Loss systems in a random environment: steady state analysis

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We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove a product-form steady state distribution of the joint queueing-environment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, for example, from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, for example, of queueing-inventory processes. We investigate further classical loss systems, where, due to finite waiting room, loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise.
Original languageEnglish
JournalQueueing Systems
Volume80
Issue number1-2
Pages (from-to)127-153
Number of pages27
ISSN0257-0130
DOIs
Publication statusPublished - 01.06.2015
Externally publishedYes

    Research areas

  • Mathematics - queueing systems, Random environment, produc form steady state, loss systems, inventory systems, availability, lost sales