Fluid limits of G/G/1+G queues under the nonpreemptive earliest-deadline-first discipline

RAMI ATAR, Anup Biswas, Haya Kaspi

Research output: Contribution to journalArticlepeer-review


A single-server queueing model is considered with customers that have deadlines. If a customer's deadline elapses before service is offered, the customer abandons the system (customers do not abandon while being served). When the server becomes available, it offers service to the customer having the earliest deadline among those that are in the queue. We obtain a fluid limit of the queue length and abandonment processes and for the occupation measure of deadlines, in the form of measure-valued processes. We characterize the limit by means of a Skorohod problem in a time-varying domain that has an explicit solution. The fluid limits also describe a certain process called the frontier that is well known to play a key role in systems operating under this scheduling policy.

Original languageEnglish
Pages (from-to)683-702
Number of pages20
JournalMathematics of Operations Research
Issue number3
StatePublished - 1 Aug 2015


  • Due dates
  • Earliest deadline first
  • Fluid limits
  • G/G/1+G
  • Law of large numbers
  • Measure-valued processes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research


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