Stochastic Process Algebra Models Research Articles

Rate Lifting for Stochastic Process Algebra by Transition Context Augmentation

This paper presents an algorithm for determining the unknown rates in the sequential processes of a Stochastic Process Algebra (SPA) model, provided that the rates in the combined flat model are given. Such a rate lifting is useful for model reverse engineering and model repair. Technically, the algorithm works by solving systems of nonlinear equations and – if necessary – adjusting the model’s synchronisation structure, without changing its transition system. The adjustments cause an augmentation of a transition’s context and thus enable additional control over the transition rate. The complete pseudo-code of the rate lifting algorithm is included and discussed in the paper, and its practical usefulness is demonstrated by two case studies. The approach taken by the algorithm exploits some structural and behavioural properties of SPA systems, which are formulated here for the first time and could be very beneficial also in other contexts, such as compositional system verification.

State Equations in Stochastic Process Algebra Models

State equations are usually used for structural or qualitative analysis, such as deadlock checking, in P/T systems. In this paper, we instead consider timed state equations in stochastic process algebra models, to derive quantified dynamic information on the system modeled in the face of the state space explosion problem. The average of these state equations is demonstrated as the linear combination of the system transitions, with the combination coefficients specified by the bias term of the empirical transition rates to their steady state. The approaches of stochastic simulation and fluid approximation, straightforwardly generated from the quantified state equations, are studied, with the consistency being investigated both theoretically and experimentally.

The QoS analysis of web services composition based on Jackson queuing network

With the popularity of distributed computing and mobile internet, services composition has become a hot research in the field of service computing. The QoS of web services composition organised by BPEL is determined by the internal structure, the probability distribution in the variables value of BPEL process and the external factors such as the hardware and software processing capabilities of web servers and the load of web servers. At present, the generalised Petri nets, queuing Petri nets, Markov processes and stochastic process algebra model which are widely used and cannot have a comprehensive analysis in obtaining the actual performance of web services composition in internet environment. In this paper, a set of mapping rules are established to transform the internal and external factors which have impacts on the QoS of web services composition into Jackson queuing network, meanwhile, a set of performance indexes and their formula are given. Based on these performance indexes, we comprehensively analyse the performance of web services composition and locate the bottleneck of web services composition when the internal and external factors are changed so that, the performance of web services composition can be predicted before its deployment.

Robust resource allocations through performance modeling with stochastic process algebra

SummaryParallel and distributed computing has led to a proliferation in solving computationally intensive mathematical, science, or engineering problems. However, such computational environments are often prone to unpredictable variations due to problem, algorithm, and system characteristics. Therefore, a robustness study of resource allocations and application scheduling is required to guarantee a desired level of performance. Given an initial workload, a mapping of applications to resources is considered to be robust if it optimizes the execution performance and guarantees a desired level of performance in the presence of unpredictable perturbations at runtime. In this research work, a stochastic process algebra, performance evaluation process algebra, is used for obtaining performance of various resource allocations via a numerical analysis of performance modeling of the parallel execution of applications on parallel computing resources. Further, a robustness analysis of various allocations is performed for finding a robust mapping from a set of initial mapping schemes. The numerical results obtained from this performance modeling of resource allocations have been validated by the simulation results of earlier research, which are available from the existing literature, thus underscoring the significance of using stochastic process algebra models in providing a cost‐effective and low overhead analysis of robustness. Copyright © 2016 John Wiley & Sons, Ltd.

Numerically Representing Stochastic Process Algebra Models

Stochastic process algebras combine a high-level system description in terms of interacting components, with a rigorous low-level mathematical model in terms of a stochastic process. These have proved to be valuable modelling formalisms, particularly in the areas of performance modelling and systems biology. However, they do suffer from the problem of state space explosion. Currently, the underlying stochastic process is generally derived via the small step operational semantics of the process algebra and relies on a syntactical representation of the states of the process. In this paper, we propose a numerical representation schema based on a counting abstraction. This automatically detects symmetries within the state space based on replicated components, and produces a compact state space. Moreover, as we demonstrate, it is amenable to other interpretations and thus other forms of computational analysis, enriching the set of qualitative and quantitative measures that can be derived from a model.

A fluid analysis framework for a Markovian process algebra

Markovian process algebras, such as PEPA and stochastic π -calculus, bring a powerful compositional approach to the performance modelling of complex systems. However, the models generated by process algebras, as with other interleaving formalisms, are susceptible to the state space explosion problem. Models with only a modest number of process algebra terms can easily generate so many states that they are all but intractable to traditional solution techniques. Previous work aimed at addressing this problem has presented a fluid-flow approximation allowing the analysis of systems which would otherwise be inaccessible. To achieve this, systems of ordinary differential equations describing the fluid flow of the stochastic process algebra model are generated informally. In this paper, we show formally that for a large class of models, this fluid-flow analysis can be directly derived from the stochastic process algebra model as an approximation to the mean number of component types within the model. The nature of the fluid approximation is derived and characterised by direct comparison with the Chapman–Kolmogorov equations underlying the Markov model. Furthermore, we compare the fluid approximation with the exact solution using stochastic simulation and we are able to demonstrate that it is a very accurate approximation in many cases. For the first time, we also show how to extend these techniques naturally to generate systems of differential equations approximating higher order moments of model component counts. These are important performance characteristics for estimating, for instance, the variance of the component counts. This is very necessary if we are to understand how precise the fluid-flow calculation is, in a given modelling situation.

Analysing distributed Internet worm attacks using continuous state-space approximation of process algebra models

Internet worms are classically described using SIR models and simulations, to capture the massive dynamics of the system. Here we are able to generate a differential equation-based model of infection based solely on the underlying process description of the infection agent model. Thus, rather than craft a differential equation model directly, we derive this representation automatically from a high-level process model expressed in the PEPA process algebra. This extends existing population infection dynamics models of Internet worms by explicitly using frequency-based spread of infection. Three types of worm attack are analysed which are differentiated by the nature of recovery from infection and vulnerability to subsequent attacks. To perform this analysis we make use of continuous state-space approximation, a recent breakthrough in the analysis of massively parallel stochastic process algebra models. Previous explicit state-representation techniques can only analyse systems of order 10 9 states, whereas continuous state-space approximation can allow analysis of models of 10 10 000 states and beyond.

Stochastic Simulation Methods Applied to a Secure Electronic Voting Model

We demonstrate a novel simulation technique for analysing large stochastic process algebra models, applying this to a secure electronic voting system example. By approximating the discrete state space of a PEPA model by a continuous equivalent, we can draw on rate equation simulation techniques from both chemical and biological modelling to avoid having to directly enumerate the huge state spaces involved. We use stochastic simulation techniques to provide traces of course-of-values time series representing the number of components in a particular state. Using such a technique we can get simulation results for models exceeding 1010000 states within only a few seconds.

Expressing performance requirements using regular expressions to specify stochastic probes over process algebra models

This paper describes how soft performance bounds can be expressed for software systems using stochastic probes over stochastic process algebra models. These stochastic probes are specified using a regular expression syntax that describes the behaviour that must be observed in a model before a performance measurement can be started or stopped. We demonstrate the use of stochastic probes on a 661, 960 state parallel, redundant web server model to verify its passage-time performance characteristics.

Towards a Product Form Solution for Stochastic Process Algebras

We examine product form equilibrium distributions for stochastic process algebra models, finding conditions that guarantee the existence of a solution for the traffic equations. These equations are a set of linear equations, which are the basis of exact analysis of product form models like queueing networks, stochastic Petri nets, as well as stochastic process algebras. This paper illustrates how the equilibrium distribution can be expressed as a product for a certain class of stochastic process algebra models that satisfy certain conditions. Although the product from criterion derived in this paper is developed in the context of Performance Evaluation Process Algebra (PEPA), the results can be easily generalised to any of the other stochastic process algebra.