Statistics/Math Seminar

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Date/Time:Tuesday, 22 Jan 2013 from 4:10 pm to 5:00 pm
Location:Carver 401
Cost:$0
URL:www.stat.iastate.edu
Contact:Jeanette La Grange
Phone:515-294-3440
Channel:College of Liberal Arts and Sciences
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"Markov Modulated Stochastic Networks in Heavy Traffic," Xin Liu, Institute for Mathematics and its Applications, University of Minnesota, St. Paul

Stochastic networks arise as models in various areas including computer systems, telecommunications, manufacturing, finance, and service industry. The networks are often too complex to be analyzed directly and thus one seeks suitable approximate models. One class of such approximations are diffusion models that can be rigorously justified when networks are operating in heavy traffic, i.e.,when the network capacity is roughly balanced with network load. In this talk, some recent study on Markov modulated stochastic networks in heavy traffic will be presented. We first consider generalized Jackson networks with Markov modulated arrival and service rates and routing structure, and develop suitable reduced models using techniques from diffusion approximations and heavy traffic theory. We then develop a comprehensive stability theory for such Markov modulated stochastic networks and their diffusion limit. At last, we study optimal control problems for Markov modulated multiclass single-server queueing systems in heavy traffic, and establish an asymptotically optimal policy which is an "average" cμ rule.