62 citations · 268 across the 25 of their papers we have counts for
8 papers · 1 filter
Synthesis and Analysis of Product-form Petri Nets
Serge Haddad, Jean Mairesse, Hoang-Thach Nguyen
For a large Markovian model, a "product form" is an explicit description of the steady-state behaviour which is otherwise generally untractable. Being first introduced in queueing…
Stability of the bipartite matching model
Ana Bušić, Varun Gupta, Jean Mairesse
We consider the bipartite matching model of customers and servers introduced by Caldentey, Kaplan, and Weiss (Adv. Appl. Probab., 2009). Customers and servers play symmetrical role…
Deficiency Zero Petri Nets and Product Form
Jean Mairesse, Hoang-Thach Nguyen
Consider a Markovian Petri net with race policy. The marking process has a "product form" stationary distribution if the probability of viewing a given marking can be decomposed as…
Series which are both max-plus and min-plus rational are unambiguous
Sylvain Lombardy, Jean Mairesse
Consider partial maps from the free monoid into the field of real numbers with a rational domain. We show that two families of such series are actually the same: the unambiguous ra…
Services within a busy period of an M/M/1 queue and Dyck paths
Moez Draief, Jean Mairesse
We analyze the service times of customers in a stable M/M/1 queue in equilibrium depending on their position in a busy period. We give the law of the service of a customer at the b…
Queues, stores, and tableaux
Moez Draief, Jean Mairesse, Neil O'Connell
Consider the single server queue with an infinite buffer and a FIFO discipline, either of type M/M/1 or Geom/Geom/1. Denote by A the arrival process and by s the services. Assume t…