785 research outputs found
Queue Length Asymptotics for Generalized Max-Weight Scheduling in the presence of Heavy-Tailed Traffic
We investigate the asymptotic behavior of the steady-state queue length
distribution under generalized max-weight scheduling in the presence of
heavy-tailed traffic. We consider a system consisting of two parallel queues,
served by a single server. One of the queues receives heavy-tailed traffic, and
the other receives light-tailed traffic. We study the class of throughput
optimal max-weight-alpha scheduling policies, and derive an exact asymptotic
characterization of the steady-state queue length distributions. In particular,
we show that the tail of the light queue distribution is heavier than a
power-law curve, whose tail coefficient we obtain explicitly. Our asymptotic
characterization also contains an intuitively surprising result - the
celebrated max-weight scheduling policy leads to the worst possible tail of the
light queue distribution, among all non-idling policies. Motivated by the above
negative result regarding the max-weight-alpha policy, we analyze a
log-max-weight (LMW) scheduling policy. We show that the LMW policy guarantees
an exponentially decaying light queue tail, while still being throughput
optimal
The pseudo-self-similar traffic model: application and validation
Since the early 1990¿s, a variety of studies has shown that network traffic, both for local- and wide-area networks, has self-similar properties. This led to new approaches in network traffic modelling because most traditional traffic approaches result in the underestimation of performance measures of interest. Instead of developing completely new traffic models, a number of researchers have proposed to adapt traditional traffic modelling approaches to incorporate aspects of self-similarity. The motivation for doing so is the hope to be able to reuse techniques and tools that have been developed in the past and with which experience has been gained. One such approach for a traffic model that incorporates aspects of self-similarity is the so-called pseudo self-similar traffic model. This model is appealing, as it is easy to understand and easily embedded in Markovian performance evaluation studies. In applying this model in a number of cases, we have perceived various problems which we initially thought were particular to these specific cases. However, we recently have been able to show that these problems are fundamental to the pseudo self-similar traffic model. In this paper we review the pseudo self-similar traffic model and discuss its fundamental shortcomings. As far as we know, this is the first paper that discusses these shortcomings formally. We also report on ongoing work to overcome some of these problems
A queueing theory description of fat-tailed price returns in imperfect financial markets
In a financial market, for agents with long investment horizons or at times
of severe market stress, it is often changes in the asset price that act as the
trigger for transactions or shifts in investment position. This suggests the
use of price thresholds to simulate agent behavior over much longer timescales
than are currently used in models of order-books.
We show that many phenomena, routinely ignored in efficient market theory,
can be systematically introduced into an otherwise efficient market, resulting
in models that robustly replicate the most important stylized facts.
We then demonstrate a close link between such threshold models and queueing
theory, with large price changes corresponding to the busy periods of a
single-server queue. The distribution of the busy periods is known to have
excess kurtosis and non-exponential decay under various assumptions on the
queue parameters. Such an approach may prove useful in the development of
mathematical models for rapid deleveraging and panics in financial markets, and
the stress-testing of financial institutions
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