Zero-automatic queues and product form

Thu-Ha Dao-Thi (1) , Jean Mairesse (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We introduce and study a new model: 0-automatic queues. Roughly, 0-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable 0-automatic queues have a product form stationary distribution and a Poisson output process. When considering the two simplest and extremal cases of 0-automatic queues, we recover the simple M/M/1 queue, and Gelenbe's G-queue with positive and negative customers.

Mots clés: Queueing theory; M/M/1 queue; G-queue; quasi-reversibility; product form; Quasi-Birth-and-Death process.

Mots clés: Quasi-Birth-and-Death process

Domaines: Mathématique discrète [cs.DM]

Thu-Ha Dao-Thi, Jean Mairesse. Zero-automatic queues and product form. Advances in Applied Probability, 2007, 39 (2), pp.429-461. ⟨hal-00164778⟩