Transient analysis of the M/M/1 queue

Authors
Leguesdron, P. Pellaumail, J. Rubino, G. Sericola, B.
Citation
P. Leguesdron, et al., Transient analysis of the M/M/1 queue, Advances in applied probability , 25(3), 1993, pp. 702-713
Journal title
Advances in applied probability → ACNP
ISSN journal
00018678
Volume
25
Issue
3
Year of publication
1993
Pages
702 - 713
Database
ACNP
SICI code
Abstract
A new approach is used to obtain the transient probabilities of the M/M/1 queueing system. The first step of this approach deals with the generating function of the transient probabilities of the uniformized Markov chain associated with this queue. The second step consists of the inversion of this generating function. A new analytical expression of the transient probabilities of the M/M/1 queue is then obtained.