Queueing Systems

, Volume 73, Issue 3, pp 295-316

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Repair systems with exchangeable items and the longest queue mechanism

  • R. RavidAffiliated withDepartment of Statistics, University of HaifaCollege of Engineering, ORT Braude
  • , O. J. BoxmaAffiliated withEURANDOMDepartment of Mathematics and Computer Science, Technische Universiteit Eindhoven Email author 
  • , D. PerryAffiliated withDepartment of Statistics, University of Haifa


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.


Repair system Longest queue Queue lengths Sojourn time

Mathematics Subject Classification

60K25 90B22