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SUMMARY:Nonparametric inference for networks of queues - Cornelia Wichelha
 us\, Universität Heidelberg
DTSTART:20090206T160000Z
DTEND:20090206T170000Z
UID:TALK16636@talks.cam.ac.uk
CONTACT:8419
DESCRIPTION:Abstract: Stochastic networks are systems of nodes which inter
 act due\nto moving customers. Typical application fields are telecommunica
 tion\nsystems\, the internet as well as systems of neurons and population\
 nmodels. For applications statistical inference of the service time\ndistr
 ibutions based on incomplete observations of the systems is of\ngreat impo
 rtance in order to classify the performance behavior. For\nexample\, a uni
 modal service time density shows a homogeneous service\nbehavior whereas a
  bimodal density may indicate that there are two\ndistinct customer popula
 tions or breakdowns of the server. In the\nstatistical literature there ar
 e up to now only results for single\nnode systems and moreover\, for the m
 ost part the analysis is done in\ncase of exponential distributed arrival 
 times only. With this talk we\ntry to close this gap and present two diffe
 rent approaches for a\nstatistical analysis study of general open networks
  of queues. We\nassume that at each node we observe the external input pro
 cess and the\nexternal departure process of customers. Our aim is to estim
 ate the\nservice time distributions at the nodes as well as the routing\np
 robabilities according to which customers move in the network. In the\nfir
 st approach the arrival processes are general point processes and\nthe ana
 lysis is based on spectral analysis methods for multivariate\npoint proces
 ses. We show consistency and asymptotic normality for our\nestimators.  In
  the second approach we deal with Poisson processes as\narrival processes 
 and construct estimators for the service time\ndistribution functions whic
 h converge uniformly. The talk is based on\njoint work with Susan Pitts an
 d Michael Schmälzle.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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