Index policies and a novel performance space structure for a class of generalised branching bandit problems

Our object of study is a new class of controlled stochastic systems called generalised branching bandits which include discounted branching bandits and generalised bandit problems as special cases. These models allow us to study queueing scheduling and project scheduling problems in which the reward earned from processing a particular job is influenced by other job types present in the system. Our mode of analysis is the achievable region approach. What is novel here is that the full system may be partitioned into two subsystems, each of which satisfies its own set of conservation laws and has as own highly structured performance space. An optimal policy for the full system is constructed from two sets of Gittins indices derived from the conservation laws governing the two subsystems.