Attention allocation for decision making queues

Vaibhav Srivastava, Ruggero Carli, Cédric Langbort, Francesco Bullo

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)378-388
Number of pages11
JournalAutomatica
Volume50
Issue number2
DOIs
StatePublished - Feb 1 2014

Keywords

  • Control of queues
  • Human decision making
  • Human-robot interaction
  • Sigmoid utility

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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