4,406 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 â like large-scale computers, clientâserver architectures, networks â 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
Compositional Performance Modelling with the TIPPtool
Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations
Not Always Sparse: Flooding Time in Partially Connected Mobile Ad Hoc Networks
In this paper we study mobile ad hoc wireless networks using the notion of
evolving connectivity graphs. In such systems, the connectivity changes over
time due to the intermittent contacts of mobile terminals. In particular, we
are interested in studying the expected flooding time when full connectivity
cannot be ensured at each point in time. Even in this case, due to finite
contact times durations, connected components may appear in the connectivity
graph. Hence, this represents the intermediate case between extreme cases of
fully mobile ad hoc networks and fully static ad hoc networks. By using a
generalization of edge-Markovian graphs, we extend the existing models based on
sparse scenarios to this intermediate case and calculate the expected flooding
time. We also propose bounds that have reduced computational complexity.
Finally, numerical results validate our models
Estimating the Probability of a Rare Event Over a Finite Time Horizon
We study an approximation for the zero-variance change of measure to estimate the probability of a rare event in a continuous-time Markov chain. The rare event occurs when the chain reaches a given set of states before some fixed time limit. The jump rates of the chain are expressed as functions of a rarity parameter in a way that the probability of the rare event goes to zero when the rarity parameter goes to zero, and the behavior of our estimators is studied in this asymptotic regime. After giving a general expression for the zero-variance change of measure in this situation, we develop an approximation of it via a power series and show that this approximation provides a bounded relative error when the rarity parameter goes to zero. We illustrate the performance of our approximation on small numerical examples of highly reliableMarkovian systems. We compare it to a previously proposed heuristic that combines forcing with balanced failure biaising. We also exhibit the exact zero-variance change of measure for these examples and compare it with these two approximations
Sensitivity analysis of a branching process evolving on a network with application in epidemiology
We perform an analytical sensitivity analysis for a model of a
continuous-time branching process evolving on a fixed network. This allows us
to determine the relative importance of the model parameters to the growth of
the population on the network. We then apply our results to the early stages of
an influenza-like epidemic spreading among a set of cities connected by air
routes in the United States. We also consider vaccination and analyze the
sensitivity of the total size of the epidemic with respect to the fraction of
vaccinated people. Our analysis shows that the epidemic growth is more
sensitive with respect to transmission rates within cities than travel rates
between cities. More generally, we highlight the fact that branching processes
offer a powerful stochastic modeling tool with analytical formulas for
sensitivity which are easy to use in practice.Comment: 17 pages (30 with SI), Journal of Complex Networks, Feb 201
Versatile Markovian models for networks with asymmetric TCP sources
In this paper we use Stochastic Petri Nets (SPNs) to study the interaction of multiple TCP sources that share one or two buffers, thereby considerably extending earlier work. We first consider two sources sharing a buffer and investigate the consequences of two popular assumptions for the loss process in terms of fairness and link utilization. The results obtained by our model are in agreement with existing analytic models or are closer to results obtained by ns-2 simulations. We then study a network consisting of three sources and two buffers and provide evidence that link sharing is approximately minimum-potential-delay-fair in case of equal round-trip times. \u
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