Throughput maximization for two station tandem systems: a proof of the Andradóttir---Ayhan conjecture

Authors:
John J. Hasenbein;Bara Kim
Affiliations:
Graduate Program in Operations Research and Industrial Engineering, Department of Mechanical Engineering, University of Texas at Austin, Austin, USA 78712;Department of Mathematics, Korea University, Seoul, Korea 136-701
Venue:
Queueing Systems: Theory and Applications
Year:
2011

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Abstract

We study a tandem queueing network with two stations, M heterogeneous flexible servers, and a finite intermediate buffer. The objective is to dynamically assign the servers to the stations in order to maximize the throughput of the system. The form of the optimal policy for M驴3 was derived in two previous papers. In one of those papers, Andradóttir and Ayhan (Operations Research 53:516---531, 2005) provide a conjecture on the form of the optimal policy for M驴4. We prove their conjecture in this paper, showing that the optimal policy is defined by monotone thresholds and the ratios of the service rates among the servers. For M1, we also prove that the optimal policy always uses the entire intermediate buffer.