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Dynamic Server Assignment With Task-Dependent Server Synergy

We study tandem queueing systems with finite buffers in which servers work more efficiently in teams than on their own and the synergy among collaborating servers can be task-dependent. Our goal is to determine the dynamic server assignment policy that maximizes the long-run average throughput. When each server works with the same ability at each task that she/he is assigned to, we show that any nonidling policy where all servers work in teams of two or more at all times is optimal. On the other hand, when the server abilities are task-dependent, we show that for Markovian systems with two stations and two servers, depending on the synergy among the servers, the optimal policy either assigns the two servers to different stations when possible, or lets them work in a team at all times. Finally, for larger Markovian systems, we provide sufficient conditions that guarantee that the optimal policy has all servers working together at all times.