A method to approximate first passage times distributions in direct time Markov processes

A numerical method to approximate first passage times distributions in direct Markov processes will be presented. It is useful to compute sojourn times in queue systems, namely in Jackson queuing networks. Using this method (Kiessler et al., 1988) achieved to clear a problem that arises in the Jackson three node acyclic networks sojourn times

Sojourn times in Jackson networks

Jackson queuing networks have a lot of practical applications, mainly in the modelling of computation and telecommunications networks. Evidently the time that one customer - a person, a job, a message … – spends in this kind of systems, its sojourn time, is an important measure of its performance. In this work the practical known results about the sojourn time distribution are collected and presented

Computing customers sojourn times in Jackson networks distribution functions and moments

Jackson queuing networks have a lot of practical applications, mainly in services and technologic devices. For the first case, an example are the healthcare networks and, for the second, the computation and telecommunications networks. Evidently the time that a customer - a person, a job, a message … – spends in this kind of systems, its sojourn time[1], is an important measure of its performance, among others. In this work, the practical statistical known results about the sojourn time of a customer, in a Jackson network, distribution are collected and presented. And an emphasis is set on the numerical methods applicable to compute the distribution function and the moments.info:eu-repo/semantics/acceptedVersio

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

Published versio

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

Submitted versio

Reliability calculation using randomization for Markovian fault-tolerant computing systems

The randomization technique for computing transient probabilities of Markov processes is presented. The technique is applied to a Markov process model of a simplified fault tolerant computer system for illustrative purposes. It is applicable to much larger and more complex models. Transient state probabilities are computed, from which reliabilities are derived. An accelerated version of the randomization algorithm is developed which exploits ''stiffness' of the models to gain increased efficiency. A great advantage of the randomization approach is that it easily allows probabilities and reliabilities to be computed to any predetermined accuracy

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