VALUETOOLS 2008
INTER-PERF 2008WNS2 2008MODENETS 2008GAMECOMM 2008SMCTOOLS 2008

    VALUETOOLS

    3rd International ICST Conference on Performance Evaluation Methodologies and Tools

    Welcome to Athens! On behalf of the whole organizing team, we wholeheartedly welcome you to the third installment of Valuetools, Valuetools 2008. The first two installments took place in Pisa (2006) and Nantes (2007). So, again, the conference is taking place in a city of rich cultural heritage. We…

    Welcome to Athens! On behalf of the whole organizing team, we wholeheartedly welcome you to the third installment of Valuetools, Valuetools 2008. The first two installments took place in Pisa (2006) and Nantes (2007). So, again, the conference is taking place in a city of rich cultural heritage. We look forward to emulating the previous two installments also in terms of their scientific success. The motivation behind Valuetools is the observation that an impressive range of methodologies and tools have been developed recently for the purpose of performance evaluation, across many disparate research fields. Valuetools is meant to be a forum that will allow researchers to compare and debate the full range of these tools and methodologies, and in addition promote the interdisciplinary flow of technical information.

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    Editor(s): John Baras and Costas Courcoubetis
    Publisher
    ICST
    ISBN
    978-963-9799-31-8
    Conference dates
    20th–24th Oct 2008
    Location
    Athens, Greece
    Appeared in EUDL
    29th Nov 2011
    Appears in
    ACM Digital Library

    Copyright © 2011–2013 ICST

    • Stochastic representations of anomalous diffusion processes: subordination approach

      Research Article in 3rd International ICST Conference on Performance Evaluation Methodologies and Tools

      Marcin Magdziarz, Aleksander Weron

      Abstract
      We introduce a subordination-based approach to modeling of anomalous diffusion processes in time-dependent force fields. Using the concept of inverse subordinators and the theory of Levy processes, w…We introduce a subordination-based approach to modeling of anomalous diffusion processes in time-dependent force fields. Using the concept of inverse subordinators and the theory of Levy processes, we construct rigorously a stochastic process, which corresponds to the fractional Fokker-Planck equation with time-dependent force. Our model provides good physical insight through the trajectories. Moreover, it allows to study different anomalous diffusion processes both analytically and numerically.
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    • Field-induced dispersion in subdiffusion

      Research Article in 3rd International ICST Conference on Performance Evaluation Methodologies and Tools

      Joseph Klafter, Igor M. Sokolov

      Abstract
      We discuss the response of continuous-time random walks to an oscillating external field within the generalized master equation approach. We concentrate on the time dependence of the two first moment…We discuss the response of continuous-time random walks to an oscillating external field within the generalized master equation approach. We concentrate on the time dependence of the two first moments of the walker's displacement. We show that for power-law waiting-time distributions with 0<α<1 corresponding to a semi-Markovian situation showing nonstationarity, the mean particle position tends to a constant; namely, the response to the external perturbation dies out. On the other hand, the oscillating field leads to a new additional contribution to the dispersion of the particle position, proportional to the square of its amplitude and growing with time. These new effects, amenable to experimental observation, result directly from the nonstationary property of the system.
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    • Heavy tailed Lévy random motions in super- and subharmonic potential wells

      Research Article in 3rd International ICST Conference on Performance Evaluation Methodologies and Tools

      Alexei Chechkin

      Abstract
      The Lévy motions (LMs) are random processes with stationary increments having a long-tailed stable probability distribution with divergent variance. As such, LMs are a natural generalization of the B…The Lévy motions (LMs) are random processes with stationary increments having a long-tailed stable probability distribution with divergent variance. As such, LMs are a natural generalization of the Brownian motion ensuing from the generalized central limit theorem. Despite their broad field of applications, LMs are far from being completely understood. Here, we consider ordinary LMs, that is Markovian processes with independent increments, subjected to an external non-linear potential force. The behavior is different for the steep superharmonic potential wells with the index c < 2 and for the gently sloping subharmonic ones, c < 2. For the superharmonic one-well potentials we found that the stationary probability density function (PDF) features a distinct bimodal shape and decays with the power-law tails which are steep enough to give rise to a finite variance, in contrast to a "free" LM. During the relaxation to stationarity the PDF exhibits unimodal-bimodal time bifurcations. In anharmonic one-well potentials we observe unimodal-bimodal bifurcations of the stationary PDF. For subharmonic one-well potentials the stationary solution does not exist if the Lévy index is smaller than the index of the well.

      For the two-well potentials we found that the mean escape time is inversely proportional to the intensity of the Lévy motion, in sharp contrast with the known exponential behavior for the Brownian motion. Furthermore, we consider the phenomenon of generating directed current by the LM in periodic asymmetric potential and demonstrate how direction and magnitude of the current can be manipulated by changing the asymmetry of the LM and the potential asymmetry. These properties of the LMs are discussed on the basis of analytical and numerical solutions of the corresponding stochastic nonlinear differential equations as well as the kinetic equations with partial derivatives of fractional order.
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    • A diffusion regime with nondegenerate slowdown

      Research Article in 3rd International ICST Conference on Performance Evaluation Methodologies and Tools

      Rami Atar

      Abstract
      In both the conventional and the Halfin-Whitt heavy traffic diffusion regimes, the slowdown (defined as the sojourn time/service time ratio) experienced by a typical customer, degenerates in the limi…In both the conventional and the Halfin-Whitt heavy traffic diffusion regimes, the slowdown (defined as the sojourn time/service time ratio) experienced by a typical customer, degenerates in the limit, to infinity and 1, respectively. In practice, however, it often occurs that delay and service time are comparable. We study a diffusion regime in which delay and service time are of the same order of magnitude. In a setting with many heterogeneous, exponential servers, (possibly with abandonment), we find the limiting joint law of these two processes.
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    • Bounds and moments for stationary delay in GI/GI/s queue

      Research Article in 3rd International ICST Conference on Performance Evaluation Methodologies and Tools

      Dmitry Korshunov

      Abstract
      Only a little is known about the tail properties of the distribution of the stationary waiting time, or delay, in multi-server queues with the FCFS service discipline, in the contrast with the one-di…Only a little is known about the tail properties of the distribution of the stationary waiting time, or delay, in multi-server queues with the FCFS service discipline, in the contrast with the one-dimensional case. In the GI/G/1 queue, the γ-th moment of the stationary delay is finite if and only if the (γ+1)-st moment of the service time distribution is finite - this goes back to Kiefer and Wolfowitz. Under subexponential-type conditions, the tail asymptotics for the stationary delay are also known; they follow the tail of the distribution of the residual service time. Recent results (W. Whitt, A. Scheller-Wolf and K. Sigman, A. Scheller-Wolf and R. Vesilo, etc.) suggest that, in the multi-server queue, the tail distribution of the stationary delay is not always as heavy as that of the residual service time, and the conditions for the finiteness of the γ-th moment differ from those in the single server queue. In our QUESTA paper (2006), we studied the two-server queue GI/GI/2 and obtained sharp asymptotics for the tail distribution of the stationary delay assuming the subexponentiality of the distribution of the residual service time. In particular, these asymptotics differ for different regions of the traffic load &rho. Now we present upper and lower bounds for the distribution tail of the stationary delay in the GI/GI/s queue, for any s ≥2. The derivation of these bounds requires new ideas and techniques. In particular, in the case of (intermediate) regularly varying service times these bounds are exact up to a constant. These bounds again depend on the traffic load. They also allow obtaining conditions for the existence of power moments, which are both necessary and sufficient.
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