially the same sub GSPN. The synchronizing transitions t synch1 and t synch2 can be either both timed or both immediate, we indicate the two resulting models as kanban timed and kanban immediate. The second GSPN models a exible manufacturing system, from [3], except that the cardinality of all arcs is constant, unlike the original model (this does not a ect the number of reachable markings) We indicate this model as FMS. We do not describe these models in more detail, the interested reader is referred to the original publications where they ....

G. Ciardo and K. S. Trivedi. A decomposition approach for stochastic reward net models. Perf. Eval., 18(1):37-59, 1993.

....performance measures of interest using software tools such as SPNP [6] but its size is too large for an exact numerical solution, even for the E 2 interconnect having only 7 nodes. In this section, we describe an approximate model based on the idea of SPN decomposition and fixed point iteration [5]. This approximate model exploits the large amount of symmetry possessed by the interconnect and essentially describes the behavior of one node under a workload that is generated by the whole interconnect fabric. Thus the basic idea is to approximate and generate a proper amount of traffic going ....

G. Ciardo and K. S. Trivedi. A decomposition approach for stochastic reward net models. Perf. Eval., 18(1):37--59, 1993.

....across processors will be needed. 5 Results We consider the model of a exible manufacturing system (FMS) shown in Fig. 4. We omit a description of this SPN, since we are focusing on a comparison of the sequential and distributed algorithms for its analysis. The interested reader can consult [9] for a detailed presentation of its behavior and the meaning of its places and transitions. For this discussion, it is sucient to observe that, as the number k of initial tokens in the three places P 1, P 2, and P3 increases, the number of states n and arcs increases sharply (see Table 1) The ....

G. Ciardo and K. S. Trivedi. 1993. A decomposition approach for stochastic reward net models, Perf. Eval., 18(1), 37-59.

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CIARDO, G. and TRIVEDI, K. S., A Decomposition Approach for Stochastic Reward Net Models, in: Performance Evaluation, vol. 18, pp. 37-59, 1993.

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G. Ciardo and K. Trivedi. A decomposition approach for stochastic reward net models. Performance Evaluation, 18(1):37-59, 1993.

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G. Ciardo and K. S. Trivedi. A Decomposition Approach for Stochastic Reward Net Models. Performance Evaluation, 18(1):37-59, 1993.

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G. Ciardo and K. S. Trivedi. A Decomposition Approach for Stochastic Reward Net Models. Performance Evaluation, 18(1):37-59, 1993.

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G. Ciardo and K. S. Trivedi. A Decomposition Approach for Stochastic Reward Net Models. Performance Evaluation, 18(1):37-59, 1993.

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G. Ciardo and K. S. Trivedi. A Decomposition Approach for Stochastic Reward Net Models. Performance Evaluation, 18(1):37-59, 1993.

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G. Ciardo and K. S. Trivedi. A Decomposition Approach for Stochastic Reward Net Models. Performance Evaluation, 18(1):37-59, 1993.

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G. Ciardo and K. Trivedi. A decomposition approach for stochastic reward net models. Performance Evaluation, 18:37--59, 1994.

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Ciardo, G. and K. S. Trivedi, A Decomposition Approach for Stochastic Reward Net Models, Performance Evaluation 18 (1993), pp. 37-59.

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G. Ciardo and K.S. Trivedi. A decomposition approach for stochastic reward net models. Performance Evaluation, 18(1):37--59, July 1993.

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