PhD Defense by Tugce Isik

Title: Optimal Control of Queueing Systems with Non-Collaborative Servers

Advisor:  Prof. Sigrun Andradottir, Prof. Hayriye Ayhan

Committee Members: Prof. Sigrun Andradottir, Prof. Hayriye Ayhan, Prof. Robert Foley, Prof. Jim Dai (Cornell University), Prof. Mark Lewis (Cornell University)

Date and Time: Tuesday, July 21st, 2015, 1:00 pm

Location: ISyE Main Building, Poole Board Room

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.  near-optimal performance for systems where the optimal policy is difficult to implement or is not analytically tractable. 

            In the first part, 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 that are near-optimal.  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 setup costs. 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.

            In the third part, we extend our analysis to queueing networks with general topology and routing.  We  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.