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.
- Control of queues
- Human decision making
- Human-robot interaction
- Sigmoid utility
ASJC Scopus subject areas
- Control and Systems Engineering
- Electrical and Electronic Engineering