Abstract
A numerical method for obtaining the optimal number of servers of a time-dependent M/Ms queueing system is presented. First, an M/M/s queueing system with time-dependent arrival rate is solved numerically to obtain the state probabilities and the expected queue sizes. Then, the optimal number of servers during each 8-h shift of a 24-h day is obtained by dynamic programming. A numerical example is solved to show the effectiveness of the approach.
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