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Journal of Applied Mathematics and Simulation
Volume 1 (1987), Issue 2, Pages 115-135

Sequential scheduling of priority queues and Arm-acquiring bandits

Department of Statistics, Purdue University, West Lafayette, IN 47907, USA

Received 20 November 1987; Accepted 21 December 1987

Copyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In a queueing network with a single server and r service nodes, a non-preemptive non-idling policy chooses a node to service at each service completion epoch. Under the assumptions of independent Poisson arrival processes, fixed routing probabilities, and linear holding cost rates, we apply Whistle's method for Arm-acquiring bandits to show that for minimizing discounted cost or long-run average cost the optimal policy is an index policy. We also give explicit expressions for those priority indices.