Performance and Reliability of Non-Markovian Heterogeneous Distributed Computing Systems

Average service time, quality-of-service (QoS), and service reliability associated with heterogeneous parallel and distributed computing systems (DCSs) are analytically characterized in a realistic setting for which tangible, stochastic communication delays are present with nonexponential distributions. The departure from the traditionally assumed exponential distributions for event times, such as task-execution times, communication arrival times and load-transfer delays, gives rise to a non-Markovian dynamical problem for which a novel age dependent, renewal-based distributed queuing model is developed. Numerical examples offered by the model shed light on the operational and system settings for which the Markovian setting, resulting from employing an exponential-distribution assumption on the event times, yields inaccurate predictions. A key benefit of the model is that it offers a rigorous framework for devising optimal dynamic task reallocation (DTR) policies systematically in heterogeneous DCSs by optimally selecting the fraction of the excess loads that need to be exchanged among the servers, thereby controlling the degree of cooperative processing in a DCSs. Key results on performance prediction and optimization of DCSs are validated using Monte-Carlo (MC) simulation as well as experiments on a distributed computing testbed. The scalability, in the number of servers, of the age-dependent model is studied and a linearly scalable analytical approximation is derived

About the Approximation of Stochastic Petri Nets by Continuous Petri Nets: Several Regions

Reliability analysis is often based on stochastic discrete event models like Markov models or stochastic Petri nets. For complex dynamical systems with numerous components, analytical expressions of the steady state are tedious to work out because of the combinatory explosion with discrete models. Moreover, the convergence of stochastic estimators is slow. For these reasons, fluidification can be investigated to estimate the asymptotic behaviour of stochastic processes with timed continuous Petri nets. The contribution of this paper is to point out the limits of the fluidification in the context of the stochastic steady state approximation. Unfortunately, the asymptotic mean marking of stochastic and continuous Petri nets with same structure and same initial marking are mainly often different. This paper shows that this difficulty is related to the partition in regions of the reachability state space and the existence of critical region

Fluid-flow solutions in PEPA to the state space explosion problem

Achieving the appropriate performance requirements for computer-communication systems is as important as the correctness of the end-result. This is particularly difficult in the case of massively parallel computer systems such as the clusters of PCs behind the likes of Google and peer-to-peer filesharing networks such as Bittorrent. Measuring the performance of such systems using a mathematical model is invariably computationally intensive. Formal modelling techniques make possible the derivation of such performance measures but currently suffer from the state-space explosion problem, that is, models become intractably large even for systems of apparently modest complexity. This work develops a novel class of techniques aimed at addressing this problem by approximating a representation of massive state spaces as more computationally-tractable real variables (fluid-flow analysis)

Petri Nets Validation of Markovian Models of Emergency Department Arrivals

International audienceModeling of hospital’s Emergency Departments (ED) is vital for optimisation of health services offered to patients that shows up at an ED requiring treatments with different level of emergency. In this paper we present a modeling study whose contribution is twofold: first, based on a dataset relative to the ED of an Italian hospital, we derive different kinds of Markovian models capable to reproduce, at different extents, the statistical character of dataset arrivals; second, we validate the derived arrivals model by interfacing it with a Petri net model of the services an ED patient undergoes. The empirical assessment of a few key performance indicators allowed us to validate some of the derived arrival process model, thus confirming that they can be used for predicting the performance of an ED

Computing Battery Lifetime Distributions

The usage of mobile devices like cell phones, navigation systems, or laptop computers, is limited by the lifetime of the included batteries. This lifetime depends naturally on the rate at which energy is consumed, however, it also depends on the usage pattern of the battery. Continuous drawing of a high current results in an excessive drop of residual capacity. However, during \ud intervals with no or very small currents, batteries do recover to a certain extend. We model this complex behaviour with an inhomogeneous Markov reward model, following the approach of the so-called Kinetic battery Model (KiBaM). \ud The state-dependent reward rates thereby correspond to the power consumption of the attached device and to the available charge, respectively. We develop a tailored numerical algorithm for the computation of the distribution of the consumed energy and show how different workload patterns influence the overall lifetime of a battery

Scalable Performance Analysis of Massively Parallel Stochastic Systems

The accurate performance analysis of large-scale computer and communication systems is directly inhibited by an exponential growth in the state-space of the underlying Markovian performance model. This is particularly true when considering massively-parallel architectures such as cloud or grid computing infrastructures. Nevertheless, an ability to extract quantitative performance measures such as passage-time distributions from performance models of these systems is critical for providers of these services. Indeed, without such an ability, they remain unable to offer realistic end-to-end service level agreements (SLAs) which they can have any confidence of honouring. Additionally, this must be possible in a short enough period of time to allow many different parameter combinations in a complex system to be tested. If we can achieve this rapid performance analysis goal, it will enable service providers and engineers to determine the cost-optimal behaviour which satisfies the SLAs. In this thesis, we develop a scalable performance analysis framework for the grouped PEPA stochastic process algebra. Our approach is based on the approximation of key model quantities such as means and variances by tractable systems of ordinary differential equations (ODEs). Crucially, the size of these systems of ODEs is independent of the number of interacting entities within the model, making these analysis techniques extremely scalable. The reliability of our approach is directly supported by convergence results and, in some cases, explicit error bounds. We focus on extracting passage-time measures from performance models since these are very commonly the language in which a service level agreement is phrased. We design scalable analysis techniques which can handle passages defined both in terms of entire component populations as well as individual or tagged members of a large population. A precise and straightforward specification of a passage-time service level agreement is as important to the performance engineering process as its evaluation. This is especially true of large and complex models of industrial-scale systems. To address this, we introduce the unified stochastic probe framework. Unified stochastic probes are used to generate a model augmentation which exposes explicitly the SLA measure of interest to the analysis toolkit. In this thesis, we deploy these probes to define many detailed and derived performance measures that can be automatically and directly analysed using rapid ODE techniques. In this way, we tackle applicable problems at many levels of the performance engineering process: from specification and model representation to efficient and scalable analysis

Approximate performability and dependability analysis using generalized stochastic Petri Nets

Since current day fault-tolerant and distributed computer and communication systems tend to be large and complex, their corresponding performability models will suffer from the same characteristics. Therefore, calculating performability measures from these models is a difficult and time-consuming task.\ud \ud To alleviate the largeness and complexity problem to some extent we use generalized stochastic Petri nets to describe to models and to automatically generate the underlying Markov reward models. Still however, many models cannot be solved with the current numerical techniques, although they are conveniently and often compactly described.\ud \ud In this paper we discuss two heuristic state space truncation techniques that allow us to obtain very good approximations for the steady-state performability while only assessing a few percent of the states of the untruncated model. For a class of reversible models we derive explicit lower and upper bounds on the exact steady-state performability. For a much wider class of models a truncation theorem exists that allows one to obtain bounds for the error made in the truncation. We discuss this theorem in the context of approximate performability models and comment on its applicability. For all the proposed truncation techniques we present examples showing their usefulness

On Zone-Based Analysis of Duration Probabilistic Automata

We propose an extension of the zone-based algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than set-theoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuously-distributed durations. For this model we develop an extension of the zone-based forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of cyclic DPA).Comment: In Proceedings INFINITY 2010, arXiv:1010.611

Methodologies synthesis

This deliverable deals with the modelling and analysis of interdependencies between critical infrastructures, focussing attention on two interdependent infrastructures studied in the context of CRUTIAL: the electric power infrastructure and the information infrastructures supporting management, control and maintenance functionality. The main objectives are: 1) investigate the main challenges to be addressed for the analysis and modelling of interdependencies, 2) review the modelling methodologies and tools that can be used to address these challenges and support the evaluation of the impact of interdependencies on the dependability and resilience of the service delivered to the users, and 3) present the preliminary directions investigated so far by the CRUTIAL consortium for describing and modelling interdependencies