TITLE: Optimal Control of Queueing Systems with Non-Collaborating Servers

ABSTRACT:

In this thesis, we focus on effective management of cross-trained workforce in manufacturing systems. In particular, we analyze non-collaborative queueing networks where cross-trained (flexible) servers are not allowed to work at a station together. Our contributions to the understanding of systems with non-collaborative flexible servers can be summarized in two parts. (i)  we characterize the structure of optimal server assignment policies and draw insights to improve decision making in these systems. (ii) we  develop easy-to-implement policies with near-optimal performance for systems where the optimal policy is difficult to implement or is not analytically tractable.   In the first study, our goal is to identify the server assignment policy that maximizes the long-run average throughput in tandem networks with finite buffers and non-collaborative flexible servers. For Markovian systems with two stations and two servers, we characterize the optimal server assignment policy and demonstrate that the structure of the optimal policy is insensitive to the service requirement distributions. For larger tandem networks, we propose server assignment heuristics. Our numerical results suggest that in these systems, near-optimal throughputs can be achieved even if the server allocation decisions are made myopically. We also examine how lack of collaboration affects the performance of queueing systems with flexible servers. We show 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.   The second part focuses on tandem queueing networks with finite buffers and flexible servers where server reassignments  result in setups. For systems of arbitrary size with general service requirement distributions, we show that the policy that maximizes the long-run average profit becomes dedicated as the setup costs increase. We also characterize the profit-optimal server assignment policy for Markovian tandem lines with two stations, homogeneous tasks, and constant setup costs. 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, we provide near-optimal server assignment heuristics. Our computational results suggest that the relative performances of dynamic and dedicated server assignment policies are also dependent on the structure of the tasks.  Finally, we extend our analysis to queueing networks with general topology and routing. For non-collaborative networks with infinite buffers, we formulate a linear program that yields an upper bound on the long-run average throughput. We also introduce a processor sharing scheme for general queueing networks, and identify the optimal processor sharing policy for tandem lines with homogeneous tasks. For Markovian systems with two stations, finite buffers, and homogeneous tasks, we prove that processor sharing achieves the non-collaborative optimal throughput as the buffer size grows. For systems where processor sharing is not implementable, we propose a class of round-robin server assignment policies and show that they approximate processor sharing in systems with two stations. We evaluate the performance of the proposed class of policies in systems with various topologies and finite buffers, and demonstrate that they are near-optimal.