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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-server 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.
Jennings et al. (Tue,) studied this question.