On the optimal control of two queues with server setup times and its analysis
SIAM Journal on Computing
Line reversibility of tandem queues with general blocking
Management Science
Assigning a single server to inhomogeneous queues with switching costs
Theoretical Computer Science
Introduction to Linear Optimization
Introduction to Linear Optimization
A two-stage tandem queue attended by a moving server with holding and switching costs
Queueing Systems: Theory and Applications
Dynamic Scheduling of a Two-Class Queue with Setups
Operations Research
Control of a Single-Server Tandem Queueing System with Setups
Operations Research
Performance of Bucket Brigades When Work Is Stochastic
Operations Research
Operations and Shipment Scheduling of a Batch on a Felxible Machine
Operations Research
Dynamic Server Allocation for Queueing Networks with Flexible Servers
Operations Research
Dynamic assignment of dedicated and flexible servers in tandem lines
Probability in the Engineering and Informational Sciences
Compensating for Failures with Flexible Servers
Operations Research
Dynamic control of a flexible server in an assembly-type queue with setup costs
Queueing Systems: Theory and Applications
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We study the dynamic assignment of flexible servers to stations in the presence of setup costs that are incurred when servers move between stations. The goal is to maximize the long-run average profit. We provide a general problem formulation and some structural results, and then concentrate on tandem lines with two stations, two servers, and a finite buffer between the stations. We investigate how the optimal server assignment policy for such systems depends on the magnitude of the setup costs, as well as on the homogeneity of servers and tasks. More specifically, for systems with either homogeneous servers or homogeneous tasks, small buffer sizes, and constant setup cost, we prove the optimality of "multiple threshold" policies (where servers' movement between stations depends on both the number of jobs in the system and the locations of the servers) and determine the values of the thresholds. For systems with heterogeneous servers and tasks, small buffers, and constant setup cost, we provide results that partially characterize the optimal server assignment policy. Finally, for systems with larger buffer sizes and various service rate and setup cost configurations, we present structural results for the optimal policy and provide numerical results that strongly support the optimality of multiple threshold policies.