Stochastic comparisons applied to G-Networks with catastrophes

We study the transient distribution of some G-networks of queues with customers and signals. After its service completion a cus- tomer 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 Gelenbe's networks with product form steady-state distribution. As the transient distribution is impossible to obtain, we derive stochas- tic upper and lower bounds on the marginal distribution for each queue following Massey's approach.