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SUMMARY:Control of Stochastic Processing Networks - R. J. Williams (Depart
 ment of Mathematics\, University of California\, San Diego)
DTSTART:20110711T133000Z
DTEND:20110711T143000Z
UID:TALK31476@talks.cam.ac.uk
CONTACT:Elena Yudovina
DESCRIPTION:Stochastic processing networks (SPNs) are a significant genera
 lization of conventional queueing networks that allow for flexible schedul
 ing through dynamic sequencing and alternate routing. SPNs arise naturally
  in a variety of applications in operations management and their control a
 nd analysis present challenging mathematical problems. One approach to the
 se problems\, via approximate diffusion control problems\, has been outlin
 ed by J. M. Harrison. Various aspects of this approach have been developed
  mathematically\, including a reduction in dimension of the diffusion cont
 rol problem. However\, other aspects have been less explored\, especially\
 , solution of the diffusion control problem\, derivation of policies by in
 terpretating such solutions\,  and limit theorems that establish optimalit
 y of such policies in a suitable asymptotic sense.\n\nIn this talk\, for a
  concrete class of networks called parallel server systems which arise in 
 service network and computer science applications\, we explore previously 
 undeveloped aspects of Harrison's scheme and illustrate the use of the app
 roach in obtaining simple control policies that are nearly optimal. Identi
 fication of a graphical structure for the network\, an invariance principl
 e and properties of local times of reflecting Brownian motion\, will featu
 re in our analysis. The talk will conclude with a summary of the current s
 tatus and description of open problems associated with the further develop
 ment of control of stochastic processing networks.\n\nThis talk will draw 
 on aspects of joint work with M. Bramson\, M. Reiman\, W. Kang and V. Pesi
 c.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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