Optimal control of queueing systems with non-collaborating servers
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This dissertation focuses on effective management of cross-trained workforce in manufacturing and service systems. In particular, non-collaborative queueing networks with cross-trained (flexible) servers are analyzed. For finite-buffered Markovian tandem networks with two stations, non-collaborative flexible servers, and no setups; the optimal server assignment policy is identified. For larger tandem networks, myopic server assignment heuristics are developed. It is also shown that the improvement that can be gained through collaboration is dependent on similarity of the tasks in the system, as well as the buffer sizes. When the server reassignments result in setup costs, the profit-optimal server assignment policy for Markovian tandem lines with two stations, homogeneous tasks is characterized to be of double threshold type. Our results demonstrate that the structure of the optimal policy depends both on the magnitude of the setup costs and the buffer size. For systems with non-homogeneous tasks and/or non-constant setup costs, near-optimal server assignment heuristics were provided. Finally, dynamic server allocation in queueing networks with general topology and routing is analyzed. For non-collaborative networks with infinite buffers, a processor sharing scheme that achieves an upper bound on the long-run average throughput is introduced. For Markovian systems with two stations, finite buffers, and homogeneous tasks, processor sharing attains the non-collaborative optimal throughput as the buffer size grows. To achieve near-optimal throughput in systems where processor sharing is not implementable, a class of round-robin policies that approximate processor sharing is proposed. Numerical results suggest these policies are near-optimal in systems with finite buffers and various topologies.