?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F271%2F&rft.title=Examination+of+optimizing+information+flow+in+networks&rft.creator=Aralumallige%2C+Deepak&rft.creator=Braun%2C+Richard&rft.creator=Churchill%2C+Aaron&rft.creator=Halliwell%2C+Garry&rft.creator=Levinson%2C+Michael&rft.creator=Li%2C+Qingxia&rft.creator=Please%2C+Colin&rft.creator=Rivas%2C+Ivonne&rft.creator=Wang%2C+Yi&rft.creator=Weber%2C+Romann&rft.creator=Witelski%2C+Tom&rft.subject=Transport+and+Automotive&rft.subject=Information+and+communication+technology&rft.description=The+central+role+of+the+Internet+and+the+World-Wide-Web+in+global+communications+has+refocused+much+attention+on+problems+involving+optimizing+information+flow+through+networks.+The+most+basic+formulation+of+the+question+is+called+the+%22max+flow%22+optimization+problem%3A+given+a+set+of+channels+with+prescribed+capacities+that+connect+a+set+of+nodes+in+a+network%2C+how+should+the+materials+or+information+be+distributed+among+the+various+routes+to+maximize+the+total+flow+rate+from+the+source+to+the+destination.+Theory+in+linear+programming+has+been+well+developed+to+solve+the+classic+max+flow+problem.+Modern+contexts+have+demanded+the+examination+of+more+complicated+variations+of+the+max+flow+problem+to+take+new+factors+or+constraints+into+consideration%3B+these+changes+lead+to+more+difficult+problems+where+linear+programming+is+insufficient.+%0D%0A%0D%0AIn+the+workshop+we+examined+models+for+information+flow+on+networks+that+considered+trade-offs+between+the+overall+network+utility+(or+flow+rate)+and+path+diversity+to+ensure+balanced+usage+of+all+parts+of+the+network+(and+to+ensure+stability+and+robustness+against+local+disruptions+in+parts+of+the+network).%0D%0AWhile+the+linear+programming+solution+of+the+basic+max+flow+problem+cannot+handle+the+current+problem%2C+the+approaches+primal%2Fdual+formulation+for+describing+the+constrained+optimization+problem+can+be+applied+to+the+current+generation+of+problems%2C+called+network+utility+maximization+(NUM)+problems.+In+particular%2C+primal%2Fdual+formulations+have+been+used+extensively+in+studies+of+such+networks.%0D%0AA+key+feature+of+the+traffic-routing+model+we+are+considering+is+its+formulation+as+an+economic+system%2C+governed+by+principles+of+supply+and+demand.+Considering+channel+capacities+as+a+commodity+of+limited+supply%2C+we+might+suspect+that+a+system+that+regulates+traffic+via+a+pricing+scheme+would+assign+prices+to+channels+in+a+manner+inversely+proportional+to+their+respective+capacities.%0D%0AOnce+an+appropriate+network+optimization+problem+has+been+formulated%2C+it+remains+to+solve+the+optimization+problem%3B+this+will+need+to+be+done+numerically%2C+but+the+process+can+greatly+benefit+from+simplifications+and+reductions+that+follow+from+analysis+of+the+problem.+Ideally+the+form+of+the+numerical+solution+scheme+can+give+insight+on+the+design+of+a+distributed+algorithm+for+a+Transmission+Control+Protocol+(TCP)+that+can+be+directly+implemented+on+the+network.%0D%0A%0D%0AAt+the+workshop+we+considered+the+optimization+problems+for+two+small+prototype+network+topologies%3A+the+two-link+network+and+the+diamond+network.+These+examples+are+small+enough+to+be+tractable+during+the+workshop%2C+but+retain+some+of+the+key+features+relevant+to+larger+networks+(competing+routes+with+different+capacities+from+the+source+to+the+destination%2C+and+routes+with+overlapping+channels%2C+respectively).+We+have+studied+a+gradient+descent+method+for+solving+obtaining+the+optimal+solution+via+the+dual+problem.+The+numerical+method+was+implemented+in+MATLAB+and+further+analysis+of+the+dual+problem+and+properties+of+the+gradient+method+were+carried+out.+Another+thrust+of+the+group's+work+was+in+direct+simulations+of+information+flow+in+these+small+networks+via+Monte+Carlo+simulations+as+a+means+of+directly+testing+the+efficiencies+of+various+allocation+strategies.&rft.date=2009&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F271%2F1%2Fmpi_nist_r9.pdf&rft.identifier=++Aralumallige%2C+Deepak+and+Braun%2C+Richard+and+Churchill%2C+Aaron+and+Halliwell%2C+Garry+and+Levinson%2C+Michael+and+Li%2C+Qingxia+and+Please%2C+Colin+and+Rivas%2C+Ivonne+and+Wang%2C+Yi+and+Weber%2C+Romann+and+Witelski%2C+Tom++(2009)+Examination+of+optimizing+information+flow+in+networks.++%5BStudy+Group+Report%5D+++++