Bounding techniques for transient analysis of G-Networks with catastrophes

We apply stochastic comparisons in order to bound the transient behavior of G-networks with catastrophes. These networks belong to Gelenbe's networks, with both positive and negative customers (or signals). We consider catastrophes where the signal deletes all customers in a queue. G-networks have a known product form steady-state distribution, but it is still impossible to obtain the transient distributions by a closed form. In the present paper, we propose to define smaller queueing systems providing bounds for subnetworks of the G-network with catastrophes. We apply stochastic comparisons by mapping functions to build bounding models. We derive transient performance measure bounds for applications as malware software infections. For instance, we obtain bounds for the first time of infection, or the number of times a station has been infected in a time interval. We study the tradeoff between the size of the subnetwork and the quality of the bounds with respect to parameters.