Benchmark policies for utility-carrying queues with impatience

Yael Deutsch, Israel David

Research output: Contribution to journalArticlepeer-review


Men and jobs alike are characterized by a single trait, which may take on categorical values according to given population frequencies. Men arrive to the system following a Poisson process and wait till jobs are assigned to them. Jobs arrive to the system following another, independent, Poisson process. An arriving job must be assigned to a waiting man immediately, or be discarded, ensuing no gain. An assignment of a job to a man yields a higher gain if they match in trait, and a lower one if not. Each man waits a limited time for a job and leaves the system if unassigned by that time limit. It is stipulated that a man who arrives first has priority to either accept the pending job, or to pass it to the next man, who makes a similar decision. The last man in the line takes the job, or it is discarded. The individually optimal policy for each man is defined by some critical time for accepting a mismatched job. We solve for the critical times, depending on the mens’ place in the queue, and obtain expressions for the ensuing optimal value functions of this system, for expected gain. The model originates from the utility-equity dilemma in assigning live organs to patients on the national waiting list. The paper reports numerical comparison of the above policy with alternative ones, for several performance measures.

Original languageEnglish
Pages (from-to)97-120
Number of pages24
JournalQueueing Systems
Issue number1-2
StatePublished - 1 Jun 2020

Bibliographical note

Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.


  • Double-ended queues
  • Fairness in queues
  • Problem of best choice
  • Sequential stochastic assignment
  • Utility-equity dilemma


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