585 research outputs found
Learning Queuing Networks by Recurrent Neural Networks
It is well known that building analytical performance models in practice is
difficult because it requires a considerable degree of proficiency in the
underlying mathematics. In this paper, we propose a machine-learning approach
to derive performance models from data. We focus on queuing networks, and
crucially exploit a deterministic approximation of their average dynamics in
terms of a compact system of ordinary differential equations. We encode these
equations into a recurrent neural network whose weights can be directly related
to model parameters. This allows for an interpretable structure of the neural
network, which can be trained from system measurements to yield a white-box
parameterized model that can be used for prediction purposes such as what-if
analyses and capacity planning. Using synthetic models as well as a real case
study of a load-balancing system, we show the effectiveness of our technique in
yielding models with high predictive power
Scaling Size and Parameter Spaces in Variability-Aware Software Performance Models (T)
In software performance engineering, what-if scenarios, architecture optimization, capacity planning, run-time adaptation, and uncertainty management of realistic models typically require the evaluation of many instances. Effective analysis is however hindered by two orthogonal sources of complexity. The first is the infamous problem of state space explosion — the analysis of a single model becomes intractable with its size. The second is due to massive parameter spaces to be explored, but such that computations cannot be reused across model instances. In this paper, we efficiently analyze many queuing models with the distinctive feature of more accurately capturing variability and uncertainty of execution rates by incorporating general (i.e., non-exponential) distributions. Applying product-line engineering methods, we consider a family of models generated by a core that evolves into concrete instances by applying simple delta operations affecting both the topology and the model's parameters. State explosion is tackled by turning to a scalable approximation based on ordinary differential equations. The entire model space is analyzed in a family-based fashion, i.e., at once using an efficient symbolic solution of a super-model that subsumes every concrete instance. Extensive numerical tests show that this is orders of magnitude faster than a naive instance-by-instance analysis
Scalable analysis of stochastic process algebra models
The performance modelling of large-scale systems using discrete-state approaches is
fundamentally hampered by the well-known problem of state-space explosion, which
causes exponential growth of the reachable state space as a function of the number
of the components which constitute the model. Because they are mapped onto
continuous-time Markov chains (CTMCs), models described in the stochastic process
algebra PEPA are no exception. This thesis presents a deterministic continuous-state
semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying
mathematics for the performance evaluation. This is suitable for models consisting
of large numbers of replicated components, as the ODE problem size is insensitive
to the actual population levels of the system under study. Furthermore, the ODE is
given an interpretation as the fluid limit of a properly defined CTMC model when the
initial population levels go to infinity. This framework allows the use of existing results
which give error bounds to assess the quality of the differential approximation. The
computation of performance indices such as throughput, utilisation, and average response
time are interpreted deterministically as functions of the ODE solution and are
related to corresponding reward structures in the Markovian setting.
The differential interpretation of PEPA provides a framework that is conceptually
analogous to established approximation methods in queueing networks based on meanvalue
analysis, as both approaches aim at reducing the computational cost of the analysis
by providing estimates for the expected values of the performance metrics of interest.
The relationship between these two techniques is examined in more detail in
a comparison between PEPA and the Layered Queueing Network (LQN) model. General
patterns of translation of LQN elements into corresponding PEPA components are
applied to a substantial case study of a distributed computer system. This model is
analysed using stochastic simulation to gauge the soundness of the translation. Furthermore,
it is subjected to a series of numerical tests to compare execution runtimes
and accuracy of the PEPA differential analysis against the LQN mean-value approximation
method.
Finally, this thesis discusses the major elements concerning the development of a
software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment
for PEPA, including modules for static analysis, explicit state-space exploration,
numerical solution of the steady-state equilibrium of the Markov chain, stochastic
simulation, the differential analysis approach herein presented, and a graphical
framework for model editing and visualisation of performance evaluation results
Mechanizing a Process Algebra for Network Protocols
This paper presents the mechanization of a process algebra for Mobile Ad hoc
Networks and Wireless Mesh Networks, and the development of a compositional
framework for proving invariant properties. Mechanizing the core process
algebra in Isabelle/HOL is relatively standard, but its layered structure
necessitates special treatment. The control states of reactive processes, such
as nodes in a network, are modelled by terms of the process algebra. We propose
a technique based on these terms to streamline proofs of inductive invariance.
This is not sufficient, however, to state and prove invariants that relate
states across multiple processes (entire networks). To this end, we propose a
novel compositional technique for lifting global invariants stated at the level
of individual nodes to networks of nodes.Comment: This paper is an extended version of arXiv:1407.3519. The
Isabelle/HOL source files, and a full proof document, are available in the
Archive of Formal Proofs, at http://afp.sourceforge.net/entries/AWN.shtm
Applying Mean-field Approximation to Continuous Time Markov Chains
The mean-field analysis technique is used to perform analysis of a systems with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agents populations evolve by means of a system of differential equations, (2) finding the emergent
deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour either by relying on simulation or by using logics. Depending on the system under analysis, performing these steps may become challenging. Often, modifications
of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique,
moving to cases where additional steps have to be used, such as systems with local communication. Finally we illustrate the application of the simulation and
uid model checking analysis techniques
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