H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Sci. of Comp. Programming, 36(1): 97-127, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....MaO ov cha in from the composition of two IMCs. This isa very simple exa mple showing howMa rkov cha insca n be compositiona lly specified with IMC. Subsequently, the model ca n be eva lua ted with sta nda rd a a ysis techniques for MaO ov cha ins, cf. 18] A much la569 ca1 study is developed in [22], wherea Ma rkov cha n model of 720 sta es is derived from Ch ains 219 000 000 000 111 111 00 11 000 000 000 111 111 111 111 00 00 00 11 11 000 000 000 111 111 111 000 111 000 000 111 111 # # # # # ## ## # hide a in E 71 a E 72 Fig. 12. Compositiona l specifica tion ofa Ma rkov cha in. a ....

H. Hermanns and J.-P. Katoen. Automated compositional markov ch ain generation for a plain-old teleph ne system. Science of Computer Programming, 36(1):97--127, 2000.

....point, that the MAP respresentations of the trac streams may become rather large, especially in case we allow for feedback loops in the queueing network. We will then have to use algorithms to reduce the size of the MAPs. We are currently investigating the use of Markovian bisimulation algorithms [5, 6] to perform such reductions; early results are promising. ....

H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Science of Computer Programming, 36(1):97-127, 2000.

....and a delay which is shared by all parties which take part in the synchronization. We do not consider this further here, but we claim that the classical timed synchronizations can be expressed by means of SPA with timeless synchronization, like SPA. This capability has been extensively used in [6], to which we refer the reader for more details. Since SPA is hence a SPA which is as powerfull as others, we decide to consider only timeless synchronization in the future. 2.2 Throughputs and State Probabilities The throughput (or probability flow) s of a CTMC state s is defined as s = s ....

....( 2] Nevertheless, we will adopt some ideas presented in this paper for our further work: We are still convinced that the distinction between timed anonymous and immediate visible actions in conjunction with timeless synchronization is a reasonable assumption. As is illustrated in [7] and [6], this type of synchronization is easily extendible to other, timed synchronization types. The use of phase type distributions between the occurrence of synchronizations (the no timeouts restriction ) is a restriction that should be relaxed in the future. For the time being, anyway, it is a ....

H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Science of Computer Programming, Oct 1998. accepted for publication.

....and a delay shared by all parties which take part in the synchronisation. We do not consider this further here, but we claim that most of the classical timed synchronisations can be expressed by means of a SPA with timeless synchronisation, like SPA. This capability has been extensively used in [10], to which we refer the reader for further details. At this point we note that our SPA and its associated decompositional solution seem to be especially suited for synchronous systems or systems with barrier synchronisation, such as they can be implemented with languages as Esterel [1] or with ....

H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Science of Computer Programming, 36(1):97-127, Dec 1999.

....on CCS extended with exponentially distributed durations, but differ in their approach to synchronisation. There has been recent work on extending SPAs to allow general distributions, for example, the extension of EMPA [4] Interactive Markov Chains [12] Interactive GSMP [5] Spades [6] and also [9,13,7]. The Matrix Geometric Method is used in [11] to solve infinite stochastic Petri Nets which have an underlying Markov chain of the QBD type (see also [10] we consider models with failure in addition to QBD. In [17] a multi server queue with non preemptive heterogeneous priority structures is ....

H. Hermanns and J. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Science of Computer Programming, to appear. 30

....model. The mainstream SPAs (PEPA [1] TIPP [5] and EMPA [6] are extensions of CCS that allow only exponentially distributed durations and differ in the approach to synchronisation. There has been recent work extending SPAs to allow general distributions including [7 9] and [10] Furthermore, in [11] an approach for analysing the performance of a plain old telephone system is introduced by defining a stochastic process algebra that separates the advance of time and action occurrences, where time can be described by a continuous phase type distribution. The induced state space is very large, ....

H. Hermanns and J Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Science of Computer Programming, to appear.

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H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Sci. of Comp. Programming, 36(1): 97-127, 2000.

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H. Hermanns, J. Katoen, Automated compositional Markov chain generation for a plain-old telephony system, Science of Computer Programming 36 (1) (1999) 97--127.

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H. Hermanns, J.P. Katoen, Automated compositional Markov chain generation for a plain old telephony system, Sci. Comput. Programming 36 (1) (2000) 97--127.

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H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephony system. Science of Computer Programming 36(1):97--127, 2000.

.... algorithms for computing strong bisimulation to Markov chains [47] for the first time a constructive and e#cient way of computing lumpability has become available In addition, the practicability of the algebraic approach to performance analysis 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 ....

....and logarithmically in the number of states. Weak Markovian bisimulation has a worst case time complexity that is cubic in the number of states. By applying compositional minimisation, compositional Markov chain specifications with very large state spaces become tractable, as outlined in [51]. 8.3 Exploiting the structure of the specification for analysis Investigating todays (and future) resource sharing systems we are usually faced with the problem that the real system is extremely complex having a variety of di#erent hardware and software components. As a consequence, a ....

[Article contains additional citation context not shown here]

H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Sci. of Comp. Programming, 1999 (to appear).

....the overall model. Among the techniques that have been developed in order to combat this notorious problem are decomposition [8] structured representation based on Kronecker expressions [9,10] and compositional state space reduction based on bisimulation equivalences and symmetry exploitation [11,12]. In this paper, we present an approach to the memory efficient representation of very large stochastic models with the help of symbolic encodings in the 2 form of Multi Terminal Binary Decision Diagrams (MTBDD) MTBDDs are an extension of Binary Decision Diagrams (BDD) 13] a graph based ....

H. Hermanns, J. Katoen, Automated compositional Markov chain generation for a plain-old telephony system, Science of Computer Programming 36 (1) (1999) 97--127.

....states and transitions. In our stochastic process algebra the advance of (probabilistic) time and the occurrence of actions is separated. This separation of discrete and continuous phases is similar to that in many timed process algebras and has been recently proposed in the stochastic setting [16,17]. Most recent proposals for incorporating general distributions into process algebra follow this approach [3,6] As a result of this separation, interaction gets an intuitive meaning wait for the slowest process with a clear stochastic interpretation. Moreover, abstraction of actions becomes ....

H. Hermanns and J.-P. Katoen. Automated Compositional Markov Chain Generation for a Plain-Old Telephone System. Science of Computer Programming, 36(1):97-127, 2000.

....[16] and extended Markovian bisimilarity [2] Minimised components can be plugged into the original model in order to circumvent the state space explosion problem. This strategy, known as compositional aggregation has been applied successfully to handle, for instance, a telephony system model [18]. Without compositional aggregation, the state space turned out to consist of more than 10 million states, while only 720 states were actually required using compositional aggregation. Applicability of compositional aggregation relies on the existence of algorithms to compute minimised ....

.... justifies to eliminate internal immediate transitions such that a SLTS, and hence an (action labelled) CTMC results from the quotient transition system (the transition system obtained by representing each equivalence class by a single state) The details of this strategy are described in [18,15]. In order to illustrate how the relation can be used to achieve this, the equivalence classes of weak Markovian bisimilarity are indicated in Fig. 5 (bottom) Note, however, that this effect relies on abstraction of immediate actions before applying weak Markovian bisimilarity. Furthermore, a ....

H. Hermanns and J.P. Katoen. Automated Compositional Markov Chain Generation for a Plain Old Telephony System. to appear in Science of Computer Programming, 1998.

....of components without touching behavioural properties. Minimised components can be plugged into the original model in order to circumvent the state space explosion problem. This strategy, known as compositional aggregation has been applied successfully to handle very complex models (see, e.g. [11]) Applicability of compositional aggregation relies on the existence of algorithms to compute minimised components. We discuss efficient algorithms for strong equivalence, and (strong and weak) Markovian bisimulation. The algorithms are variants of well known partition refinement algorithms [19, ....

H. Hermanns, J.P. Katoen. Automated Compositional Markov Chain Generation for a Plain Old Telephony System. to appear in Science of Computer Programming, 1998.

No context found.

H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Sci. of Comp. Programming, 1999 (to appear).

....of an abstract stochastic model. Here we construct a simple Markov chain model of the gyros, and of their controller. The model is a toy example, developed to give a flavour of Markov chain modelling with process algebra. The model is developed in the algebra of interactive Markov chains (IMC) [18, 20], an extension of basic Lotos [6] Basic processes Each gyro might fail after an exponentially distributed amount of time (it is known that exponential distributions fit relatively well to failures of technical equipment) The failure rate # is the same for all gyros. A GYRO specification is as ....

....6 HST = trap crash STOP restart HST in STABILISER [sleep] BASE Time constraints Of course, preparing the shuttle mission takes time, and one might wish to incorporate the expected (random) delay in the model. To do so, we can use a constraint oriented style, as advocated in [20]. This style allows one to add constraints on the timing of certain sequences of interactions, such as between prepare and launch by means of a dedicated operator. For instance, on prepare delay launch by (#) STOP in HST adds an exponentially distributed delay with rate # between prepare and ....

[Article contains additional citation context not shown here]

H. Hermanns and J.P. Katoen. Automated compositional Markov chain generation for a plain-old telephony system. Science of Computer Programming 36(1):97--127, 2000.

....[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 measure of interest is mostly done informally. The analysis of the CTMC most often boils down to the determination of steadystate and transient state probabilities. Steady state probabilities refer to the system behaviour on the long run while the transient ....

....CTMCs and CSL. Section 3 presents a reduction of the model checking problem for time bounded until to a transient analysis on CTMCs. Section 4 discusses lumping equivalence and preservation of CSL properties. Section 5 reports on the checking of properties on a large plain old telephone system [21]. Section 6 concludes the paper. 2 CTMCs and CSL In this section, we briefly recall the basic concepts of CTMCs [28] and the logic CSL [3, 6] We slightly depart from the standard notations for CTMCs and consider a CTMC as an ordinary transition system (Kripke structure) where the edges are ....

[Article contains additional citation context not shown here]

H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Sci. of Comp. Programming, 36(1): 97--127, 2000.

....[16] and extended Markovian bisimilarity [2] Minimised components can be plugged into the original model in order to circumvent the state space explosion problem. This strategy, known as compositional aggregation has been applied successfully to handle, for instance, a telephony system model [18]. Without compositional aggregation, the state space turned out to consist of more than 10 million states, while only 720 states were actually required using compositional aggregation. Applicability of compositional aggregation relies on the existence of algorithms to compute minimised ....

.... justifies to eliminate internal immediate transitions such that a SLTS, and hence an (action labelled) CTMC results from the quotient transition system (the transition system obtained by representing each equivalence class by a single state) The details of this strategy are described in [18, 15]. In order to illustrate how the relation can be used to achieve this, the equivalence classes of weak Markovian bisimilarity are indicated in Fig. 5 (bottom) Note, however, that this effect relies on abstraction of immediate actions before applying weak Markovian bisimilarity. Furthermore, a ....

H. Hermanns and J.P. Katoen. Automated Compositional Markov Chain Generation for a Plain Old Telephony System. to appear in Science of Computer Programming, 1998.

.... 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 determination of steady state and transient state probabilities. Steady state probabilities refer to the system behaviour on the long run while the transient ....

....CTMCs and CSL. Section 3 presents a reduction of the model checking problem for time bounded until to a transient analysis on CTMCs. Section 4 discusses lumping equivalence and preservation of CSL properties. Section 5 reports on the checking of properties on a large plain old telephone system [19]. Section 6 concludes the paper. 2 CTMCs and CSL In this section, we briefly recall the basic concepts of CTMCs [26] and the logic CSL [3, 6] We slightly depart from the standard notations for CTMCs and consider a CTMC as an ordinary transition system (Kripke structure) where the edges are ....

[Article contains additional citation context not shown here]

H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Sci. of Comp. Programming, 36(1): 97--127, 2000.

.... 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: 31 53 4893247, e mail: katoen cs.utwente.nl. The analysis of the CTMC most often boils down to the determination of steadystate and transient state probabilities. ....

....CTMCs and CSL. Section 3 presents a reduction of the model checking problem for time bounded until to a transient analysis on CTMCs. Section 4 discusses lumping equivalence and preservation of CSL properties. Section 5 reports on the checking of properties on a large plain old telephone system [21]. Section 6 concludes the paper. 2 CTMCs and CSL In this section, we brie y recall the basic concepts of CTMCs [28] and the logic CSL [3, 6] We slightly depart from the standard notations for CTMCs and consider a CTMC as an ordinary transition system (Kripke structure) where the edges are ....

[Article contains additional citation context not shown here]

H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Sci. of Comp. Programming, 36(1): 97-127, 2000.

....from Markov chains [26] In fact, CSL and the algorithm can be generalised such that transient and steady state measures are expressible and can be approximated. We also plan to consider CTMCs that may contain nondeterminism, like stochastic transition systems [17] or interactive Markov chains [21, 22]. We believe that by extending our approach with schedulers [27] in a similar way as for the discrete time probabilistic case this is feasible. Acknowledgement. We thank Markus Siegle for discussion about our initial ideas concerning MTDDs. Ed Brinksma provided valuable comments on an earlier ....

H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Sci. of Comp. Programming, 1999.

No context found.

H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Sci. of Comp. Programming, 1999.

No context found.

H. Hermanns and J Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Science of Computer Programming, to appear.

No context found.

H. Hermanns and J.P. Katoen. Automated compositional Markov chain generation for a plain-old telephony system. Science of Computer Programming, 36(1):97--127, December 1999.

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