Abstract
AbstractIn the present paper, the single-server queue model M|G|1|∞ with unreliable server subject to catastrophes is considered. The transient and stationary distributions of virtual waiting time, busy period and idle state probability for two basic models with reliable and unreliable server are obtained. Different generalizations of basic models are considered: model with batch arrival of customers, model with non-homogeneous streams of customers and catastrophes, model with k types of customers, model with k types of priority customers. For those models, the virtual waiting time distribution and idle state probability are found.KeywordsVirtual waiting timeSingle-server queueCatastrophesUnreliable serverIdle state probability
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