26,450 research outputs found
Process algebra for performance evaluation
This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions
Construction and Verification of Performance and Reliability Models
Over the last two decades formal methods have been extended towards performance and reliability evaluation. This paper tries to provide a rather intuitive explanation of the basic concepts and features in this area.
Instead of striving for mathematical rigour, the intention is to give an illustrative introduction to the basics of stochastic models, to stochastic modelling using process algebra, and to model checking as a technique to analyse stochastic models
Hybrid performance modelling of opportunistic networks
We demonstrate the modelling of opportunistic networks using the process
algebra stochastic HYPE. Network traffic is modelled as continuous flows,
contact between nodes in the network is modelled stochastically, and
instantaneous decisions are modelled as discrete events. Our model describes a
network of stationary video sensors with a mobile ferry which collects data
from the sensors and delivers it to the base station. We consider different
mobility models and different buffer sizes for the ferries. This case study
illustrates the flexibility and expressive power of stochastic HYPE. We also
discuss the software that enables us to describe stochastic HYPE models and
simulate them.Comment: In Proceedings QAPL 2012, arXiv:1207.055
Patch-based Hybrid Modelling of Spatially Distributed Systems by Using Stochastic HYPE - ZebraNet as an Example
Individual-based hybrid modelling of spatially distributed systems is usually
expensive. Here, we consider a hybrid system in which mobile agents spread over
the space and interact with each other when in close proximity. An
individual-based model for this system needs to capture the spatial attributes
of every agent and monitor the interaction between each pair of them. As a
result, the cost of simulating this model grows exponentially as the number of
agents increases. For this reason, a patch-based model with more abstraction
but better scalability is advantageous. In a patch-based model, instead of
representing each agent separately, we model the agents in a patch as an
aggregation. This property significantly enhances the scalability of the model.
In this paper, we convert an individual-based model for a spatially distributed
network system for wild-life monitoring, ZebraNet, to a patch-based stochastic
HYPE model with accurate performance evaluation. We show the ease and
expressiveness of stochastic HYPE for patch-based modelling of hybrid systems.
Moreover, a mean-field analytical model is proposed as the fluid flow
approximation of the stochastic HYPE model, which can be used to investigate
the average behaviour of the modelled system over an infinite number of
simulation runs of the stochastic HYPE model.Comment: In Proceedings QAPL 2014, arXiv:1406.156
The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications
The statement of the mean field approximation theorem in the mean field
theory of Markov processes particularly targets the behaviour of population
processes with an unbounded number of agents. However, in most real-world
engineering applications one faces the problem of analysing middle-sized
systems in which the number of agents is bounded. In this paper we build on
previous work in this area and introduce the mean drift. We present the concept
of population processes and the conditions under which the approximation
theorems apply, and then show how the mean drift is derived through a
systematic application of the propagation of chaos. We then use the mean drift
to construct a new set of ordinary differential equations which address the
analysis of population processes with an arbitrary size
Branching processes, the max-plus algebra and network calculus
Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory
A model checker for performance and dependability properties
Markov chains are widely used in the context of
performance and reliability evaluation of systems of various
nature. Model checking of such chains with respect to
a given (branching) temporal logic formula has been proposed
for both the discrete [8] and the continuous time setting
[1], [3]. In this short paper, we describe the prototype
model checker for discrete and continuous-time
Markov chains, where properties are expressed in appropriate
extensions of CTL.We illustrate the general benefits
of this approach and discuss the structure of the tool
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