THE COMPLEXITY OF OPTIMAL QUEUING NETWORK CONTROL1

We show that several well-known optimization problems related to the optimal control of queues are provably intractable |independently of any unproven conjecture such as P6 =NP. In particular, we show that several versions of the problem of optimally controlling a simple network of queues with simple arrival and service distributions and multiple customer classes is complete for exponential time. This is perhaps the rst such intractability result for a well-known optimization problem. We also show that the restless bandit problem (the generalization of the multi-armed bandit problem to the case in which the unselected processes are not quiescent) is complete for polynomial space.