Rejection rules in the M/G/1 queue

David Perry, Søoren Asmussen

Research output: Contribution to journalArticlepeer-review


We consider a M/G/1 queue modified such that an arriving customer may be totally or partially rejected depending on a r.v. (the barricade) describing his impatience and on the state of the system. Three main variants of this scheme are studied. The steady-state distribution is expressed in terms of Volterra equations and the relation to storage processes, dams and queues with state-dependent Poisson arrival rate is discussed. For exponential service times, we further find the busy period Laplace transform in the case of a deterministic barricade, whereas for exponential barricade it is shown by a coupling argument that the busy period can be identified with a first passage time in an associated birth-death process.

Original languageEnglish
Pages (from-to)105-130
Number of pages26
JournalQueueing Systems
Issue number1-2
StatePublished - Mar 1995


  • Birth-death process
  • Volterra equation
  • busy period
  • coupling
  • impatient customers
  • martingale stopping theorem
  • queue
  • storage process
  • virtual waiting time

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics


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