We show that if performance measures in a stochastic scheduling problem satisfy a set of so-called partial conservation laws (PCL), which extend previously studied generalized conservation laws (GCL), then the problem is solved optimally by a priority-index policy for an appropriate range of...

We develop a mathematical programming approach for the classical PSPACE - hard restless bandit problem in stochastic optimization. We introduce a hierarchy of n (where n is the number of bandits) increasingly stronger linear programming relaxations, the last of which is exact and corresponds to...