Control of a Single-Server Tandem Queueing System with Setups

• Published in: Operations research Vol. 46; no. 2; pp. 218 - 230
• Main Authors: Duenyas, Izak, Gupta, Diwakar, Olsen, Tava Lennon
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01-03-1998; Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: Applied sciences; Average cost; Carrying costs; control of tandem queues; Cost estimates; Descendants; Exact sciences and technology; Heuristic; Heuristics; Markov analysis; Mathematical models; Minimization of cost; Network servers; Operational research and scientific management; Operational research. Management science; Operations research; Optimal policy; Production controls; Queues; Queuing theory; Queuing theory. Traffic theory; Random variables; Scheduling; Simulation; Statistical analysis; Studies; tandem; Cost minimization; Markov decision; Simulation; Optimal control; Average cost; Heuristic method; Tandem queue; Scheduling; Single server queue; Waiting time
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.46.2.218

This paper considers the control of a single-server tandem queueing system with setups. Jobs arrive to the system according to a Poisson process and are produced to order. A single server must perform a number of different operations on each job. There is a setup time for the server to switch between different operations. We assume that there is a holding cost at each operation, which is nondecreasing in operation number (i.e., as value is added to a job, it becomes more expensive to hold). The control problem is to decide which job the server should process at each point in time.
We formulate this control problem as a Markov-Decision Process. We partially characterize the optimal policy, develop an exact analysis of exhaustive and gated polling policies, and develop an effective heuristic policy. The results of a simulation study, which tests the performance of the policies considered, are reported. These computational results indicate that our heuristic is effective for a wide variety of cases.