Abstract
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.
partially supported by French research project ANR-SETI06-02
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Castel-Taleb, H., Fourneau, JM., Pekergin, N. (2011). Stochastic comparisons applied to G-Networks with catastrophes. In: Gelenbe, E., Lent, R., Sakellari, G., Sacan, A., Toroslu, H., Yazici, A. (eds) Computer and Information Sciences. Lecture Notes in Electrical Engineering, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9794-1_11
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DOI: https://doi.org/10.1007/978-90-481-9794-1_11
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