Loss systems in a random environment: steady state analysis
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Loss systems in a random environment: steady state analysis. / Krenzler, Ruslan; Daduna, Hans.
in: Queueing Systems, Jahrgang 80, Nr. 1-2, 01.06.2015, S. 127-153.Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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TY - JOUR
T1 - Loss systems in a random environment: steady state analysis
AU - Krenzler, Ruslan
AU - Daduna, Hans
PY - 2015/6/1
Y1 - 2015/6/1
N2 - 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.
AB - 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.
KW - Mathematics
KW - queueing systems
KW - Random environment
KW - produc form steady state
KW - loss systems
KW - inventory systems
KW - availability
KW - lost sales
U2 - 10.1007/s11134-014-9426-6
DO - 10.1007/s11134-014-9426-6
M3 - Journal articles
VL - 80
SP - 127
EP - 153
JO - Queueing Systems
JF - Queueing Systems
SN - 0257-0130
IS - 1-2
ER -