Evaluating fluid semantics for passive stochastic process algebra cooperation

Fluid modelling is a next-generation technique for analysing massive performance models. Passive cooperation is a popular cooperation mechanism frequently used by performance engineers. Therefore having an accurate translation of passive cooperation into a fluid model is of direct practical application. We compare different existing styles of fluid model translation of passive cooperation in a stochastic process algebra and show how the previous model can be improved upon significantly. We evaluate the new passive cooperation fluid semantics and show that the first-order fluid model is a good approximation to the dynamics of the underlying continuous-time Markov chain. We show that in a family of possible translations to the fluid model, there is an optimal translation which can be expected to introduce least error. Finally, we use these new techniques to show how the scalability of a passively-cooperating distributed software architecture could be assessed

A new tool for the performance analysis of massively parallel computer systems

We present a new tool, GPA, that can generate key performance measures for very large systems. Based on solving systems of ordinary differential equations (ODEs), this method of performance analysis is far more scalable than stochastic simulation. The GPA tool is the first to produce higher moment analysis from differential equation approximation, which is essential, in many cases, to obtain an accurate performance prediction. We identify so-called switch points as the source of error in the ODE approximation. We investigate the switch point behaviour in several large models and observe that as the scale of the model is increased, in general the ODE performance prediction improves in accuracy. In the case of the variance measure, we are able to justify theoretically that in the limit of model scale, the ODE approximation can be expected to tend to the actual variance of the model

Fluid aggregations for Markovian process algebra

Quantitative analysis by means of discrete-state stochastic processes is hindered by the well-known phenomenon of state-space explosion, whereby the size of the state space may have an exponential growth with the number of objects in the model. When the stochastic process underlies a Markovian process algebra model, this problem may be alleviated by suitable notions of behavioural equivalence that induce lumping at the underlying continuous-time Markov chain, establishing an exact relation between a potentially much smaller aggregated chain and the original one. However, in the modelling of massively distributed computer systems, even aggregated chains may be still too large for efficient numerical analysis. Recently this problem has been addressed by fluid techniques, where the Markov chain is approximated by a system of ordinary differential equations (ODEs) whose size does not depend on the number of the objects in the model. The technique has been primarily applied in the case of massively replicated sequential processes with small local state space sizes. This thesis devises two different approaches that broaden the scope of applicability of efficient fluid approximations. Fluid lumpability applies in the case where objects are composites of simple objects, and aggregates the potentially massive, naively constructed ODE system into one whose size is independent from the number of composites in the model. Similarly to quasi and near lumpability, we introduce approximate fluid lumpability that covers ODE systems which can be aggregated after a small perturbation in the parameters. The technique of spatial aggregation, instead, applies to models whose objects perform a random walk on a two-dimensional lattice. Specifically, it is shown that the underlying ODE system, whose size is proportional to the number of the regions, converges to a system of partial differential equations of constant size as the number of regions goes to infinity. This allows for an efficient analysis of large-scale mobile models in continuous space like ad hoc networks and multi-agent systems

Performance evaluation methodologies and tools : selected papers from VALUETOOLS 2008

International audienceThis Special Issue of Performance Evaluation Journal is a selection of nine high-ranked papers from the third edition of the International Conference on Performance Evaluation Methodologies and Tools (Valuetools'2008) that was held on October 20-24, 2008, in Athens, Greece. The aim of the Valuetools conference series is to enable and strengthen scientific exchange and cooperation between disparate research communities involved in the performance evaluation of computer, communication and service systems, and to promote the interdisciplinary flow of technical information among industry systems designers and researchers. Valuetools'2008 was composed of a general track and four associated workshops: Gamecomm'08 (The 2nd ICST/ACM International Workshop on Game Theory in Communication Networks), SMCTools'08 (The 3rd International Workshop on Tools for solving Structured Markov Chains), Inter-Perf'08 (Workshop on Interdisciplinary Systems Approach in Performance Evaluation and Design of Computer & Communication Systems) and WNS2'08 (The Second Workshop on NS-2). Of the nine papers selected for this special issue, eight came from the conference general track and one from the associated workshop Inter-Perf. All the selected papers received excellent reviews for their conference version. These papers were revised and extended to meet the journal standards, and their journal version was peer-reviewed for this Special Issue by three reviewers. The included papers, whose topics range from queuing theory to wireless networks analysis and control, are: * Yoni Nazarathy and Gideon Weiss. Positive Harris Recurrence and Diffusion Scale Analysis of a Push Pull Queueing Network; - Jonatha Anselmi and Paolo Cremonesi. A New Framework Supporting the Bottleneck Analysis of Multiclass Queueing Networks; - David Raz, Hanoch Levy and Benjamin Avi-Itzhak. Class Treatment in Queueing Systems: Discrimination and Fairness Aspects; - Peter Harrison, Naresh Patel and Soraya Zertal. Response Time Distribution of Flash Memory Accesses; Richard Hayden and Jeremy Bradley. Evaluating Fluid Semantics for Passive Stochastic Process Algebra Cooperation; - Iordanis Koutsopoulos and George Iosifidis. Distributed Resource Allocation Algorithms for Peer-to-peer Networks; - Eitan Altman, Tamer Basar, Francesco De Pelligrini. Optimal Monotone Forwarding Policies in Delay Tolerant Mobile Ad-Hoc Networks; - Philippe Godlewski, Masood Maqbool, Marceau Coupechoux and Jean-Marc Kélif. Analytical Evaluation of Various Frequency Reuse Schemes in Cellular OFDMA Networks; - Eitan Altman, Konstantin Avrachenkov and Andrey Garnaev. Fair Resources Allocation in Wireless Networks in the Presence of a Jammer. Together, these papers indeed represent the breadth of tools available for performance evaluation, as well as their various applications