H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sc., 2000 (to appear).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....cha nge. The idempotencela w (I) clea rly contra dicts the ra ce condition wea ssume. Instea d,a revised la w (I # ) is needed tha t reflects the minimum property (C) of exponentia l distributions. It is listed in Ta ble 8 together with the ma in equa tiona l la ws cha ra cterising lumpa bility [20]. 4 Interactive Markov Chains This section joins the models of the preceding two sections, continuous time Ma rkov cha ns a d la elled tra sition system ina n orthogona fa shion. It does so bymea ns of two types of prefixes. Thea ction prefixed expression a.Pma intera9 on az ion aaO rds beha ....

....extends [13] the respective notions onbaO6 processa lgebra processesa ndMa1 ov cha ins. Thisa nswers indeed why we ha ve reused the symbol tha ha been used in Section 2.4a lrea dy to denote strong bisimila rity on PA . We obta in the following desira ble results: PAc and MCc , as done in [20]. In th is case a more involved definition of strong and weak bisimulation is needed th at must now incorporate maximal progress.Th e way we proceedh ere is sketch ed in [19, Sec. 6.1] and elaborated in [7] Th e solution is didactically more appealing, buth s th drawbackth t divergence may imply ....

H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. Theoretical Computer Science, 2001. to appear.

....system whose states correspond to process terms can be derived as the semantic model of a process algebraic specification. For a discussion of the full set of semantic rules for Markovian process algebras similar to our language L we refer the interested reader to the literature, see e.g. [6, 48, 53, 55, 64]. Here we only mention two selected rules. The first is the rule for synchronisation of two processes via Markovian transitions which can be written as follows: Q Gamma Q P j[S]jQ b;OE( j[S]jQ b 2 S Note that this rule is parametric in a function OE determining the rate of ....

H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. Theoretical Computer Science, 2001. to appear.

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H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sc., 2000 (to appear).

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H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. Theoretical Computer Science, 274(1-2):43--87, 2002.

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H. Hermanns, U. Herzog, J.-P. Katoen, Process algebra for performance evaluation, Th. Comp. Sci. 274 (1-2) (2002) 43--87.

....Markov chains (CTMCs) are the basic mathematical model underlying many formalisms for the description and analysis of stochastic discrete event dynamic systems. Examples of signi cant formalisms which are mapped onto CTMCs are stochastic Petri nets (SPNs) 18] stochastic process algebras (SPAs) [9,31,35], queueing networks (QNs) 14,43] and stochastic automata networks (SANs) 42,43] All these formalisms allow a convenient and structured model description which is mapped onto a CTMC and subsequently analyzed using established numerical techniques for the stationary or transient analysis [43] ....

.... t , and the accumulated reward in the interval [t 1 ; t 2 ) is computed as R t 2 t 1 t dt. 2.3 Component based descriptions We consider Markov models consisting of components that interact via synchronized transitions. Such descriptions are common for stochastic process algebras [9,31,35], superposed stochastic Petri nets [24,38] stochastic automata networks [42,43] or queueing networks[14,43] The model consists of K components numbered 1 through K that communicate via synchronization events from a set E S . Additionally, a set of local events EL describes transitions which do ....

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H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sc., 274:43-87, 2002.

....of lumpability and bisimulation to the distinguishing power of the logic. We exemplify this property for CSRL, since this includes the other logics as subsets. Bisimulation (lumping) equivalence. Lumpability enables the aggregation of CTMCs and MRMs without a#ecting performance properties [47, 10, 40, 35]. We adapt the standard notion slightly in order to deal with MRMs with statelabellings. We only sketch the concepts here, and refer to the papers [4, 5] for more details. For some MRM = S, R, L, #) we say that an equivalence relation R on S is a bisimulation if whenever (s, s # ) R then ....

H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. Theoretical Computer Science, 274(1-2):43--87, 2002.

.... hiding specialised algorithms from the performance engineer; ameans to s ecify both functional and performance properties in a single f amework. Organisationof the paper.This gives a flavour of the approaches mentioned above. A more detailed treatment of the pro algebra part can be found in [28,31,29]; the model checking partis des9]1 ed in full detail in [7,5] For a broader overview and introduction into formal methods and performance evaluation we refer to [13] The paperis organis9 as follows Sec. 2presfi ts ss introductory material onCTMCs Sec. 3s] eys ss chas fi pro ces algebras ....

....logic approach and sd9 of the model checking algorithms Sec. 5concludes the paper anddis]G 1] ss future resre9 hdirections 2Continuous Time Markov Chains sisc9 introduces exponentialdis1: 19CS14 continuous:G]4 Markov chains and their behaviour.This is done in an informal way, we refer to [29, 27] fordetails 2.1 Exp tial Distributions probabilitydis449C44: function)is a function thatast9] a probability (a real value between 0 and 1) to each element ofs] givens9] This si is uss1S called these9[ se9[ andis often interpretedas time, of eitherdiser94 (N)or continuous (R#0 ) nature. As ....

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H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. Theoretical Computer Science, 2001. To appear.

....available prototype tool ETMCC. 1 Introduction Performance and dependability analysis are crucial tasks during the design cycle of parallel and distributed IT systems. The common approach to performability modelling is to use some high level formalism for model specification (e.g. SPN [1] or SPA [6]) to derive a flat CTMC from the model and to analyse the CTMC with numerical methods. The definition of the aim of analysis, i.e. the specification of the measures of interest, has not been formalised in the past. Recently, temporal logics have been proposed for the specification of ....

H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sci., 2000. to appear.

.... 0 (s; s 0 ) a 9 9 K OE( t; t 0 ) a 2 A) s a 1 t (s; s 0 ) a (t; s 0 ) a = 2 A) s a 2 t (s 0 ; s) a (s 0 ; t) a = 2 A) s a 9 9 K ;1 t (s; s 0 ) a 9 9 K (t; s 0 ) a = 2 A) s a 9 9 K ;2 t (s 0 ; s) a 9 9 K (s 0 ; t) a = 2 A) As in [24], the construction for synchronisation of Markovian transitions is parametric in a function OE determining the rate of synchronisation, in response to the fact that different synchronisation policies are possible [20,18,19,7] Definition 7 Let A Act and S 1 = S 1 ; s 1 ; Act 1 ; 1 ; AP 1 ; ....

H. Hermanns, U. Herzog, J.-P. Katoen, Process algebra for performance evaluation, Th. Comp. Sci. To appear.

....system models are nowadays developed by means of semi formal methods such as UML or SDL. In order to overcome the insularity problem, there is a growing tendency towards the integration of performance modelling and analysis into (semi )formal methods, such as Petri nets [1] process algebra [21], or SDL [12] This integration has potential benefits for the application of both formal methods and performance analysis: Using a formal method, performance models of interest are readily supported by the German Research Council DFG under HE 1408 6 1. available for analysis. Conversely, ....

.... a single state, using an appropriate notion of equivalence (such as bisimulation) During the last decade, stochastic process algebra (SPA) has emerged as a promising way to carry out compositional performance and reliability modelling, mostly on the basis of continuous time Markov chains (CTMCs) [21]. Following the same philosophy as ordinary process algebra, the stochastic behaviour of a system is described as the composition of the stochastic behaviours of its components. However, all standard analysis algorithms for stochastic models are purely statebased. They compute interesting ....

[Article contains additional citation context not shown here]

H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sci., 2001 (to appear).

....system models are nowadays developed by means of semi formal methods such as UML or SDL. In order to overcome the insularity problem, there is a growing tendency towards the integration of performance modelling and analysis into (semi )formal methods, such as Petri nets [1] process algebra [21], or SDL [12] This integration has potential benefits for the application of both formal methods and performance analysis: Using a formal method, performance models of interest are readily available for analysis. Conversely, the availability of quantitative insight into a # Contact author. ....

.... a single state, using an appropriate notion of equivalence (such as bisimulation) During the last decade, stochastic process algebra (SPA) has emerged as a promising way to carry out compositional performance and reliability modelling, mostly on the basis of continuous time Markov chains (CTMCs) [21]. Following the same philosophy as ordinary process algebra, the stochastic behaviour of a system is described as the composition of the stochastic behaviours of its components. However, all standard analysis algorithms for stochastic models are purely statebased. They compute interesting ....

[Article contains additional citation context not shown here]

H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sci., 2001 (to appear).

....size and complexity of systems, obtaining such models in a direct way becomes more and more cumbersome and error prone. An e#ective solution to this problem is to generate CTMCs from higher level specifications, like queueing networks, stochastic Petri nets [1] or stochastic process algebras [20, 24]. # Contact author. Tel. 31 53 4895675, fax: 31 53 4893247, e mail: katoen cs.utwente.nl. Although these approaches have shown to be rather valuable several (industrial) case studies have been carried out and mature tool support is available [19, 21] the specification of the ....

H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sc., 2000 (to appear).

....size and complexity of systems, obtaining such models in a direct way becomes more and more cumbersome and error prone. An effective solution to this problem is to generate CTMCs from higher level specifications, like queueing networks, stochastic Petri nets [1] or stochastic process algebras [18, 22]. Although these approaches have shown to be rather valuable several (industrial) case studies have been carried out and mature tool support is available [17, 19] the specification of the measure of interest is mostly done informally. The analysis of the CTMC most often boils down to the ....

H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sc., 2000 (to appear).

....size and complexity of systems, obtaining such models in a direct way becomes more and more cumbersome and error prone. An e ective solution to this problem is to generate CTMCs from higher level speci cations, like queueing networks, stochastic Petri nets [1] or stochastic process algebras [20, 24]. Although these approaches have shown to be rather valuable several (industrial) case studies have been carried out and mature tool support is available [19, 21] the speci cation of the measure of interest is mostly done informally. Contact author. Tel. 31 53 4895675, fax: ....

H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sc., 2000 (to appear).

....majority of applications of Markov chain modelling involves CTMCs, as opposed to DTMCs. 2 In particular, CTMCs are the underlying semantic model of major high level performance modelling formalisms such as stochastic Petri nets [1] stochastic automata networks [26] stochastic process algebras [24, 21], Markovian queueing networks [12] and various extensions thereof. Model checking of CTMCs has been discussed in [8] introducing a (branching) temporal logic called continuous time stochastic logic (CSL) to express properties over CTMCs. This logic is an extension of the (equally named) logic ....

H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sci., 2000 (to appear).

No context found.

H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebras for performance evaluation. Theoretical Computer Science, 2001.

No context found.

H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. Theoretical Computer Science, 274(1-2):43--87, 2002.

No context found.

H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. Theoretical Computer Science, 274(1-2):43 - 87, 2002.

No context found.

H. Hermanns, U. Herzog, and J. Katoen. Process algebra for performance evaluation. Theoretical Computer Science, 274(1--2):43--87, 2002.

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H. Hermanns, U. Herzog, and J. Katoen. Process algebra for performance evaluation. Theoretical Computer Science, 274(1--2):43--87, 2002.

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H. Hermanns, U. Herzog, and Katoen J.P., Process algebra for performance evaluation, Theoretical Computer Science 274 (2002), no. 1-2, 43--87.

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H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sci., 274(1-2):43--87, 2002.

No context found.

H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. Theoretical Computer Science, 274(1--2):43--86, 2002.

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