Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions

The PEPA workbench: A tool to support a process algebra-based approach to performance modelling

. In this paper we present a new technique for performance modelling and a tool supporting this approach. Performance Evaluation Process Algebra (PEPA) [1] is an algebraic language which can beused to build models of computer systems which capture information about the performance of the system. The PEPA language serves two purposes as a formal description language for computer system models. The performance-related information in the model may be used to predict the performance of the system whereas the behavioural information in the model may be exploited when reasoning about the functional behaviour of the system (e.g. when finding deadlocks or when exhibiting equivalences between sub-components). In this paper we concentrate on the performance aspects of the language. A method of reasoningaboutPEPA modelsproceedsby considering the derivation graph obtained from the model using the underlying operational semantics of the PEPA language. The derivation graph is systematically reduced ..

Evaluating the Robustness of Resource Allocations Obtained through Performance Modeling with Stochastic Process Algebra

Recent developments in the field of parallel and distributed computing has led to a proliferation of solving large and computationally intensive mathematical, science, or engineering problems, that consist of several parallelizable parts and several non-parallelizable (sequential) parts. In a parallel and distributed computing environment, the performance goal is to optimize the execution of parallelizable parts of an application on concurrent processors. This requires efficient application scheduling and resource allocation for mapping applications to a set of suitable parallel processors such that the overall performance goal is achieved. However, such computational environments are often prone to unpredictable variations in application (problem and algorithm) and system characteristics. Therefore, a robustness study 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 that mapping optimizes execution performance and guarantees a desired level of performance in the presence of unpredictable perturbations at runtime. In this research, a stochastic process algebra, Performance Evaluation Process Algebra (PEPA), is used for obtaining resource allocations via a numerical analysis of performance modeling of the parallel execution of applications on parallel computing resources. The PEPA performance model is translated into an underlying mathematical Markov chain model for obtaining performance measures. Further, a robustness analysis of the allocation techniques is performed for finding a robustmapping from a set of initial mapping schemes. The numerical analysis of the performance models have confirmed similarity with the simulation results of earlier research available in existing literature. When compared to direct experiments and simulations, numerical models and the corresponding analyses are easier to reproduce, do not incur any setup or installation costs, do not impose any prerequisites for learning a simulation framework, and are not limited by the complexity of the underlying infrastructure or simulation libraries

A Compositional Semantics for Stochastic Reo Connectors

In this paper we present a compositional semantics for the channel-based coordination language Reo which enables the analysis of quality of service (QoS) properties of service compositions. For this purpose, we annotate Reo channels with stochastic delay rates and explicitly model data-arrival rates at the boundary of a connector, to capture its interaction with the services that comprise its environment. We propose Stochastic Reo automata as an extension of Reo automata, in order to compositionally derive a QoS-aware semantics for Reo. We further present a translation of Stochastic Reo automata to Continuous-Time Markov Chains (CTMCs). This translation enables us to use third-party CTMC verification tools to do an end-to-end performance analysis of service compositions.Comment: In Proceedings FOCLASA 2010, arXiv:1007.499

Optimisation of Definition Structures & Parameter Values in Process Algebra Models Using Evolutionary Computation

Process Algebras are a Formal Modelling methodology which are an effective tool for defining models of complex systems, particularly those involving multiple interacting processes. However, describing such a model using Process Algebras requires expertise from both the modeller and the domain expert. Finding the correct model to describe a system can be difficult. Further more, even with the correct model, parameter tuning to allow model outputs to match experimental data can also be both difficult and time consuming. Evolutionary Algorithms provide effective methods for finding solutions to optimisation problems with large and noisy search spaces. Evolutionary Algorithms have been proven to be well suited to investigating parameter fitting problems in order to match known data or desired behaviour. It is proposed that Process Algebras and Evolutionary Algorithms have complementary strengths for developing models of complex systems. Evolutionary Algorithms require a precise and accurate fitness function to score and rank solutions. Process Algebras can be incorporated into the fitness function to provide this mathematical score. Presented in this work is the Evolving Process Algebra (EPA) framework, designed for the application of Evolutionary Algorithms (specifically Genetic Algorithms and Genetic Programming optimisation techniques) to models described in Process Algebra (specifically PEPA and Bio-PEPA) with the aim of evolving fitter models. The EPA framework is demonstrated using multiple complex systems. For PEPA this includes the dining philosophers resource allocation problem, the repressilator genetic circuit, the G-protein cellular signal regulators and two epidemiological problems: HIV and the measles virus. For Bio-PEPA the problems include a biochemical reactant-product system, a generic genetic network, a variant of the G-protein system and three epidemiological problems derived from the measles virus. Also presented is the EPA Utility Assistant program; a lightweight graphical user interface. This is designed to open the full functionality and parallelisation of the EPA framework to beginner or naive users. In addition, the assistant program aids in collating and graphing after experiments are completed

From coordination to stochastic models of QoS

Reo is a channel-based coordination model whose operational semantics is given by Constraint Automata (CA). Quantitative Constraint Automat