The Complexity of Optimal Queuing Network Control

  • Authors:
  • Christos H. Papadimitriou;John N. Tsitsiklis

  • Affiliations:
  • -;-

  • Venue:
  • Mathematics of Operations Research
  • Year:
  • 1999

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Abstract

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 P (not equal) 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 first 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.