Repair systems with exchangeable items and the longest queue mechanism

R. Ravid, O. J. Boxma, D. Perry

Research output: Contribution to journalArticlepeer-review


We consider a repair facility consisting of one repairman and two arrival streams of failed items, from bases 1 and 2. The arrival processes are independent Poisson processes, and the repair times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The rule according to which backorders are satisfied by repaired items is the longest queue rule: At the completion of a service (repair), the repaired item is delivered to the base that has the largest number of failed items. We point out a direct relation between our model and the classical longer queue model. We obtain simple expressions for several probabilities of interest, and show how all two-dimensional queue length probabilities may be obtained. Finally, we derive the sojourn time distributions.

Original languageEnglish
Pages (from-to)295-316
Number of pages22
JournalQueueing Systems
Issue number3
StatePublished - Mar 2013


  • Longest queue
  • Queue lengths
  • Repair system
  • Sojourn time

ASJC Scopus subject areas

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


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