Towards a Product Form Solution for Stochastic Process Algebras

With the advent of the Internet of Things (IoT) as a major force of change in industry, Cyber Physical Systems (CPS) is right for building the concept smart Environment. In CPS, the internal computational and physical elements generally interact, reflect and influence each other in order to obtain and analyze human behaviors and their social activities, finally to help them facilitate experiences. Nevertheless, the system complexity and scale become challenges of discrete state modelling formalisms especially in the capability issue. For the stochastic process algebra, performance evaluation process algebra (PEPA), a fluid approximation approach dealing with this problem has been developed, which approximates the continuous time Markov chain underlying a model using ordinary differential equations (ODEs). This paper establishes some basic properties for the ODE based approximation, e.g., uniqueness, existence and boundedness of ODE solutions. Our research in particular presents a convergence of the solutions for nonsynchronised models.

Intelligent Traffic Systems (ITS), as integrated systems including control technologies, communication technologies, vehicle sensing and vehicle electronic technologies, have provided valuable solutions to the increasingly serious traffic problems. Hence, in order to achieve efficient management of all types of transportation resources and make better use of ITS, it is necessary and significant to continue study in depth on the architecture and performance of ITS. This paper adopts one kind of stochastic process algebra (SPA)—Performance Evaluation Process Algebra (PEPA) to model and evaluate the process of real-time positioning and route planning in ITS. Meanwhile, the fluid flow approximation is employed to conduct a performance analysis through PEPA models, then the maximize utilization and the throughput of the system can be achieved and analyzed.

The increase in scale provided by distributed computing systems has expanded scientific discovery and engineering solutions. Stochastic modeling with Performance Evaluation Process Algebra (PEPA) has been used to evaluate the robustness of static resource allocations in parallel and distributed computing systems. These evaluations have previously been performed through the PEPA Plug-In for the Eclipse Integrated Development Environment and have been limited by factors that include: i) the size and complexity of the underlying, in-use PEPA model, ii) a small number of resource allocation models available for analysis, and iii) the human interaction necessary to configure the PEPA Eclipse Plug-In, thus limiting potential automation. As the size and complexity of the underlying PEPA models increases, the number of states to be evaluated for each model also greatly increases, leading to a case of state space explosion. In this work, we validate the Imperial PEPA Compiler (IPC) as a replacement for the PEPA Eclipse Plug-In for the robustness analysis of resource allocations. We make available an implementation of the IPC as a Singularity container, as part of a larger online repository of PEPA resources. We then develop and test a programmatic method for generating PEPA models for resource allocations. When combined with our IPC container, this method allows automated analysis of resource allocation models at scale. The use of the IPC allows the evaluation of larger models than it is possible when using the PEPA Eclipse Plug-In. Moreover, the increases in scale in both model size and number of models, support the development of improved makespan targets for robustness metrics, including those among applications subject to perturbations at runtime, as found in typical parallel and distributed computing environments.

In this paper we constructed a formal performance model for a secure and scalable e-voting scheme known as DRE-i voting scheme. The well-known formal stochastic performance evaluation process algebra (PEPA) language and PEPA Eclipse plug-in were used to represent the voting scheme and analyse its performance characteristics. Timely responses of remote electronic voting protocols are important to increase voters’ confidence in e-voting systems. Therefore we evaluated the average response time that voters may observe when they cast their votes using remote electronic voting systems, such as DRE-i, and we also evaluated the throughput and queue length of the DRE-i server’s actions for different number of voters inside the DRE-i e-voting system. The performance evaluation of the DRE-i scheme reveals that PEPA language is efficient in investigating the performance properties of large scale e-voting schemes.

The Stochastic Process Algebra (SPA) formalism for performance models of communicating systems is briefly reviewed, focussing on the subset of Markovian Process Algebra (MPA). MPA facilitates analytical solutions for equilibrium state probabilities, in principle, but direct methods are severely limited by the size of the state space. By considering the reversed process of a stationary Markov chain, product-forms are derived for the equilibrium state probabilities in stochastic networks defined by a collection of cooperating MPA agents. Key to the analysis is the property of compositionality. Under quite general conditions, the well known product-forms for networks of queues (Jackson’s theorem) and G-networks (with both positive and negative customers) can be simply obtained. Two new product forms are also derived by systematically following this mechanical approach.

Stochastic Petri Nets and Stochastic Process Algebras can both be used for the qualitative and quantitative analysis of parallel and distributed systems. However, sometimes the complexity of the system can make such analysis infeasible, due to the large size of the state space underlying the model. To overcome this problem different aggregation techniques have been proposed in both formalisms. Two of them are compared in this paper.

The four papers in this special issue apply tools and techniques from computer performance evaluation in the very different domain of modelling biological systems. This might seem to be a very odd thing to do but the practice of analysing biological systems in this way is becoming increasing common. As data about the internal components of biological systems is becoming more readily available, biologists are increasingly asking questions about how systems function. In addition to conducting laboratory experiments, they are supported in this exploration by in silico experimentation based on models. The view taken of the biological processes focusses on the stimuli and responses, a view akin to that taken of engineered systems in systems engineering. Thus this new endeavour in biology is known as Systems Biology . Performance analysts have a long tradition of modelling systems in order to understand and predict their function. Their focus is particularly on the dynamic aspects of the system, the use of, and contention for, resources, and the impact of uncertainty or randomness. These issues are important in the biological setting also, and so it is perhaps inevitable that we see some people and techniques from performance modelling being applied in systems biology. In particular some of the high-level modelling formalisms which have supported Markovian performance modelling in the last few decades (stochastic Petri nets, stochastic process algebras, etc.) are being applied in the biological domain. Furthermore analysis techniques, such as Markovian analysis, Monte Carlo simulation and probabilistic model checking have also been adoped. In this volume we have sought to give a snapshot of a variety of work which is going on at this interface between systems biology and more traditional quantitative analysis techniques. It is by no means an exhaustive account of this exciting area, but rather a taster which will hopefully whet your appetite to find out more. To open the volume, the editors provide a survey paper describing the motivations and goals of the systems biology endeavour, summarising the existing modelling techniques and outlining some instances of cross-over between performance modelling and systems biology. This includes an account of the use of ordinary differential equations (ODE) and stochastic simulation to analyse biological systems, and the adoption of high-level modelling formalisms such as Petri nets and process algebras to drive these ODE models and simulations. In their paper Kwiatkowska, Norman and Parker show the application of logic and probabilistic model checking to the analysis of biological signalling pathways. They use the PRISM probabilistic model-checker to check formulae of the CSL logic against CTMC-based models of the MAPK cascade, a sequence of biochemical reactions which sends a message within a cell. The paper provides an introduction to the CSL logic as well as the reactive modules language implemented by the PRISM model checker. Performance measures of interest are described using reward structures and the analysis achieved by PRISM is able to show how the percentage of activated MAPK, a key component of the pathway, and the number of MAPK-MAPKK reactions, vary as a function of time, for different values of the initial number of MAPKs. The paper by Jeschke, Ewald, Park, Fujimoto and Uhrmacher addresses the drive for increased physical accuracy in simulation models which represent the spatial aspects of cell biology. Standard approaches to stochastic simulation of cellular systems assume that the cell is a homogeneous soup of biochemical components. The truth is far removed from this, as the cell has a lot of internal structure which can have a profound effect on the dynamics of reactions. Setting aside the assumption that the reacting chemical species are well-stirred, spatial approaches divide the volume into sub-volumes and apply a structured method which identifies the next reaction to occur in each subvolume. The cost of such an increase in accuracy in the simulation model is a much increased running time so the authors use a parallel and distributed approach to improve performance. To close this special issue we have a paper by DemattB, Priami and Romanel which uses the BlenX language and the Beta Workbench software to analyse the MAPK pathway considered also by Kwiatkowska, Norman and Parker. The BlenX language, and the Beta-binders process calculus which was its inspiration, are examples of a new generation of languages which have been designed specifically for the biological domain, as an alternative to using existing languages designed for modelling computer systems. The paper shows how a well-designed platform for modelling and simulation can lift the user's experience and make their use of process calculi more valuable, delivering insights which would not have been seen otherwise.

We introduce immediate transitions as an extension of Stochastic Process Algebras (SPA). We distinguish two different classes of immediate transitions: probabilistic branching and management activities. We discuss both approaches and develop a theory for the probabilistic branching case. Although we use TIPP as a sample language within this paper, the theory can easily be adapted to other Stochastic Process Algebras and can therefore be seen as a general result for probabilistic branching in SPA.

Performance analysis of multi–agent system can be done by experiments with real system, simulation or analytic methods. Now, multi–agent technologies, e.g., (Deloach et al., 2001; JADE), are often based on Unified Modeling Lanuage (UML) (Booch et al., 1999; UML, 2007) or its modifications. The following analytical approaches: queuing network models (Kahkipuro, 1999), stochastic automata networks (Steward et al., 1995), stochastic Petri nets (King & Pooley, 1999), stochastic process algebra (Pooley, 1999), Markov chains can be used in performance evaluation of multi–agent systems. In this chapter, an analytical approach, which is based on Petri nets, is developed. This approach is applied to performance evaluation of layered multi–agent system. These layers are associated with the following types of agents: manager, bidder, and searcher ones. Time–out mechanisms are used in communication between agents. Our method is based on approximation using Erlang distribution. Erlang distributions create the family of distributions with different number of stages. In the paper (Babczynski & Magott, 2006a), an approximation method which is based on Erlang distribution has been applied for the above layered multi–agent system. In that paper, there was no bounds for time of waiting for messages from the agents. In present chapter, time–out mechanisms are used in communication between the agents. The chapter is an extension of the paper (Babczynski & Magott, 2006b) where PERT based approach was presented. Accuracy of our approximation method is verified using simulator. This simulator has been previously used in simulation experiments with the following multi–agent systems: personalized information system (Babczynski et al., 2004a), industrial system (Babczynski et al., 2004b), system with static agents and system with mobile agent (Babczynski et al., 2005). These systems have been expressed in standard FIPA (FIPA) which the JADE technology (JADE) is complied with. The chapter is organized as follows. In section 2, the multi–agent system is described. Then our approximation method is presented. In section 4, accuracy of our approximation method is verified by comparison with simulation results. Finally, there are conclusions.

Performance evaluation of component-based software systems: A survey

Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets

We define a stochastic Petri net (SPN) semantics for stochastic process algebras (SPAs), a recently introduced formalism that offers a novel approach for performance modeling. The proposed semantics is evaluated in terms of three criteria: concurrency and retrievability, as defined by Olderog (1987, 1991) for untimed net semantics, and Markov equivalence for the stochastic aspects.

For the lack of safety and reliability of the information in the cloud computing environment, in order to create a more flexible and adaptable security mechanism, the combination of cloud computing and credible concept is a major research direction in today’s security. Based on the view mentioned above, this paper strengthens the research of trust computing technology to solve the security issues in cloud and cloud-based trust transfer, on the basis of the practical work of the experts and scholars on the trust transfer technology, and expands the theoretical model of the trust chain. This paper uses the stochastic process algebra and Petri nets as a modeling tool to build two trust chain models, demonstrates the credibility of certain behavioral characteristics of the chain, analyzes several constraints of credible chain, and provides a valuable reference for engineering practice of the credible chain.

The incorporation of time into classical process algebras aiming at the integration of functional design and performance analysis has become very popular recently. There are many ways to include time in process algebras. Current research in this area concentrates mainly on the annotation of actions with exponentially distributed random variables. This allows us to make use of a large repertoire of analysis algorithms. This paper presents some first results of ongoing work which aims at providing a tool for the efficient performance evaluation and functional analysis of computer and communication systems based on the stochastic process algebra paradigm. It provides facilities for model creation, reachability analysis, as well as several numerical algorithms for the solution of the underlying Markov chain and the computation of characteristic performance measures.

Queueing Petri nets with product form solution