Numerical optimization of a queueing system by dynamic programming
A numerical method for determining the optimal number of servers of a time-dependent multiserver queueing system is presented. First, a queueing system with time-dependent arrival rate is solved numerically to obtain the state probabilities and the expected number of customers in queue. The corresponding finite set of linear differential-difference equations is solved by the fourth-order Runge-Kutta method. Then, using the just obtained probabilities and queue sizes, dynamic programming is implemented to determine the optimal number of servers during each 8-h shift of a 24-h day. A numerical example, considering the arrival and service of aircrafts in an airport, is solved.
linear differential-difference equations
scientific article; zbMATH DE number 4110062