Sojourn time estimation in an M/G/∞ queue with partial information

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We propose an estimator for the cumulative distribution function G of the sojourn time in a steady-state M/G/∞ queueing system, when the available data consists of the arrival and departure epochs alone, without knowing which arrival corresponds to which departure. The estimator generalizes an estimator proposed in Brown (1970), and is based on a functional relationship between G and the distribution function of the time between a departure and the rth latest arrival preceding it. The estimator is shown to outperform Brown's estimator, especially when the system is heavily loaded.

Original languageEnglish
Pages (from-to)1044-1056
Number of pages13
JournalJournal of Applied Probability
Issue number4
StatePublished - Dec 2013


  • M/G/∞
  • Semiparametric estimation
  • Smoluchowski process
  • Sojourn Time estimation

ASJC Scopus subject areas

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


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