Stabilizing a Queue Subject to Activity-Dependent Server Performance

@article{Lin2021StabilizingAQ,
  title={Stabilizing a Queue Subject to Activity-Dependent Server Performance},
  author={Michael Lin and Richard J. La and Nuno C. Martins},
  journal={IEEE Transactions on Control of Network Systems},
  year={2021},
  volume={8},
  pages={1579-1591}
}
We consider a discrete-time system, comprising a first-come-first-served queue, a nonpreemptive server, and a scheduler that governs the assignment of tasks in the queue to the server. The server has an availability state that indicates, at each instant, whether the server is busy working on a task or is available. In the latter case, if the queue is nonempty, then a task-assignment control policy implemented by the scheduler either assigns a new task to the server or allows it to rest. The… 

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