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UID:www.tcs.tifr.res.in/event/1582
DTSTAMP:20250714T043955Z
SUMMARY:Mixing Times for Countable State Markov Chains: A case study of the
  Erlang-C queue
DESCRIPTION:Speaker: Siva Theja Maguluri (Georgia Institute of Technology)\
 n\nAbstract: \nLast few years have seen rapid developments in the mathemat
 ical tools for studying mixing times of Markov chains. However\, most of t
 he focus has been on finite-state Markov chains. Several engineering probl
 ems involve study of countable state Markov chains. Most popular examples 
 are queueing systems that are used to model various resource allocation pr
 oblems in networks\, data centers\, ride-hailing etc. In this work\, we fo
 cus on the Erlang-C system (also known as M/M/n queue)\, and bound the Chi
 -square distance between the finite time queue length distribution and the
  stationary distribution for a finite number of servers. We then use these
  bounds to study the behavior in the many-server heavy-traffic asymptotic 
 regimes. The Erlang-C model exhibits a phase transition at the so-called H
 alfin-Whitt regime. We show that our mixing rate matches the limiting beha
 vior in the Super-Halfin-Whitt regime\, and matches up to a constant facto
 r in the Sub-Halfin-Whitt regime.We obtain these results using the Lyapuno
 v-Poincaré approach\, where we first carefully design a Lyapunov function
  to obtain a negative drift outside a finite set. Within the finite set\, 
 we develop different strategies depending on the properties of the finite 
 set to get a handle on the mixing behavior via a local Poincaré inequalit
 y. A key aspect of our methodological contribution is in obtaining tight g
 uarantees in these two regions\, which when combined give us tight mixing 
 time bounds. We believe that this approach is of independent interest for 
 studying mixing in reversible countable-state Markov chains more generally
 \, and will serve as a stepping stone towards understanding the transient 
 behavior of more general queueing systems.\nShort Bio:Siva Theja Maguluri 
 is Fouts Family Early Career Professor and an Associate Professor in the H
 . Milton Stewart School of Industrial and Systems Engineering at Georgia T
 ech. He obtained his Ph.D. and MS in ECE as well as MS in Applied Math fro
 m UIUC\, and B.Tech in Electrical Engineering from IIT Madras. His researc
 h interests span the areas of Control\, Optimization\, Algorithms and Appl
 ied Probability. In particular\, he works on Reinforcement Learning theory
 \, scheduling\, resource allocation and revenue optimization problems that
  arise in a variety of systems. His research and teaching are recognized t
 hrough several awards including the  “Best Publication in Applied P
 robability award\, NSF CAREER award\, second place award at INFORMS JFIG b
 est paper competition\, Student best paper award at IFIP Performance\, CTL
 /BP Junior Faculty Teaching Excellence Award\, and “Student Recognit
 ion of Excellence in Teaching: Class of 1934 CIOS Award.\n \n
URL:https://www.tcs.tifr.res.in/web/events/1582
DTSTART;TZID=Asia/Kolkata:20250714T110000
DTEND;TZID=Asia/Kolkata:20250714T120000
LOCATION:A-201 (STCS Seminar Room)
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