PhD Defense by Junqi Hu
Thesis Title: Scheduling in Queueing Systems with Specialized or Error-prone Servers
Dr. Sigrun Andradottir, School of Industrial and Systems Engineering, Georgia Tech
Dr. Hayriye Ayhan, School of Industrial and Systems Engineering, Georgia Tech
Dr. Robert Foley, School of Industrial and Systems Engineering, Georgia Tech
Dr. Siva Theja Maguluri, School of Industrial and Systems Engineering, Georgia Tech
Dr. Tugce Isık, Department of Industrial Engineering, Clemson University
Date and Time: 11 am-1 pm, Thursday, July 2th, 2020
Meeting URL (for BlueJeans):
Meeting ID (for BlueJeans):
843 322 229
Consider a multi-server queueing system with tandem stations, finite intermediate buffers, and an infinite supply of jobs in front of the first station. Our goal is to maximize the long-run average throughput of the system by dynamically assigning the servers to the stations.
For the first part of this thesis, we analyze a form of server coordination named task assignment where each job is decomposed into subtasks assigned to one or more servers, and the job is finished when all its subtasks are completed. We identify the optimal task assignment policy of a queueing station when the servers are either static, flexible, or collaborative. Next, we compare task assignment approaches with other forms of server assignment, namely teamwork and non-collaboration, and obtain conditions for when and how to choose a server coordination approach under different service rates. In particular, task assignment is best when the servers are highly specialized; otherwise, teamwork or non-collaboration are preferable depending on whether the synergy level among the servers is high or not. Then, we provide numerical results that quantify our previous comparison. Finally, we analyze server coordination for longer lines, where there are precedence relationships between some of the tasks. We show that for static task assignment, internal buffers at the stations are preferable to intermediate buffers between the stations, and we present numerical results that suggest our comparisons for one station systems generalize to longer lines.
The second part of this thesis studies server allocation when the servers can work in teams and the team service rates can be arbitrary. Our objective is to improve the performance of the system by dynamically assigning servers to teams and teams to stations. We first establish sufficient criteria for eliminating inferior teams, and then we identify the optimal policy among the remaining teams for the two-station case. Next, we investigate the special cases with structured team service rates and with teams of specialized servers. Finally, we provide heuristic policies for longer lines with teams of specialized server where the servers are generalists, and numerical results that suggest that our heuristic policies are near-optimal.
In the final part of this dissertation, we consider the scenario where a job might be broken and wasted when being processed by a server. Servers are flexible but non-collaborative, so that a job can be processed by at most one server at any time. We identify the dynamic server assignment policy that maximizes the long-run average throughput of the system with two stations and two servers. We find that the optimal policy is either a single or a double threshold policy on the number of jobs in the buffer, where the thresholds depend on the service rates and defect probabilities of the two servers. For larger systems, we provide a partial characterization of the optimal policy. In particular, we show that the optimal policy may involve server idling, and if there exists a distinct dominant server at each station, then it is optimal to always assign the servers to the stations where they are dominant. Finally, we propose heuristic server assignment policies motivated by experimentation with three-station lines and analysis of systems with infinite buffers. Numerical results suggest that our heuristics yield near-optimal performance for systems with more than two stations.