Analysis of Free Time Intervals between Buyers at Cash Register using Generating Functions

Detlef Hartleb, Detlef Hartleb, Andreas Ahrens, Ojaras Purvinis, Jelena Zaščerinska, Jelena Zaščerinska

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 independent of the size of the shop whereas the payment processing intervals at the cash register are quite regularly distributed.

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