17,560 research outputs found
Regenerative Simulation for Queueing Networks with Exponential or Heavier Tail Arrival Distributions
Multiclass open queueing networks find wide applications in communication,
computer and fabrication networks. Often one is interested in steady-state
performance measures associated with these networks. Conceptually, under mild
conditions, a regenerative structure exists in multiclass networks, making them
amenable to regenerative simulation for estimating the steady-state performance
measures. However, typically, identification of a regenerative structure in
these networks is difficult. A well known exception is when all the
interarrival times are exponentially distributed, where the instants
corresponding to customer arrivals to an empty network constitute a
regenerative structure. In this paper, we consider networks where the
interarrival times are generally distributed but have exponential or heavier
tails. We show that these distributions can be decomposed into a mixture of
sums of independent random variables such that at least one of the components
is exponentially distributed. This allows an easily implementable embedded
regenerative structure in the Markov process. We show that under mild
conditions on the network primitives, the regenerative mean and standard
deviation estimators are consistent and satisfy a joint central limit theorem
useful for constructing asymptotically valid confidence intervals. We also show
that amongst all such interarrival time decompositions, the one with the
largest mean exponential component minimizes the asymptotic variance of the
standard deviation estimator.Comment: A preliminary version of this paper will appear in Proceedings of
Winter Simulation Conference, Washington, DC, 201
SensibleSleep: A Bayesian Model for Learning Sleep Patterns from Smartphone Events
We propose a Bayesian model for extracting sleep patterns from smartphone
events. Our method is able to identify individuals' daily sleep periods and
their evolution over time, and provides an estimation of the probability of
sleep and wake transitions. The model is fitted to more than 400 participants
from two different datasets, and we verify the results against ground truth
from dedicated armband sleep trackers. We show that the model is able to
produce reliable sleep estimates with an accuracy of 0.89, both at the
individual and at the collective level. Moreover the Bayesian model is able to
quantify uncertainty and encode prior knowledge about sleep patterns. Compared
with existing smartphone-based systems, our method requires only screen on/off
events, and is therefore much less intrusive in terms of privacy and more
battery-efficient
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