The GreatSPN tool: recent enhancements

GreatSPN is a tool that supports the design and the qualitative and quantitative analysis of Generalized Stochastic Petri Nets (GSPN) and of Stochastic Well-Formed Nets (SWN). The very first version of GreatSPN saw the light in the late eighties of last century: since then two main releases where developed and widely distributed to the research community: GreatSPN1.7 [13], and GreatSPN2.0 [8]. This paper reviews the main functionalities of GreatSPN2.0 and presents some recently added features that significantly enhance the efficacy of the tool

Modeling performance of Hadoop applications: A journey from queueing networks to stochastic well formed nets

Nowadays, many enterprises commit to the extraction of actionable knowledge from huge datasets as part of their core business activities. Applications belong to very different domains such as fraud detection or one-to-one marketing, and encompass business analytics and support to decision making in both private and public sectors. In these scenarios, a central place is held by the MapReduce framework and in particular its open source implementation, Apache Hadoop. In such environments, new challenges arise in the area of jobs performance prediction, with the needs to provide Service Level Agreement guarantees to the enduser and to avoid waste of computational resources. In this paper we provide performance analysis models to estimate MapReduce job execution times in Hadoop clusters governed by the YARN Capacity Scheduler. We propose models of increasing complexity and accuracy, ranging from queueing networks to stochastic well formed nets, able to estimate job performance under a number of scenarios of interest, including also unreliable resources. The accuracy of our models is evaluated by considering the TPC-DS industry benchmark running experiments on Amazon EC2 and the CINECA Italian supercomputing center. The results have shown that the average accuracy we can achieve is in the range 9–14%

One Net Fits All: A unifying semantics of Dynamic Fault Trees using GSPNs

Dynamic Fault Trees (DFTs) are a prominent model in reliability engineering. They are strictly more expressive than static fault trees, but this comes at a price: their interpretation is non-trivial and leaves quite some freedom. This paper presents a GSPN semantics for DFTs. This semantics is rather simple and compositional. The key feature is that this GSPN semantics unifies all existing DFT semantics from the literature. All semantic variants can be obtained by choosing appropriate priorities and treatment of non-determinism.Comment: Accepted at Petri Nets 201

On the relations between Markov chain lumpability and reversibility

In the literature, the notions of lumpability and time reversibility for large Markov chains have been widely used to efficiently study the functional and non-functional properties of computer systems. In this paper we explore the relations among different definitions of lumpability (strong, exact and strict) and the notion of time-reversed Markov chain. Specifically, we prove that an exact lumping induces a strong lumping on the reversed Markov chain and a strict lumping holds both for the forward and the reversed processes. Based on these results we introduce the class of λρ-reversible Markov chains which combines the notions of lumping and time reversibility modulo state renaming. We show that the class of autoreversible processes, previously introduced in Marin and Rossi (Proceedings of the IEEE 21st international symposium on modeling, analysis and simulation of computer and telecommunication systems MASCOTS, pp. 151–160, 2013), is strictly contained in the class of λρ-reversible chains

New solvers for asymmetric systems in GreatSPN

In this paper we present the extended symbolic reachability graph/dynamic symbolic reachability graph (ESRG/DSRG) framework to model and solve (asymmetric) SWN models. This framework combines several tools: GreatSPN for the model design, WNESRG to build the ESRG of the designed model, ESRG2MC to refine the ESRG and generate the corresponding MC, WNDSRG to build the DSRG and the corresponding MC. MCSolver is used to solve the MC and compute the steady state marking probability. The following section is dedicated to the detailed presentation of this new framework

Lumping Partially Symmetrical Stochastic Models

The performance and dependability evaluation of complex systems by means of dynamic stochastic models (e.g. Markov chains) may be impaired by the combinatorial explosion of their state space. Among the possible methods to cope with this problem, symmetry-based ones can be applied to systems including several similar components. Often however these systems are only partially symmetric: their behavior is in general symmetric except for some local situation when the similar components need to be differentiated. In this paper two methods to efficiently analyze partially symmetrical models are presented in a general setting and the requirements for their efficient implementation are discussed. Some case studies are presented to show the methods' effectiveness and their applicative interest

Efficient lumpability check in partially symmetric systems

State space based performance analysis of stochastic models may be impaired by the state space explosion but such problem can be mitigated in symmetrical behaving systems by aggregating equivalent states and transitions. An effective way of exploiting symmetries when the system is modeled using the stochastic well-formed net (SWN) formalism, is to generate the symbolic reachability graph (SRG) and automatically derive a lumped continuous time Markov chain (CTMC) of the same size as the SRG from it. For partially symmetric systems, the extended SRG (ESRG) can be used instead, but the derivation of a lumped CTMC in this case is not as direct as in the SRG case: in fact the ESRG structure might need a refinement to satisfy the lumpability conditions. In this paper a new efficient algorithm to derive a lumped CTMC from the ESRG is presented, and the results obtained by experimenting its implementation within the GreatSPN environment are discussed. The algorithm combines the Paige and Tarjan's partition refinement algorithm (extended to work with weighted arcs) and a previously proposed lumpability check algorithm (built specifically for the use with the ESRG) and outperforms both of them. The implementation of the algorithm within the GreatSPN environment would allow the several users that have chosen this package to apply the proposed technique

Efficient lumpability check in partially symmetric systems

International audienceState space based performance analysis of stochastic models may be impaired by the state space explosion but such problem can be mitigated in symmetrical behaving systems by aggregating equivalent states and transitions. An effective way of exploiting symmetries when the system is modeled using the stochastic well-formed net (SWN) formalism, is to generate the symbolic reachability graph (SRG) and automatically derive a lumped continuous time Markov chain (CTMC) of the same size as the SRG from it. For partially symmetric systems, the extended SRG (ESRG) can be used instead, but the derivation of a lumped CTMC in this case is not as direct as in the SRG case: in fact the ESRG structure might need a refinement to satisfy the lumpability conditions. In this paper a new efficient algorithm to derive a lumped CTMC from the ESRG is presented, and the results obtained by experimenting its implementation within the GreatSPN environment are discussed. The algorithm combines the Paige and Tarjan's partition refinement algorithm (extended to work with weighted arcs) and a previously proposed lumpability check algorithm (built specifically for the use with the ESRG) and outperforms both of them. The implementation of the algorithm within the GreatSPN environment would allow the several users that have chosen this package to apply the proposed technique