Applicationsto stochastic schedulings,equentialclinicaltrialsand a class of searchproblemsare discussed. Keywords:BANDITPROCESSES;DYNAMICALLOCATIONINDICES; TWO-ARMEDBANDITPROBLEM; MARKOVDECISIONPROCESSESO; PTIMALRESOURCEALLOCATIONS; EQUENTIALRANDOM SAMPLING;CHEMICALRESEARCH;CLINICALTRIALS;SEARCH A schedulinpgroblem ...