In this paper the authors define a model of exponential queuing networks where servers may have a dedicated inventory. If a server of the network has this specificity, any service at this node needs one item from the local stock. Moreover, if a customer arrives at the node when the local inventory is empty it is lost at the node but not at the network. This policy of service requires the development of suitable rerouting strategies for rejected customers. In this context the authors apply three rerouting principles that are called stalling, blocking and skipping and investigate these in detail. In the first step the authors study queuing network models obtained by integrating a server with an attached inventory into a Jacksonian network. Specifically, they consider two different policies to manage the replenishment orders for the inventory at the server. They investigate such models with different replenishment lead time intensities while the inventory is depleted. For these queuing network models they derive explicit expressions for the corresponding stationary distributions which turn out to be of product form. In the second step the authors develop queuing network models of Jackson type, where several nodes may have an attached inventory. In this context, they prove the existence of product form stationary distributions for the system processes. Leonardo Pasini

Recensione dell'articolo: (Schwarz, Maike; Wichelhaus, Cornelia; Daduna, Hans - " Product form models for queueing networks with an inventory " - Stoch.Models 23 (2007), no.4, 627–663.)

PASINI, Leonardo
2009-01-01

Abstract

In this paper the authors define a model of exponential queuing networks where servers may have a dedicated inventory. If a server of the network has this specificity, any service at this node needs one item from the local stock. Moreover, if a customer arrives at the node when the local inventory is empty it is lost at the node but not at the network. This policy of service requires the development of suitable rerouting strategies for rejected customers. In this context the authors apply three rerouting principles that are called stalling, blocking and skipping and investigate these in detail. In the first step the authors study queuing network models obtained by integrating a server with an attached inventory into a Jacksonian network. Specifically, they consider two different policies to manage the replenishment orders for the inventory at the server. They investigate such models with different replenishment lead time intensities while the inventory is depleted. For these queuing network models they derive explicit expressions for the corresponding stationary distributions which turn out to be of product form. In the second step the authors develop queuing network models of Jackson type, where several nodes may have an attached inventory. In this context, they prove the existence of product form stationary distributions for the system processes. Leonardo Pasini
2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11581/333783
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