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CATEGORIES:Optimization and Incentives Seminar
SUMMARY:Nonparametric inference for networks of queues - C
ornelia Wichelhaus\, Heidelberg university\, Germa
ny.
DTSTART;TZID=Europe/London:20090206T160000
DTEND;TZID=Europe/London:20090206T170000
UID:TALK15640AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/15640
DESCRIPTION:Stochastic networks are systems of nodes which int
eract due to moving customers. Typical application
fields are telecommunication systems\, the intern
et as well as systems of neurons and population mo
dels. For applications statistical inference of th
e service time distributions based on incomplete o
bservations of the systems is of great importance
in order to classify the performance behavior. For
example\, a unimodal service time density shows a
homogeneous service behavior whereas a bimodal de
nsity may indicate that there are two distinct cus
tomer populations or breakdowns of the server. In
the statistical literature there are up to now onl
y results for single node systems and moreover\, f
or the most part the analysis is done in case of e
xponential distributed arrival times only. With th
is talk we try to close this gap and present two d
ifferent approaches for a statistical analysis stu
dy of general open networks of queues. We assume t
hat at each node we observe the external input pro
cess and the external departure process of custome
rs. Our aim is to estimate the service time distri
butions at the nodes as well as the routing probab
ilities according to which customers move in the n
etwork. In the first approach the arrival processe
s are general point processes and the analysis is
based on spectral analysis methods for multivariat
e point processes. We show consistency and asympto
tic normality for our estimators. In the second ap
proach we deal with Poisson processes as arrival p
rocesses and construct estimators for the service
time distribution functions which converge uniform
ly. The talk is based on joint work with Susan Pit
ts and Michael SchmÃ¤lzle.\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Neil Walton
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