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 -