19,729 research outputs found
Critically loaded multi-server queues with abandonments, retrials, and time-varying parameters
In this paper, we consider modeling time-dependent multi-server queues that
include abandonments and retrials. For the performance analysis of those, fluid
and diffusion models called "strong approximations" have been widely used in
the literature. Although they are proven to be asymptotically exact, their
effectiveness as approximations in critically loaded regimes needs to be
investigated. To that end, we find that existing fluid and diffusion
approximations might be either inaccurate under simplifying assumptions or
computationally intractable. To address that concern, this paper focuses on
developing a methodology by adjusting the fluid and diffusion models so that
they significantly improve the estimation accuracy. We illustrate the accuracy
of our adjusted models by performing a number of numerical experiments
Many-server queues with customer abandonment: numerical analysis of their diffusion models
We use multidimensional diffusion processes to approximate the dynamics of a
queue served by many parallel servers. The queue is served in the
first-in-first-out (FIFO) order and the customers waiting in queue may abandon
the system without service. Two diffusion models are proposed in this paper.
They differ in how the patience time distribution is built into them. The first
diffusion model uses the patience time density at zero and the second one uses
the entire patience time distribution. To analyze these diffusion models, we
develop a numerical algorithm for computing the stationary distribution of such
a diffusion process. A crucial part of the algorithm is to choose an
appropriate reference density. Using a conjecture on the tail behavior of a
limit queue length process, we propose a systematic approach to constructing a
reference density. With the proposed reference density, the algorithm is shown
to converge quickly in numerical experiments. These experiments also show that
the diffusion models are good approximations for many-server queues, sometimes
for queues with as few as twenty servers
Deterministic Sampling and Range Counting in Geometric Data Streams
We present memory-efficient deterministic algorithms for constructing
epsilon-nets and epsilon-approximations of streams of geometric data. Unlike
probabilistic approaches, these deterministic samples provide guaranteed bounds
on their approximation factors. We show how our deterministic samples can be
used to answer approximate online iceberg geometric queries on data streams. We
use these techniques to approximate several robust statistics of geometric data
streams, including Tukey depth, simplicial depth, regression depth, the
Thiel-Sen estimator, and the least median of squares. Our algorithms use only a
polylogarithmic amount of memory, provided the desired approximation factors
are inverse-polylogarithmic. We also include a lower bound for non-iceberg
geometric queries.Comment: 12 pages, 1 figur
Discrete Approximations of Metric Measure Spaces of Controlled Geometry
We find a necessary and sufficient condition for a doubling metric space to
carry a (1,p)-Poincare inequality. The condition involves discretizations of
the metric space and Poincare inequalities on graphs.Comment: 23 Page
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