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SUMMARY:Nonparametric inference for networks of queues - Cornelia Wichelha
 us\, Heidelberg university\, Germany.
DTSTART:20090206T160000Z
DTEND:20090206T170000Z
UID:TALK15640@talks.cam.ac.uk
CONTACT:Neil Walton
DESCRIPTION:Stochastic networks are systems of nodes which interact due to
  moving customers. Typical application fields are telecommunication system
 s\, the internet as well as systems of neurons and population models. For 
 applications statistical inference of the service time distributions based
  on incomplete observations of the systems is of great importance in order
  to classify the performance behavior. For example\, a unimodal service ti
 me density shows a homogeneous service behavior whereas a bimodal density 
 may indicate that there are two distinct customer populations or breakdown
 s of the server. In the statistical literature there are up to now only re
 sults for single node systems and moreover\, for the most part the analysi
 s is done in case of exponential distributed arrival times only. With this
  talk we try to close this gap and present two different approaches for a 
 statistical analysis study of general open networks of queues. We assume t
 hat at each node we observe the external input process and the external de
 parture process of customers. Our aim is to estimate the service time dist
 ributions at the nodes as well as the routing probabilities according to w
 hich customers move in the network. In the first approach the arrival proc
 esses are general point processes and the analysis is based on spectral an
 alysis methods for multivariate point processes. We show consistency and a
 symptotic normality for our estimators. In the second approach we deal wit
 h Poisson processes as arrival processes and construct estimators for the 
 service time distribution functions which converge uniformly. The talk is 
 based on joint work with Susan Pitts and Michael Schmälzle.\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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