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Working vacation queue models are well applied in the modeling and analysis of the router in optical networks. The GI/Geo/c queue with working vacations is studied in this paper. Through establishing two-dimensional Markov chain and using matrix-geometric solution method, the stability condition is derived. Adopting UL-type RG-factorization of irreducible Markov chain, the stationary distribution is given. Based on these, the probability distribution of queue-length and PGF of waiting time are obtained in the end.

Network security risk assessment is an important means of acquiring and mastering the current and future state of network, which is of great significance to maintain the safe operation of the network. This paper presents an improved risk assessment method based on Markov game that has simply changed the past, in which the risk status of the network assets were classified into fixed categories. Depending on the game relationship between fixing vulnerabilities and threat attacking, this method has more detailed characterization of the network risk. Network attacks and vulnerabilities are sorted, which reduces the state space, making the scale of model input greatly reduced, improving the assessment of large-scale network efficiency. Simulation results demonstrate the feasibility and effectiveness of this method.