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

Authors:
A. Novak;P. Taylor;D. Veitch
Affiliations:
Department of Mathematics and Statistics, University of Melbourne, Australia;Department of Mathematics and Statistics, University of Melbourne, Australia;ARC Special Research Center for Ultra-Broadband Information Networks (CUBIN), an affiliated program of National ICT Australia, Department of Electrical and Electronic Engineering, University of Me ...
Venue:
Queueing Systems: Theory and Applications
Year:
2006

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Abstract

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.