Bounding Techniques for Transient Analysis of G-Networks With Catastrophes
The authors 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). They 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, they propose to define smaller queueing systems providing bounds for subnetworks of the G-network with catastrophes. They apply stochastic comparisons by mapping functions to build bounding models.