Server staffing to meet time-varying demand

We consider a multiserver service system with general nonstationary arrival and service-time processes in which s(t), the number of servers as a function of time, needs to be selected to meet projected loads. We try to choose s(t) so that the probability of a delay (before beginning service) hits or falls just below a target probability at all times. We develop an approximate procedure based on a time-dependent normal distribution, where the mean and variance are determined by infinite-sewer approximations. We demonstrate that this approximation is effective by making comparisons with the exact numerical solution of the Markovian M(t)/M/S-t model.