On Large Delays in Multi-Server Queues with Heavy Tails

S. Foss, D. Korshunov

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value of the traffic load ? which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a “principle of s - k big jumps” in this case (here k is the integer part of ?), which gives the most probable way for the stationary waiting time to be large.

Another corollary of the bounds obtained is to provide a new proof of necessity and sufficiency of conditions for the existence of moments of the stationary waiting time.

Original languageEnglish
Pages (from-to)201-218
JournalMathematics of Operations Research
Issue number2
Early online date20 Mar 2012
Publication statusPublished - 2012


  • FCFS multi-server queue
  • stationary waiting time
  • heavy tails
  • large deviations
  • long-tailed distribution
  • subexponential distribution
  • existence of moments


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