Distributed computation of transient state distributions and passage time quantiles in large semi-Markov models

Submitted versio

Distributed Computation of Passage Time Quantiles and Transient State Distributions in Large Semi-Markov Models

Published versio

Hypergraph-based parallel computation of passage time densities in large semi-Markov models

AbstractPassage time densities and quantiles are important performance and quality of service metrics, but their numerical derivation is, in general, computationally expensive. We present an iterative algorithm for the calculation of passage time densities in semi-Markov models, along with a theoretical analysis and empirical measurement of its convergence behaviour. In order to implement the algorithm efficiently in parallel, we use hypergraph partitioning to minimise communication between processors and to balance workloads. This enables the analysis of models with very large state spaces which could not be held within the memory of a single machine. We produce passage time densities and quantiles for very large semi-Markov models with over 15 million states and validate the results against simulation

Derivation of passage-time densities in PEPA models using ipc: the imperial PEPA compiler

We present a technique for defining and extracting passage-time densities from high-level stochastic process algebra models. Our high-level formalism is PEPA, a popular Markovian process algebra for expressing compositional performance models. We introduce ipc, a tool which can process PEPA-specified passage-time densities and models by compiling the PEPA model and passage specification into the DNAmaca formalism. DNAmaca is an established modelling language for the low-level specification of very large Markov and semi-Markov chains. We provide performance results for ipc/DNAmaca and comparisons with another tool which supports PEPA, PRISM. Finally, we generate passage-time densities and quantiles for a case study of a high-availability web server. 1

Distributed Response Time Analysis of GSPN Models with MapReduce

widely used in the performance analysis of computer and communications systems. Response time densities and quantiles are often key outputs of such analysis. These can be extracted from a GSPN’s underlying semi-Markov process using a method based on numerical Laplace transform inversion. This method typically requires the solution of thousands of systems of complex linear equations, each of rank n, where n is the number of states in the model. For large models substantial processing power is needed and the computation must therefore be distributed. This paper describes the implementation of a Response Time Analysis module for the Platform Independent Petri net Editor (PIPE2) which interfaces with Hadoop, an open source implementation of Google’s MapReduce distributed programming environment, to provide distributed calculation of response time densities in GSPN models. The software is validated with analytically calculated results as well as simulated ones for larger models. Excellent scalability is shown. I

Performance queries on Semi-Markov Stochastic Petri nets with an extended continuous Stochastic logic

Semi-Markov Stochastic Petri Nets (SM-SPNs) are a highlevel formalism for defining semi-Markov processes. We present an extended Continuous Stochastic Logic (eCSL) which provides an expressive way to articulate performance queries at the SM-SPN model level. eCSL supports queries involving steady-state, transient and passage time measures. We demonstrate this by formulating and answering eCSL queries on an SM-SPN model of a distributed voting system with up to ¢¤£¦ ¥ states.

Performance Trees: Implementation And Distributed Evaluation

In this paper, we describe the first realisation of an evaluation environment for Performance Trees, a recently proposed formalism for the specification of performance properties and measures. In particular, we present details of the architecture and implementation of this environment that comprises a client-side model and performance query specification tool, and a server-side distributed evaluation engine, supported by a dedicated computing cluster. The evaluation engine combines the analytic capabilities of a number of distributed tools for steady-state, passage time and transient analysis, and also incorporates a caching mechanism to avoid redundant calculations. We demonstrate in the context of a case study how this analysis pipeline allows remote users to design their models and performance queries in a sophisticated yet easy to use framework, and subsequently evaluate them by harnessing the computing power of a Grid cluster back-end.Accepted versio

Asynchronous iterative solution for dominant eigenvectors with applications in performance modelling and PageRank

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