S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebrabased Approach to Performance Modelling. In Proc. of the 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, number 794 in LNCS, pages 353--368, Vienna, May 1994. Springer-Verlag.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....specification methods have been developed, most notably those based on stochastic Petri nets, stochastic process algebras, and stochastic activity networks. With appropriate tools supporting these specification methods, such as, for instance, provided by TIPPtool [36] the PEPA workbench [23], GreatSPN [13] UltraSAN [56] or SPNP [14] it is relatively comfortable to specify performance models of which the associated CTMCs have millions of states. In combination with state of the art numerical means to solve the resulting linear system of equations (for steady state measures) or the ....

S. Gilmore and J. Hillston. The PEPA workbench: a tool to support a process algebra-based approach to performance modelling. In Computer Performance Evaluation, Modeling Techniques and Tools, LNCS 794: 353-368, Springer-Verlag, 1994.

....assigned to components so they can be referred to more easily elsewhere: for example in the system composition line or defining the behaviour that some other component will take on at the end of a prefix construct. 2.3 Existing Tools and Related Work 2.3. 1 Java PEPA Workbench The PEPA Workbench [Gilmore and Hillston, 1994, Hunter, 1999] is a tool used for the analysis of PEPA models. It can compute the underlying Markov process and the transition matrix of a model. As detailed in the previous section, the steady state can be calculated, giving relative frequencies of the system states. This information is written ....

Gilmore, S. and Hillston, J. (1994). The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In Proceedings of the Seventh International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, number 794 in Lecture Notes in Computer Science, pages 353--368, Vienna. Springer-Verlag.

.... has been illustrated by several examples, see e.g. 12,34,51,60] and important advances have been made in exploiting the structure of the compositionality for analysis purposes, for an overview see [64] Several algorithms have been implemented in tools, like the TIPPtool [48] PEPA Workbench [33] and TwoTowers (for EMPA) 13] For LOTOS preliminary proposals for stochastic extensions were presented by 10 Rico and von Bochmann [90] using semi Markov chains, and by Valderrutten et al. 102] who derived queueing networks from extended LOTOS specifications. A similar, informal approach, has ....

S. Gilmore and J. Hillston. The PEPA Workbench: A tool to support a process algebra-based approach to performance modelling. In G. Haring and G. Kotsis, eds, Modelling Techniques and Tools for Computer Performance Evaluation, LNCS 794, pages 353--368, 1994.

....with SPA In this section, the various tools available for performance modelling with SPA are described. The focus is on tools for modelling with PEPA, especially since the main tool is extended to incorporate some of the theory presented in Chapter 3. 2.6. 1 The PEPA Workbench The PEPA Workbench [29, 18] processes a textual description of a PEPA model, and generates output which can be used to calculate a steady state probability distribution for the model. The Workbench performs some well formedness checks on the model as it attempts to internally generate a derivation graph. These checks ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proceedings of 7th Conf. on Mod. Techniques and Tools for Computer Perf. Eval., volume 794 of LNCS, pages 353--368, 1994.

.... tool for the functional and performance analysis of concurrent and distributed systems compositionally modeled in the stochastically timed process algebra EMPA [3] The purpose of TwoTowers is similar to that of other stochastically timed process algebra based tools, such as the PEPA Workbench [7] and the TIPP tool [8] However, besides the difference in the expressive power of the algebras used by these tools and the fact that TwoTowers also implements a multiparadigm approach involving generalized stochastic Petri nets [3] which however is outside the scope of this paper) the ....

S. Gilmore, J. Hillston, "The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling", in Proc. of PERFORMANCE TOOLS '94, LNCS 794:353-368, 1994

.... [4, 5] SPNP [6] for generalized stochastic Petri nets (GSPN) UltraSAN [8] for stochastic activity networks, a class of stochastic Petri nets, DSPNexpress [20] for stochastic Petri nets with exponentially distributed or deterministic delays, SPN2MGM [13] for quasi birth death models, PEPA [11] and TIPP [17] for stochastic process algebras, to enumerate a few; for an overview, see for example [14] The results of this paper are part of the development of a new tool which is planned to having some interesting # Extended Version of [29] ESS2000, August 29, 2000 features. Di#erent ....

S. Gilmore and J. Hilston. The PEPA workbench: A tool to support a process algebra based approach to performance modelling. In G. Haring and G. Kotsis, editors, Computer Performance Evaluation, Modelling Techniques and Tools, volume 794 of LNCS, pages 121--146. Springer, Berlin, Heidelberg, New York, 1994.

....Mathematica session Lex Yacc proved transition system Autograph Instruction files Structures Functors Process and resources names Figure 1: The cost analyser. 4 The tool Some other tools for performance analysis based on stochastic process algebras have been implemented, see, e.g. [10, 12, 3]. Our approach mainly differ from them, in that we derive the stochastic information automatically from the functional specification of systems, relying on our enhanced operational semantics. Furthermore, we naturally deal with mobility as our input language is p calculus. Our tool has been ....

GILMORE, S., AND HILLSTON, J. The PEPA workbench: A tool to support a process algebrabased approach to performance modelling. In Proceedings of Int. Conference on Modelling Techniques and Tools For Computer Performance Evaluation (1994).

....to this problem consists of allowing also the action durations to be expressed in a probabilistic wayby means of random variables. This solution has led to the birth of stochastic process algebras like MTIPP, proposed by N. G otz U. Herzog M. Rettelbach [4] 5] PEPA, proposedby J. Hillston [6][3], andMPA, proposedbyM. Bernardo L. DonatielloR. Gorrieri [1] 2] A common feature of these three stochastic process algebras is that with each of their terms (satisfying some general conditions) is associated a homogeneous continuous time Markov chain (HCTMC) i.e. these three stochastic process ....

S. Gilmore, J. Hillston "The PEPA Workbench: a Tool to Support a Process Algebra-Based Approach to Performance Modelling" Technical Report University of Edinburgh, Edinburgh (UK), 1993

....A is the set of actions, and the transition relation ff Gamma specifies which action causes one state to evolve into another. The LTS describes all possible evolutions of the components, either individually or in cooperation and can be automatically computed using the PEPA Workbench [6], a prototype tool which supports modeling and analysis with PEPA. Qualitative properties, such as absence of deadlocks or the reachability of a given state, can be studied by investigating it. Model checking techniques [3] can also be used to verify system properties expressed using logical ....

S. Gilmore and J. Hillston, `The PEPA workbench: A tool to support a Process Algebra based approach to performance modelling', in Proc. 7th Int. Conf. on Mod. Techniques and Tools for Computer Perf. Eval., volume 794 of LNCS, (1994).

.... LOTOS (ET LOTOS) Leonard97] and Timed Probabilistic CCS (TPCCS) Hansson91] For the modelling of stochastic systems (where events occur at a time determined by a random variable) stochastic process algebra have also been proposed, for example, Performance Evaluation of Process Algebra (PEPA) [Gilmore94] and Stochastic Process Algebra for Discrete Event Simulation (SPADES) Argenio98] Extensions such as these unavoidably increase the complexity of the semantics for the process algebra. Furthermore, for stochastic process algebra, to maintain a finite and tractable semantic model it is usually ....

.... be found in [Lakas96a] and [Lakas96b] Alternative methods of performance analysis include queueing models [Bertsekas92] and stochastic Petri nets [Marsan95] A further method of performance analysis is through stochastic extensions to process algebra, such as PEPA (based on Markovian processes) [Gilmore94] and TIPP (based on generalised stochastic processes) Hermanns94] 4.3. Synthesis of monitors and controllers A third use for event schedulers occurs once you step out of the formal world into a more practical world. This is being addressed as part of the ongoing work in the V QoS project ....

S. Gilmore, J. Hillston, " The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling" , Proceedings of the 7th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, Vienna, March 1994.

....1 ph ; from this description the block matrices are derived, and the steadystate probabilities calculated using the MGM for a number of distributions including Erlang and hyper exponential. We also specify the examples in PEPA, for a fixed maximum queue size, and solve it using the PEPA workbench [8], taking care to model the more complex distributions in terms of exponentials. We report on our experiments comparing the memory requirements, processing time and the rate of convergence of the MGM and the PEPA workbench [14] Related work: The mainstream SPAs (PEPA [14] TIPP [28] and EMPA [1] ....

....perform reachability analysis of the underlying multi graph. For example, if the queue is M=E 2 =1 or M=H 2 (k) 1 or M=M=1, we only redefine the values of the representation for the distributions governing arrivals and service. 24 6. 6 Experimental Results We have compared the PEPA Workbench [8] against our Matlab implementation for calculating the steady state probabilities through the MGM, taking care to model the more complex distributions in PEPA in terms of exponentials. In all cases except synchronization the results of PEPA and PEPA 1 ph agree up to three decimal places. For ....

S. Gilmore and J. Hillston. The PEPA Workbench: a tool to support a process algebra-based approach to performance modelling. In Proc. 7th Int. Conference on Modelling Techniques and Tools for Computer Performance Analysis, volume 794 of Lecture Notes in Computer Science, pages 353--368. Springer, 1994.

....the tool supports semi automatic compositional reduction of complex models based on equivalence preserving reduction. This enables the tool to handle large state spaces (the running example given here is small, due to didactical reasons and limited space) Among related work, the PEPA Workbench [9] is another tool for performance evaluation, where Markov chain models are also specified by means of a process algebra. The paper is organised as follows: In Sec. 2, we summarise the theoretical backgroundof stochastic process algebras. Sec. 3 gives an overview of the tool s components. All ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process AlgebraBased Approach to Performance Modelling. In 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, Wien, 1994.

....r) P , allowing components with (potentially) infinite behaviour to be specified. Cooperation: Cooperation allows components to be composed in parallel. P Delta S Q denotes that P and Q are composed in parallel and only synchronise when both perform actions from the cooperation set S . A tool [9] exists to support the calculation of performance metrics from a PEPA model. It generates the Markov process from the PEPA model and solves it either symbolically, if the model is small, or numerically. Performance measures are calculated by associating rewards with activities in the model, for ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proceedings of the Seventh International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, volume 794 of LNCS, pages 353--368. Springer-Verlag, 1994.

....multi graph. For example, if the queue is M=E 2 =1 or M=H 2 (k) 1 or M=M=1, we only redefine the values of ph 1 and ph 2 and calculate the submatrices of the generator matrix directly (that is, we need only apply Algorithm 1 and Algorithm 2 once) We have compared PEPA (using the PEPA Workbench [20] and Matlab solver) against our Matlab implementation for calculating the steady state probabilities through MGM, and obtained the following results. In all cases the results of PEPA and PEPA 1 ph agree up to three decimal places. For each case we have computed R by the iteration method (with ....

S. Gilmore and J. Hillston. The PEPA Workbench: a tool to support a process algebra-based approach to performance modelling. In Proc. 7th Int. Conference on Modelling Techniques and Tools for Computer Performance Analysis, volume 794 of Lecture Notes in Computer Science, pages 353--368. Springer, 1994.

....stationary as well as transient analysis. The tool is capable of handling large state spaces, and it incorporates some very advanced features, such as the semiautomatic compositional aggregation of complex models. Among related work, the PEPA Workbench, developed by Hillston et al. in Edinburgh [19], is another tool for performance evaluation, where Markov chain models are also specified by means of a process algebra. The tool TWOTOWERS [6] based on two existing tools (one for functional analysis and one for performance analysis) also employs a stochastic process algebra as its ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process AlgebraBased Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, pages 353-- 368, Wien, May 1994.

....and bisimulations. Seg95] also presents a broad overview of the work on probabilistic systems done in the context of process algebras (aiming mostly on performance evaluation rather than verification, though) Some of this work has been applied to the development of tools, for instance, see [GH94,HMR96,BDG97] 2 Preliminaries 2.1 Stochastic processes A stochastic process is a family of random variables fX t j t 2 Tg defined on a given probability space and indexed by the time parameter t. If the timeparameter space T is discrete (e.g. the set of natural numbers IN ) then we have a ....

S. Gilmore and J. Hillston. The PEPA workbench: a tool to support a process-algebra based approach to performance modeling. In Conf. on modeling techniques and tools for computer performance evaluation, 1994.

....EMPA r TwoTowers the concurrent system description of Tool Driver Integrated Kernel CWB NC Functional Verification Figure 1.1 TwoTowers builds on CWB NC and MarCA. The purpose of TwoTowers is similar to that of other stochastically timed process algebra based tools, such as the PEPA Workbench [11] and the TIPP tool [14] However, besides the difference in the expressive power of the algebras used by these tools [5] the underlying philosophy is quite different. TwoTowers profits from two well known software tools to carry out the functional and performance analysis. This is advantageous ....

Gilmore, S. and Hillston, J. (1994) The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling, in Proc. of the 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation. Lecture Notes in Computer Science, 794, 353--368.

....Science, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. Email: fahe,mzk,smmg cs.bham.ac. uk of thus obtained stochastic process algebras we mention PEPA (Performance Evaluation Process Algebra) 8] TIPP [7] and EMPA [3] We use PEPA, and more specifically the PEPA workbench [4], to model and analyse a variety of lift systems. Although the PEPA tool is still in early stages of development and rather rudimentary, it has already been successfully applied to industrial problems, e.g. the robot control system [5, 10] However, all the models encountered by us were linear in ....

S.Gilmore and J.Hillston. The PEPA Workbench: A tool to Support a Process Algebra-based Approach to Performance Modelling. In G.Haring and G.Kotsis, editors, volume 794 of LNCS, Springer-Verlag, 1994. Pages 353368.

....compositional modelling and analysis. The tool is capable of handling large state spaces, although the running example given in this paper is of very moderate size, due to didactical reasons and limitation of space. Among related work, the PEPA Workbench, developed by Hillston et al. in Edinburgh [14], is another tool for performance evaluation, where Markov chain models are also specified by means of a process algebra. The paper is organised as follows: In Sec. 2, we summarise the theoretical background of stochastic process algebras. Sec. 3 gives an overview of the tool s components and ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-Based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, Wien, May 1994.

....Markov Chain (CTMC) underlying a TIPP specification. The input language and the emphasis on numerical evaluation rather than analytical evaluation represent the main difference to the PEPA Workbench, another modelling tool for SPA that relies upon symbolic evaluation of the underlying Markov chain [6]. 1 INTRODUCTION 2 The structure of the TIPP tool is shown in Fig. 1. Model descriptions are syntactically and semantically analysed using a parser written in the functional programming language Standard ML. The parser has been generated using the tools ML YACC and LEXGEN from the New Jersey ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-Based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, 7th Int. Conference on Modelling Techniques and Tools for Computer Performance Evaluation, pages 353--368, Wien, May 1994.

....aggregation as we will discuss analysing a simple communication protocol. 1 Introduction Since the beginning of nineties a variety of Stochastic Process Algebras (SPA) have been proposed as alternative approaches to performance modelling, see e.g. 1, 3, 10, 13] The development of software tools [6, 9] to support the SPA analysis has allowed to show the usability of the formalism for studying relatively complex systems. These languages, as many other high level modelling formalisms, suffer from the so called state space explosion problem: even relatively small models can generate a large state ....

S. Gilmore and J. Hillston. The PEPA workbench: A tool to support a Process Algebra based approach to performance modelling. In Proc. Seventh International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, Vienna, 1994.

....are satisfied. Several methods attempted to integrate qualitative and quantitative information in the same description technique. A Real time CCS is presented in [19, 9] where agents are associated with constant value delays. A timed bisimulation is then defined in order to compare the systems. In [8, 10] the authors present process algebras where delays are stochastically distributed and systems are compared over a Markovian bisimulation. In a more performance oriented work, 14] presented an extension of LOTOS for performance analysis. Due to the fact that the qualitative and the quantitative ....

S. Gilmore and J. Hillston. The PEPA workbench: A tool to support a process algebra-based approach to performance modelling. In Proceedings of the 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, Vienna, 1994.

....weak bisimilarity: SS1 jjj SS2) j[A]j I SS2 j[A]j I 0 To preserve weak Markovian bisimilarity would mean that we would obtain exact results, however, this cannot be achieved for this particular type of models. 5 Tool Support At the moment there are two tools available, the PEPA Workbench [15] and our TIPPtool [30] The TIPPtool is a prototype modelling tool which contains most of the specification and evaluation features of todays stochastic process algebras. Its main characteristics are ffl LOTOS oriented input language as well as a graphical notation based on extended finite state ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-Based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, Wien, May 1994.

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Gilmore, S. and Hillston, J. (1994) The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In Proc. 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, Vienna, May 3--6, LNCS 794, pp. 353--368. Springer-Verlag.

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S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In Proc. of 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, number 794 in LNCS, pages 353--368, Vienna, May 1994. Springer-Verlag.

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Gilmore, S., Hillston, J.: The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In: Proc. of the 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation. Number 794 in LNCS, Vienna, Springer-Verlag (1994) 353--368

....can be tested without having to apply the semantics to the whole model, although investigation of the state space of individual components may be necessary. Moreover, these conditions should be su#ciently formal that they can be incorporated into one of the MPA tools, such as the PEPA Workbench [22], allowing the recognition of the structure to be automated. Note that in each case, the current characterisation is known to be incomplete in the sense that there are MPA models which give rise to Markov processes of the appropriate class which would not be recognised by the current conditions. ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proceedings of the Seventh International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, volume 794 of LNCS, pages 353--368. Springer-Verlag, 1994.

.... PEPA Workbench The design philosophy behind the PEPA workbench was to provide a set of simple tools to allow a skilled user of the PEPA language to delegate to machine assistance some of the routine tasks in checking PEPA descriptions and performing calculations of transition graphs and rewards [19]. The workbench takes the form of a Standard ML image with the functionality implemented as Standard ML functions which have been pre compiled. This provides a convenient and secure mechanism for exporting the PEPA Workbench while also conveniently providing a powerful command line interface in ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-Based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, 7th Int. Conference on Modelling Techniques and Tools for Computer Performance Evaluation, pages 353--368, Wien, May 1994.

....PEPA serves as a high level notation for Markov modelling: it is possible to automatically generate a continuous time Markov process directly from the PEPA model which faithfully encodes the behavioural and temporal aspects of the modelled system. Details of this mapping can be found elsewhere [9]. Other high level notations for Markov processes, such as GSPN [10] or SAN [11] could equally have been used but the compositional structure of PEPA seemed well suited to the structure of the auction system. Using a formal model, such as a process algebra, allows us to additionally verify the ....

....of the Markov process underlying a PEPA model, the modeller can undertake an experimental investigation of the system. The PEPA Workbench is a suite of tools which perform the well formedness checking of PEPA models as well as the generation and solution of the corresponding Markov process [9]. It detects faults such as deadlocks and cooperations which do not involve active participants. In the most recent version, it includes support for a modal logic, allowing behavioural requirements of a model to be formally expressed and automatically checked [12] In essence, the translation ....

S. Gilmore and J. Hillston. The PEPA Workbench: A tool to support a process algebra based approach to performance modelling. In Proc. 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, number 794 in Lecture Notes in Computer Science, pages 353--368, Vienna, May 1994. Springer-Verlag.

....a modal, and not a temporal, logic. However, as we will explain, we have found that a modal logic is su#cient for specifying a reward structure over a model assumed to be in equilibrium. This approach to specifying performance measures over PEPA models has been incorporated into the PEPA Workbench [13]. Finally, recognising that the logic expressions may be intimidating to some users, we have developed a high level model query language. This language has foundations in the stochastic logic. Earlier work by Clark proposed the use of a modal logic to define the reward structure over a PEPA model ....

....temporal aspects of the PEPA model. The PEPA Workbench is used to check the well formedness of PEPA models and to generate their Markov process representation. It detects faults such as deadlocks and cooperations which do not involve active participants. It is described in full in an earlier paper [13]. The steady state distribution may be found by applying any one of a number of linear algebra solution methods to the generator matrix. We have recently extended the Workbench with the capability to reduce models to a canonical form internally, thereby automatically aggregating the model [16] ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proc. of 7th Conf. on Mod. Techniques and Tools for Computer Perf. Eval., volume 794 of LNCS, pages 353--368, 1994.

....modal, and not a temporal, logic. However, as we will explain, we have found that a modal logic is sufficient for specifying a reward structure over a model assumed to be in equilibrium. This approach to specifying performance measures over PEPA models has been incorporated into the PEPA Workbench [13]. Finally, recognising that the logic expressions may be intimidating to some users, we have developed a high level model query language. This language has foundations in the stochastic logic. Earlier work by Clark proposed the use of a modal logic to define the reward structure over a PEPA model ....

....temporal aspects of the PEPA model. The PEPA Workbench is used to check the well formedness of PEPA models and to generate their Markov process representation. It detects faults such as deadlocks and cooperations which do not involve active participants. It is described in full in an earlier paper [13]. The steady state distribution may be found by applying any one of a number of linear algebra solution methods to the generator matrix. We have recently extended the PEPA Workbench with the capability to reduce models to a canonical form internally, thereby automatically aggregating the model ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebrabased Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proceedings of 7th Conf. on Mod. Techniques and Tools for Computer Perf. Eval., volume 794 of LNCS, pages 353--368, 1994.

....approaches stress compositionality, i.e. the system is viewed as a collection of subsystems that are smaller and more easily modelled. In particular 1 Corresponding author email: jeh dcs.ed.ac.uk several Markovian process algebras (MPAs) have been presented in recent years. These include PEPA [8,14], MTIPP [10] and EMPA [1] Initially the benefits of the compositional structure within these languages have been investigated for model construction and model simplification [9,15,19,23] However the real strength of this approach will result from the exploitation of this structure to aid model ....

....presented in [3] all elements of the system, including the resources, are explicitly and formally represented in the model. The advantage of using MPA for this work is the formality of the approach and the subsequent automation of the technique within a modelling tool, such as the PEPA Workbench [8]. In order to tackle models of the size and complexity needed for the performance analysis of the next generation of computer systems, efficient techniques for the construction, manipulation and solution of large Markov processes will be required. PEPA provides a formal, structured, yet ....

S. Gilmore and J. Hillston, The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling, in: G. Haring and G. Kotsis, eds., Proc. of 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation (Lecture Notes in Computer Science, vol. 794, Springer, 1994) 353--368.

....the model description to generate an aggregated CTMC in a compositional way [4] This is of great practical importance because, like all state based modelling techniques, MPA models suffer from the state space explosion problem. Although prototype tools have been developed for model exploration [5, 6, 7], little work has been done to exploit to the full the potential to use equivalence relations to achieve effective aggregation and thus to put the theoretic results to practical use. In this paper we describe an algorithm to carry out efficient aggregation and its implementation in the PEPA ....

....C(P 0 1 ; P 0 2 ) L (ff 2 L) The rate R of the activity which is performed in cooperation is computed from the individual rates r 1 and r 2 as in the corresponding cooperation rule in Figure 1. 3. 4 Implementation The state space reduction algorithm has been added to the PEPA Workbench [5], the modelling package which implements the PEPA language and provides a variety of solution and analysis facilities for PEPA models. The algorithm is presented in pseudo code form in Figure 5. The driving force of the algorithm is provided by the procedure vfderive which, given a derivative of ....

[Article contains additional citation context not shown here]

S. Gilmore and J. Hillston. The PEPA Workbench: A tool to support a process algebra based approach to performance modelling. In Proc. Seventh International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, number 794 in Lecture Notes in Computer Science, pages 353--368, Vienna, May 1994. Springer-Verlag.

....of C i , q(C i ; C j ) 0. The q(C i ; C j ) or q ij , are the off diagonal elements of the infinitesimal generator matrix of the Markov process, Q. Diagonal elements are formed as the negative sum of the non diagonal elements of each row, i.e. q ii = Gammaq(C i ) The PEPA Workbench [14] is a suite of software tools which may be used to analyse PEPA models. In particular it can generate the generator matrix corresponding to a model in a form suitable for solution by any standard numerical technique. We assume that all PEPA models are time homogeneous since the rate and type of an ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proceedings of the Seventh International Conference on Modelling Technqiues and Tools for Computer Performance Evaluation, volume 794 of LNCS, pages 353--368. Springer-Verlag, 1994.

.... theoretical results have shown that it is possible to exploit these equivalence relations at the level of the model description to generate an aggregated Continuous Time Markov Chain (CTMC) in a compositional way [4] However, although prototype tools have been developed for model exploration [5], more work remains to be done to exploit to the full the potential to use equivalence relations to achieve effective aggregation. In this paper we proceed with the investigation of this problem. We take as inspiration previous results from a class of stochastic coloured Petri nets called ....

....P 0 1 P 2 (ff;r 2 ) Gamma Gamma Gamma P 0 2 (P 1 ; P 2 ) L (ff;R) Gamma Gamma Gamma C(P 0 1 ; P 0 2 ) L (ff 2 L) R = r 1 r ff P 1 r 2 r ff P 2 min(r ff P1 ; r ff P2 ) 4. 6 Implementation The state space reduction algorithm has been added to the PEPA Workbench [5], the modelling package which implements the PEPA language and provides a variety of solution and analysis facilities for PEPA models. The modification to the PEPA Workbench required the alteration of the data structure which is used to represent PEPA models as an abstract syntax tree within the ....

[Article contains additional citation context not shown here]

S. Gilmore and J. Hillston. The PEPA Workbench: A tool to support a process algebra based approach to performance modelling. In Proc. Seventh International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, number 794 in Lecture Notes in Computer Science, pages 353--368, Vienna, May 1994. Springer-Verlag.

....behaviour of the system, in keeping with the process algebra approach. The result is the PEPA reward language, which uses the logic to define a reward structure, and is described in detail in Section 4. A prototype implementation has been developed to work in conjunction with the PEPA Workbench [GH94]. A similar approach, using a temporal logic, was recently proposed by Hermanns. In [Her] he proposes the use of logic formulae to partition a process algebra model, each partition exhibiting a particular behaviour. Thus, whereas a temporal logic formula is used to verify the functional behaviour ....

....Resource 0 Figure 1: Derivation Graph of System 2.2 The PEPA Workbench PEPA models of realistic systems are much more complex than the simple example shown above and tool support is vital to aid the generation and manipulation of the Markov model. To this end, the PEPA Workbench was developed [GH94]. It allows models to be defined using PEPA. These are then processed by the Workbench which creates a representation of the infinitesimal generator matrix. This is in a form suitable for analysis by several computer algebra, and especially linear algebra, packages. Thus the Markov process can be ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proceedings of 7th Conf. on Mod. Techniques and Tools for Computer Perf. Eval., volume 794 of LNCS, pages 353--368, 1994.

....of combinators. Furthermore, a subset of the language terms which are guaranteed to result in ergodic Markov processes has been identified. These restrictions limit the way in which the combinators may be used within a model, but not which combinators are used. An overview of PEPA can be found in [13] and more detail is available in [14] TIPP and PEPA are very similar. It is important to note that instances of the same action type may exhibit different activity rates in both languages. Passive actions, in which the rate is left unspecified, are included in both these formalisms. MPA ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebrabased Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proceedings of the Seventh International Conference on Modelling Technqiues and Tools for Computer Performance Evaluation, volume 794 of LNCS, pages 353--368. SpringerVerlag, 1994.

....with space for only two blocks gives rise to a model with 316 states, and 612 states when there are four blocks per pallet. Both TIPP and PEPA are supported by prototype tools developed for these purposes. The TIPP tool is described in (Dulz and Herzog, 1995) The PEPA workbench is described in (Gilmore and Hillston, 1994). 6.1 Tool use and model solution The models presented in this paper were solved using the TIPP tool developed at the University of Erlangen. The evaluation proceeds in three steps: The first is compilation of the SPA terms. The output of this tool is a transition system which contains all the ....

GILMORE, S. and HILLSTON, J. (1994). The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In Haring, G. and Kotsis, G., editors, Proceedings of the Seventh International Conference on Modelling Technqiues and Tools for Computer Performance Evaluation volume 794 of LNCS pages 353--368. SpringerVerlag.

....such a model, a system designer can determine whether a candidate design meets both the behavioural and the temporal requirements demanded of it. Stochastic process algebras such as PEPA provide ample support for the component based construction of models. Robust tools such as the PEPA Workbench [2] facilitate the numerical solution of these models when calculating the e#ective performance of the system under study. However, two important parts of the modelling process are at present insu#ciently well supported: i) the specification and checking of performance properties which are to be ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proceedings of 7th Conf. on Mod. Techniques and Tools for Computer Perf. Eval., volume 794 of LNCS, pages 353--368, 1994.

....results for a modified system in which the deadlock has been removed. This integrated analysis will be demonstrated by means of the example in Section 4. Reachability analysis and CTMC generation can be carried out automatically as has been demonstrated by tools recently developed for MPA and PEPA [9]. 4 Example: A Distributed Mail System In this section we present an example, derived from a recently published case study [5] which illustrates the approach we have presented in the previous section. It describes the use of CCS to investigate a functional problem which arose in a distributed ....

....model verification. Many other authors have recognised the advantages of such a combined methodology, based for example on SDL [3, 4] and LOTOS [26, 4] The techniques for model construction and model solution described in this paper have already been implemented in tools for both MPA and PEPA [9]. The possibilities for future work are numerous we feel that the full potential of stochastic process algebras is yet to be realised. When the compositional structure of the models can be used to inform the solution of the CTMC, the tractability of these models will be greatly enhanced. A ....

S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Computer Performance Evaluation'94: Modelling Techniques and Tools, pages 353--368. Springer LNCS 794, 1994.

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S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebrabased Approach to Performance Modelling. In Proc. of the 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, number 794 in LNCS, pages 353--368, Vienna, May 1994. Springer-Verlag.

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S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In Proc. of the 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, number 794 in LNCS, pages 353--368, Vienna, May 1994. Springer-Verlag.

No context found.

S. Gilmore and J. Hillston. The PEPA workbench: a tool to support a process algebra-based approach to performance modelling. In Computer Performance Evaluation, Modeling Techniques and Tools, LNCS 794: 353-368, Springer-Verlag, 1994.

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S. Gilmore and J. A. Hillston. The PEPA Workbench: A Tool to support a Process Algebra-based Approach to Performance Modelling. In Proc. of the 7 Int. Conference on Modelling Techniques and Tools for Performance Evaluation, volume 794 of Lecture Notes in Computer Science, pages 353--368. Springer, 1994.

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S. Gilmore and J. Hillston. The PEPA workbench: A tool to support a process algebra-based approach to performance modelling. In G. Haring and G. Kotsis, editors, Proceedings of the 7th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation), volume 794 of LNCS, pages 353-368. Springer, 1994.

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S. Gilmore and J. Hillston. The PEPA Workbench: a tool to support a process algebra-based approach to performance modelling. In Proc. 7th Int. Conference on Modelling Techniques and Tools for Computer Performance Analysis, volume 794 of Lecture Notes in Computer Science, pages 353-368. Springer, 1994.

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S. Gilmore, J. Hillston, "The PEPA Workbench: A Tool to Support a Process Algebra Based Approach to Performance Modelling," in Proc. Seventh Intern. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, Vienna, 1994.

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S. Gilmore, J. Hillston, The PEPAworkbench: a tool to support a process algebra-based approach to performance modelling, in: G. Haring, G. Kotsis (Eds.), Seventh International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, Wien, 1994, pp. 353--368.

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S. Gilmore and J. Hillston. The PEPA workbench: A tool to support a process algebrabased approach to performance modelling. In 7th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, May 1994.

No context found.

S.Gilmore and J.Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proceedngs of 7th Conf. on Mod. Techniques and Tools for Computer Perf. Eval., volume 794 of LNCS, pages 353-368, 1994.

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