Queueing Systems

, Volume 53, Issue 3, pp 105–114 | Cite as

The distribution of the number of arrivals in a subinterval of a busy period of a single server queue

  • A. Novak
  • P. Taylor
  • D. Veitch


In the course of attempting to estimate the arrival rate of a single server queue using an active probing experiment, the authors found it necessary to derive the distribution of the number of arrivals between two probes under the conditions that the busy period of the queue lasts this long. In this paper we derive this distribution. The key building blocks in the derivation of the distribution are the classical ballot theorem and its generalized forms.


Active probing Ballot theorem Busy period M/D/1 M/G/1 


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneAustralia
  2. 2.ARC Special Research Center for Ultra-Broadband Information Networks (CUBIN), an affiliated program of National ICT Australia, Department of Electrical and Electronic EngineeringUniversity of MelbourneAustralia

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