A time-dependent busy period queue length formula for the M/Ek/1 queue
Jung, Woo Baek.
Seung, Ki Moon.
Ho, Woo Lee.
Date of Issue2014
School of Mechanical and Aerospace Engineering
In this paper, a closed-form time-dependent busy period queue length probability is obtained for the M/Ek/1M/Ek/1 queue. This probability is frequently needed when we compare the length of the busy period and the maximum amount of service that can be rendered to the existing customers. The transient probability is given in terms of the generalized modified Bessel function of the second type of Griffiths et al. (2006a). The queue length probability for the M/M/1M/M/1 queue is also presented as a special case.
Statistics & probability letters
© 2014 Elsevier B.V. This is the author created version of a work that has been peer reviewed and accepted for publication by Statistics & Probability Letters, Elsevier B.V.. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.spl.2014.01.004].