Elvio Gilberto Amparore

A component-based solution for reducible Markov regenerative processes

Irreducible Markov Regenerative Processes (MRPs) are solved by either building and storing the embedded DTMC (EMC) beforehand (explicit approach), or by applying implicit techniques, in which the EMC is never computed or stored. The implicit approach usually outperforms the explicit one, both in terms of time and memory. This paper introduces an implicit and component-based method for the steady-state solution of reducible Markov regenerative processes: the strongly connected components of the characteristic matrices of the process are used to identify a structure of components that is exploited by the solution process to discriminate components of the process that have a simple or a complex structure, and corresponding lower and higher solution costs. The solution then considers one component at a time, applying to each of them the simplest solution technique adequate to the actual component complexity. An implicit approach is followed, which saves the cost of building and storing the EMC, but makes non trivial the identification of the strongly connected components. The paper shows the efficacy of the method both in theory and on a set of MRPs arising from queueing networks, stochastic Petri nets and from the stochastic model checking of Markov chains. In particular it is shown that the cost of the model checking of the Until formula of the stochastic logic CSL^T^A reduces to that of CSL if the component method is used.

Stochastic) Model Checking in GreatSPN

GreatSPN is a tool for the definition and solution of Generalized Stochastic Petri Nets (GSPN). This paper presents the model checking features that have been recently introduced in GreatSPN. Through a new (Java-based) graphical interface for the GSPN model definition, the user can now access model checking of three different logics: the classical branching temporal logic CTL, and two stochastic logics, CSL and its superset CSLTA. This allows to integrate easily classical and probabilistic verification. A distinctive feature of the CTL model checker is the ability of generating counterexamples and witnesses. The CTL model checker employs symbolic data structures (decision diagrams) implemented in the Meddly library [6], developed Iowa State University, while the CSLTA model checker uses advanced solution methods, recently published, for Markov Renewal Processes.

Model checking CSL TA with Deterministic and Stochastic Petri Nets

CSLTA is a stochastic temporal logic for continuous-time Markov chains (CTMC), that can verify the probability of following paths specified by a Deterministic Timed Automaton (DTA). A DTA expresses both logic and time constraints over a CTMC path, yielding to a very flexible way of describing performance and dependability properties. This paper explores a model checking algorithm for CSLTA based on the translation into a Deterministic and Stochastic Petri Net (DSPN). The algorithm has been implemented in a simple Model Checker prototype, that relies on existing DSPN solvers to do the actual numerical computations.

A component-based solution method for non-ergodic Markov regenerative processes

This paper presents a new technique for the steady state solution of non-ergodic Markov Regenerative Processes (MRP), based on a structural decomposition of the MRP. Each component may either be a CTMC or a (smaller) MRP. Classical steady state solution methods of MRP are based either on the computation of the embedded Markov chain (EMC) defined over regenerative states, leading to high complexity in time and space (since the EMC is usually dense), or on an iterative scheme that does not require the construction of the EMC. The technique presented is particularly suited for MRPs that exhibit a semi-sequential structure. In this paper we present the new algorithm, its asymptotic complexity, and its performance in comparison with classical MRP techniques. Results are very encouraging, even when the MRP only loosely exhibits the required semi-sequential structure.

A New GreatSPN GUI for GSPN Editing and CSLTA Model Checking

This tool demonstration paper describes a new Graphical User Interface for the interactive modeling and verification of GSPN systems with the stochastic logic CSLTA. The GUI provides a modern and fully-featured environment designed around a complete modeling workflow: The user designs a GSPN model, a DTA (automaton describing properties for the CSLTA logic), and can simulate the GSPN behavior and the model checking process with an interactive simulation (a sort of “joint token game”). The tool then supports CSLTA model-checking and the computation of classical performance indices and qualitative properties. The aim is to provide a state-of-the-art integrated environment for the quantitative and qualitative analysis of GSPNs with the support of GreatSPN solvers and of the MC4CSLTA model checker.

30 Years of GreatSPN

GreatSPN is a tool for the stochastic analysis of systems modeled as (stochastic) Petri nets. This chapter describes the evolution of the GreatSPN framework over its life span of 30 years, from the first stochastic Petri net analyzer implemented in Pascal, to the current, fancy, graphical interface that supports a number of different model analyzers. This chapter reviews, with the help of a manufacturing system example, how GreatSPN is currently used for an integrated qualitative and quantitative analysis of Petri net systems, ranging from symbolic model checking techniques to a stochastic analysis whose efficiency is boosted by lumpability.

A Structured Solution Approach for Markov Regenerative Processes

Two different methods have been introduced in the past for the numerical analysis of Markov Regenerative Processes. The first one generates the embedded Markov chain explicitly and solves afterwards the often dense system of linear equations. The second method avoids computation of the embedded Markov chain by performing a transient analysis in each step. This method is called “matrix free” and it is often more efficient in memory and time. In this paper we go one step further by even avoiding the storage of the generator matrices required by the matrix-free method, thanks to the use of a Kronecker representation.

Improving and Assessing the Efficiency of the MC4CSLTA Model Checker

CSLTA is a stochastic logic which is able to express properties on the behavior of a CTMC, in particular in terms of the possible executions of the CTMC (like the probability that the set of paths that exhibits a certain behavior is above/below a certain threshold). This paper presents the new version of the the stochastic model checker MC4CSLTA, which verifies CSLTA formulas against a Continuous Time Markov Chain, possibly expressed as a Generalized Stochastic Petri Net. With respect to the first version of the model checker presented in [1], version 2 features a totally new solution algorithm, which is able to verify complex, nested formulas based on the timed automaton, while, at the same time, is capable of reaching a time and space complexity similar to that of the CSL model checkers when the automaton specifies a neXt or an Until formulas. In particular, the goal of this paper is to present a new way of generating the MRP, which, together with the new MRP solution method presented in [2] provides the two cornerstone results which are at the basis of the current version. The model checker has been evaluated and validated against PRISM [3] (for whose CSLTA formulas which can be expressed in CSL) and against the statistical model checker Cosmos[4] (for all types of formulas).

Expressing and computing passage time measures of GSPN models with HASL

Passage time measures specification and computation for Generalized Stochastic Petri Net models have been faced in the literature from different points of view. In particular three aspects have been developed: (1) how to select a specific token (called the tagged token) and measure the distribution of the time employed from an entry to an exit point in a subnet; (2) how to specify in a flexible way any condition on the paths of interest to be measured, (3) how to efficiently compute the required distribution. In this paper we focus on the last two points: the specification and computation of complex passage time measures in (Tagged) GSPNs using the Hybrid Automata Stochastic Logic (HASL) and the statistical model checker COSMOS. By considering GSPN models of two different systems (a flexible manufacturing system and a workflow), we identify a number of relevant performance measures (mainly passage-time distributions), formally express them in HASL terms and assess them by means of simulation in the COSMOS tool. The interest from the measures specification point of view is provided by the possibility of setting one or more timers along the paths, and setting the conditions for the paths selection, based on the measured values of such timers. With respect to other specification languages allowing to use timers in the specification of performance measures, HASL provides timers suspension, reactivation, and rate change along a path.

Probe Automata for Passage Time Specification

Passage time distribution has drawn increasing attention over the past years as an important measure to define and verify service level agreements. The definition of passage time requires the specification of a condition to start/stop the computation, and possibly of a restriction on the system behavior to be considered between start and stop. Different characterizations have been defined in the past, either state-based, action-based or a mix of the two, either for Markov chains, or for stochastic Petri nets and process algebras. In this paper we propose probe automata as a way to specify passage time for GSPNs that allows one to select entering, goal, and forbidden states, as well as paths of interest starting from any reachable state. The specification is in terms of conditions over the current marking, the transition (sequence) being fired, as well as over the marking reached through the firing. Probe automata subsume previous definitions of passage time for GSPNs and for Tagged GSPNs, the extension of GSPNs that was defined in the past for computing passage time of a {\em tagged token} in a GSPN.