Stochastic comparisons applied to G-Networks with catastrophes
Résumé
We study the transient distribution of some G-networks of queues with customers and signals. After its service completion a customer moves to another queue and may become a signal. We consider catastrophes where the signal deletes all customers in a queue. Both networks with negative customers and with catastrophes belong to well known of Gelenbe's networks with product form steady-state distribution. As the transient distribution is impossible to obtain, we derive stochastic upper and lower bounds on the marginal distribution for each queue following Massey's approach.