Discrete-time controlled Markov processes with average cost criterion: a survey
SIAM Journal on Control and Optimization
Stochastic dynamic programming and the control of queueing systems
Stochastic dynamic programming and the control of queueing systems
Dynamic Control of a Queue with Adjustable Service Rate
Operations Research
Dynamic admission and service rate control of a queue
Queueing Systems: Theory and Applications
Optimal Rate Control for Delay-Constrained Data Transmission Over a Wireless Channel
IEEE Transactions on Information Theory
Computing the Effects of Operator Attention Allocation in Human Control of Multiple Robots
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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We consider the optimal servicing of a queue with sigmoid server performance. There are various systems with sigmoid server performance, including systems involving human decision making, visual perception, human-machine communication and advertising response. Tasks arrive at the server according to a Poisson process. Each task has a deadline that is incorporated as a latency penalty. We investigate the trade-off between the reward obtained by processing the current task and the penalty incurred due to the tasks waiting in the queue. We study this optimization problem in a Markov decision process (MDP) framework. We characterize the properties of the optimal policy for the MDP and show that the optimal policy may drop some tasks; that is, may not process a task at all. We determine an approximate solution to the MDP using the certainty-equivalent receding horizon optimization framework and derive performance bounds on the proposed receding horizon policy. We also suggest guidelines for the design of such queues.