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UID:6@lincs.fr
DTSTART;TZID=Europe/Paris:20170222T140000
DTEND;TZID=Europe/Paris:20170222T150000
DTSTAMP:20170329T133112Z
URL:https://www.lincs.fr/events/more-info-coming/
SUMMARY:Insensitivity of Loss Systems under Randomized SQ(d) Algorithms
DESCRIPTION:\n\n\nAbstract:\nIn many applications such as cloud computing\,
 managing server farm resources etc. an incoming task or job has to be
 matched with an appropriate server in order to minimise the latency
 associated with the processing. Ideally the best choice would be to match a
 job to the fastest available server. However when there are thousands of
 servers obtaining the information on server tasks is expensive. Pioneered
 in the 1990's the idea of randomised sampling of a few servers was proposed
 by Vvedenskaya and Dobrushin in Russia and Mitzmenmacher in the US and
 popularised as the "power of two" schemes which basically means that
 sampling two servers randomly and sending the job to the "better" server
 (i.e. with the shortest queue\, or most resources) provides most of the
 benefits of sampling all the servers.In the talk I will discuss
 multi-server loss models under power-of-d routing scheme when service time
 distributions are general with finite mean. Previous works on these models
 assume that the service times are exponentially distributed and
 insensitivity was suggested through simulations. Showing insensitivity to
 service time distributions has remained an open problem. We address this
 problem by considering service time distributions as Mixed-Erlang
 distributions that are dense in the class of general distributions on (0\,
 infty). We derive the mean field equations (MFE) of the empirical
 distributions for the system and establish the existence and uniqueness of
 the fixed point of the MFE. Furthermore we show that the fixed point of the
 MFE corresponds to the fixed point obtained from the MFE corresponding to a
 system with exponential service times showing that the fixed point is
 insensitive to the distribution. We provide numerical evidence of the
 global asymptotic stability of the fixed point\, which would then imply
 that the fixed point is indeed the stationary distribution. We conclude
 with a brief discussion of the case of the MFE with general service times
 showing that the MFE is now characterized by a pde whose stationary point
 coincides with the fixed point in the case with exponential service
 times.The techniques developed in this paper are applicable to study mean
 field limits for Markov processes on general state spaces and insensitivity
 properties of other queueing models.\n\n\nBiography:\nThe speaker was
 educated at the Indian Institute of Technology\, Bombay (B.Tech\, 1977)\,
 Imperial College\, London (MSc\, DIC\, 1978) and obtained his PhD under A.
 V. Balakrishnan at UCLA in 1983.He is currently a University Research Chair
 Professor in the Dept. of ECE at the University of Waterloo\,Ont.\, Canada
 where he has been since September 2004. Prior to this he was Professor of
 ECE at PurdueUniversity\, West Lafayette\, USA. He is a D.J. Gandhi
 Distinguished Visiting Professor at the Indian Institute of Technology\,
 Bombay. He is a Fellow of the IEEE and the Royal Statistical Society. He is
 a recipient of the Best Paper Awards at INFOCOM 2006\, the International
 Teletraffic Congress 2015\, Performance 2015\, and was runner-up for the
 Best Paper Award at INFOCOM 1998.His research interests are in modeling\,
 control\, and performance analysis of both wireline and wirelessnetworks\,
 and in applied probability and stochastic analysis with applications to
 queueing\, filtering\, and optimization.\n\n\n
CATEGORIES:Seminars,Youtube
LOCATION:LINCS Meeting Room 40\, 23\, avenue d'Italie\, Paris\, 75013\,
 France
GEO:48.8283983;2.3568972000000485
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=23\, avenue d'Italie\,
 Paris\, 75013\, France;X-APPLE-RADIUS=100;X-TITLE=LINCS Meeting Room
 40:geo:48.8283983,2.3568972000000485
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TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
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DTSTART:20161030T020000
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
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