This paper concerns the problem to determine the optimal agent disposition in a call
center. We here assume that calling by customer is described by the Poisson
distribution with the random parameter following a gamma distribution.
This implies that the negative binomial distribution for agent disposition is
obtained by mixing the mean of the Poisson distribution with a gamma distribution.
This paper proposes an interpretation of the optimal agent disposition by
considering the unknown Poisson parameter. In particular, the uncertainty of
Poisson parameter comes from the irregularity of calling time interval.