Stochastic ordering for Markov processes on partially ordered spaces
Mathematics of Operations Research
Performance Evaluation
Queueing Networks and Markov Chains
Queueing Networks and Markov Chains
Dealing with software viruses: A biological paradigm
Information Security Tech. Report
Aggregated bounding Markov processes applied to the analysis of tandem queues
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Stochastic Automata Networks with Master/Slave Synchronization: Product Form and Tensor
ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
A queueing network model with catastrophes and product form solution
Operations Research Letters
Combined CAC and forced handoff for mobile network performability
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
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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.