How nearly do arriving customers see time-average behavior?

Erol A. Peköz, Sheldon M. Ross, Sridhar Seshadri

Research output: Contribution to journalArticlepeer-review


Customers arriving at a queue do not usually see its time-average behavior unless arrivals occur according to a Poisson process. In this article we study how nearly customers see time-average behavior. We give total variation error bounds for comparing the distance between the time- and customer-average distributions of a queueing system in terms of properties of the interarrival distribution. Some refinements are given for special cases and numerical computations are used to demonstrate the performance of the inequalities.

Original languageEnglish (US)
Pages (from-to)963-971
Number of pages9
JournalJournal of Applied Probability
Issue number4
StatePublished - Dec 2008
Externally publishedYes


  • Arrival theorem
  • Arrivals that see time averages

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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