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The Complexity of Optimal Queuing Network Control

Christos H. Papadimitriou and John N. Tsitsiklis
Mathematics of Operations Research
Vol. 24, No. 2 (May, 1999), pp. 293-305
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3690486
Page Count: 13
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The Complexity of Optimal Queuing Network Control
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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 ≠ 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.

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