Transient analysis of the M/M/1 queue

Patrice Leguesdron (1) , Jean Pellaumail (1) , Gerardo Rubino (1) , Bruno Sericola (1)

1 MODEL - Modeling Random Systems

A new approach is given to obtain the transient probabilities of the M/M/1 queueing system. A 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.

Domaines: Autre [cs.OH]

Patrice Leguesdron, Jean Pellaumail, Gerardo Rubino, Bruno Sericola. Transient analysis of the M/M/1 queue. [Research Report] RR-1976, INRIA. 1993. ⟨inria-00074697⟩