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Product form models for queueing networks with an inventory

We investigate a new class of stochastic networks that exhibit a product form steady state distribution. The stochastic networks developed here are integrated models for networks of service stations and inventories. We integrate a server with attached inventory under (r, Q)- or (r, S)-policy into Ja...

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Hauptverfasser: Schwarz, Maike (VerfasserIn) , Wichelhaus, Cornelia (VerfasserIn) , Daduna, Hans (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 02 Nov 2007
In: Stochastic models
Year: 2007, Jahrgang: 23, Heft: 4, Pages: 627-663
ISSN:1532-4214
DOI:10.1080/15326340701645975
Online-Zugang:Verlag, Volltext: http://dx.doi.org/10.1080/15326340701645975
Volltext
Verfasserangaben:Maike Schwarz, Cornelia Wichelhaus, Hans Daduna

MARC

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520 |a We investigate a new class of stochastic networks that exhibit a product form steady state distribution. The stochastic networks developed here are integrated models for networks of service stations and inventories. We integrate a server with attached inventory under (r, Q)- or (r, S)-policy into Jackson or Gordon-Newell networks. Replenishment lead times are non-zero and random and depend on the load of the system. While the inventory is depleted the server with attached inventory does not accept new customers (lost sales regime), but we assume that the lost sales are not lost to the system. We pursue three different approaches to handle routing with respect to this node during the time the inventory is empty. We derive stationary distributions of joint queue lengths and inventory processes in explicit product form. The stationary distributions are then used to calculate performance measures of the respective systems. We discuss the advantages and disadvantages of product form modeling in the context of service-inventory systems. Finally, we sketch two network models where several nodes may have an attached inventory. 
650 4 |a Inventory level 
650 4 |a Inventory policy 
650 4 |a Inventory systems 
650 4 |a INVENTORY theory 
650 4 |a Jackson networks 
650 4 |a Performance analysis 
650 4 |a Product form solution 
650 4 |a QUEUEING networks 
650 4 |a QUEUING theory 
650 4 |a Service level 
650 4 |a SERVICE stations 
650 4 |a Stationary distributions 
650 4 |a STOCHASTIC processes 
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