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UID:www.tcs.tifr.res.in/event/63
DTSTAMP:20230914T125908Z
SUMMARY:Comparison Theorems and the Validity of Heavy Traffic Limit Distrib
 utions for Stochastic Networks
DESCRIPTION:Speaker: Ravi R. Mazumdar\nUniversity of Waterloo\nDepartment o
 f Electrical and Computer Engineering\n200 University Avenue We\n\nAbstrac
 t: \nThe issue of stability of stochastic networks continues to be one of 
 the central issues in applications along with the computation of the stati
 onary distribution. Under heavy traffic conditions\, in recent works by Ga
 marnik and Zeevi (AAP'06) and Budhiraja and Lee (MOR'09) they showed that 
 the steady state limits of networks with i.i.d inputs that satisfy a FCLT 
 converge to the corresponding stationary distribution of the limit SRBM (S
 emi-martingale Reflecting Brownian Motion) or in other words the large tim
 e limit and the scaling limit can be interchanged. Their arguments were ba
 sed on Lyapunov techniques.\n\nIn this talk we consider networks with Levy
  inputs and show that the corresponding interchange result holds via direc
 t arguments without the need for Lyapunov techniques. Indeed the results f
 ollow in a direct manner from some well known results on stochastic networ
 ks with Levy inputs due to Kella and Whitt.\n\nIn the second part of the t
 alk I will show some new comparison theorems for stochastic networks that 
 yield useful results for showing conditions when monotonicity will hold. W
 e conclude with a generalization of these results to general reflected dif
 fusions with jumps even allowing for state-dependent reflections when the 
 continuity of the Skorohod map cannot be shown (joint work with Dr. Franci
 sco Piera (University of Chile) and Jean-Paul Haddad (Waterloo)).\n\nBio: 
 The speaker was educated at the Indian Institute of Technology\, Bombay (B
 .Tech\, 1977)\, Imperial College\, London (MSc\, DIC\, 1978) and UCLA (PhD
 \, 1983). He is currently a University Research Chair Professor in the Dep
 t. 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 Purdue Univ
 ersity\, West Lafayette\, USA where he continues to be an Adjunct Professo
 r. He is a Fellow of the IEEE and the Royal Statistical Society. He is a r
 ecipient of INFOCOM 2006 Best Paper Award and was runner-up for the Best P
 aper Award at INFOCOM 1998. He has served as an editor of the IEEE/ACM Tra
 ns on Networking (2004-09) and as guest editor for a number of special iss
 ues of networking and applied probability related journals. He is also the
  author of a forthcoming monograph on performance modeling statistical mul
 tiplexing in networks to be published by Morgan and Claypool in early 2010
 . His research interests are in modeling\, control\, and performance analy
 sis of both wireline and wireless networks\, and in applied probability an
 d stochastic analysis with applications to queueing\, filtering\, and cont
 rol.\n
URL:https://www.tcs.tifr.res.in/web/events/63
DTSTART;VALUE=DATE:20100125
LOCATION:AG-80
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