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Authors: Detlef Hartleb 1 ; 2 ; Andreas Ahrens 2 ; Ojaras Purvinis 3 and Jelena Zaščerinska 4 ; 2

Affiliations: 1 ETSIST, Universidad Politécnica de Madrid, Madrid, Spain ; 2 Hochschule Wismar, University of Technology, Business and Design, Wismar, Germany ; 3 Kaunas University of Technology, Kaunas, Lithuania ; 4 Centre for Education and Innovation Research, Riga, Latvia

Keyword(s): Bottleneck, Buyers’ Burstiness, Cashiers’ Bottleneck, Cash Register, Buyers’ Waiting Time Gaps, Generating Functions.

Abstract: The optimization of bursty business processes requires stochastic models with measurable parameters. Often simplifications worked out in the analysis of such models lead to inaccuracies when events occur in a bursty manner. In this work, a novel approach based on generating functions is introduced for modelling the bursty appearance of buyers via gap processes when paying at the cash register. The obtained approach is verified by analysing the payment process at the cash register by taking the free time intervals (gaps) between buyers as well as the payment processing time at the cash register into account. As both payment-related processes can be described by gap processes, the use of generating functions allows close-form solutions when analysing the payment process at the cash register. As an example the payment process is analysed in two supermarket of different sizes in Lithuania. The obtained results show that the free time intervals at the cash register are quite bursty indepe ndent of the size of the shop whereas the payment processing intervals at the cash register are quite regularly distributed. (More)

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Paper citation in several formats:
Hartleb, D.; Ahrens, A.; Purvinis, O. and Zaščerinska, J. (2020). Analysis of Free Time Intervals between Buyers at Cash Register using Generating Functions. In Proceedings of the 10th International Conference on Pervasive and Parallel Computing, Communication and Sensors - PECCS, ISBN 978-989-758-477-0; ISSN 2184-2817, pages 42-49. DOI: 10.5220/0010172700420049

@conference{peccs20,
author={Detlef Hartleb. and Andreas Ahrens. and Ojaras Purvinis. and Jelena Zaščerinska.},
title={Analysis of Free Time Intervals between Buyers at Cash Register using Generating Functions},
booktitle={Proceedings of the 10th International Conference on Pervasive and Parallel Computing, Communication and Sensors - PECCS,},
year={2020},
pages={42-49},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010172700420049},
isbn={978-989-758-477-0},
issn={2184-2817},
}

TY - CONF

JO - Proceedings of the 10th International Conference on Pervasive and Parallel Computing, Communication and Sensors - PECCS,
TI - Analysis of Free Time Intervals between Buyers at Cash Register using Generating Functions
SN - 978-989-758-477-0
IS - 2184-2817
AU - Hartleb, D.
AU - Ahrens, A.
AU - Purvinis, O.
AU - Zaščerinska, J.
PY - 2020
SP - 42
EP - 49
DO - 10.5220/0010172700420049

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