ENBIS: European Network for Business and Industrial Statistics

Stability of queue-series under pertubations with applications in retail and logistic processes

22 September 2009, 16:55 – 17:15

Abstract

Submitted by

Florian Sobieczky

Authors

Florian Sobieczky, Gerhard Rappitsch

Affiliation

TU-Graz

Abstract

A series of single-server queues is analysed with respect to stability under changes of the input and service-distributions. These changes are defined by perturbations of the transition probability matrices of the corresponding random walk models (‘birth-death processes’). As an application, the cost-functional related to a queue- series modelling a shop’s buying-stocking-selling process is optimised under the constraint of stability under these pertubations. In particular, we consider a retailers infrastructure with an incoming distribution of goods, a simple stock-and-shelf concept, and a specific product-portfolio. We focus on the optimisation of the cost-functional for infrastructures using RFID-transponders, both in stock- and shelf areas.

Keywords: birth-death processes, series of queues, perturbations of random walks

AMS classification: 90B22, 60K20, 60K25

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