  Staffing rules serve as an essential management tool in service industries to
attain target service levels. Traditionally, the square-root safety rule, based
on the Poisson arrival assumption, has been commonly used. However, empirical
findings suggest that arrival processes often exhibit an ``over-dispersion''
phenomenon, in which the variance of the arrival exceeds the mean. In this
paper, we develop a new doubly stochastic Poisson process model to capture a
significant dispersion scaling law, known as Taylor's law, showing that the
variance is a power function of the mean. We further examine how
over-dispersion affects staffing, providing a closed-form staffing formula to
ensure a desired service level. Interestingly, the additional staffing level
beyond the nominal load is a power function of the nominal load, with the power
exponent lying between $1/2$ (the square-root safety rule) and $1$ (the linear
safety rule), depending on the degree of over-dispersion. Simulation studies
and a large-scale call center case study indicate that our staffing rule
outperforms classical alternatives.
