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Call center service times are lognormal: A Fokker–Planck description

Stefano Gualandi

Department of Mathematics, University of Pavia, via Ferrata 1, Pavia 27100, Italy

E-mail Address: stefano.gualandi@unipv.it

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and

Giuseppe Toscani

Department of Mathematics, University of Pavia, via Ferrata 1, Pavia 27100, Italy

IMATI CNR, via Ferrata 1, Pavia 27100, Italy

E-mail Address: giuseppe.toscani@unipv.it

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https://doi.org/10.1142/S0218202518500410Cited by:33 (Source: Crossref)

Abstract

Call centers are service networks in which agents provide telephone-based services. An important part of call center operations is represented by service durations. In recent statistical analysis of real data, it has been noted that the distribution of service times reveals a remarkable fit to the lognormal distribution. In this paper, we discuss a possible source of this behavior by resorting to classical methods of statistical mechanics of multi-agent systems. The microscopic service time variation leading to a linear kinetic equation with lognormal equilibrium density is built up introducing as main criterion for decision a suitable value function in the spirit of the prospect theory of Kahneman and Twersky.

Communicated by N. Bellomo

Keywords:

AMSC: 35Q84, 82B21, 91D10, 94A17

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