Abstract
A state space partitioning and surrogate distribution approximation (SDA) approach for analyzing the time-dependent behavior of queueing systems is described for finite-capacity, single server queueing systems with time-dependent phase arrival and service processes. Regardless of the system capacity, c, the approximation requires the numerical solution of only k 1 + 3 k 1 k 2 differential equations, where k 1 is the number of phases in the arrival process and k 2 is the number of phases in the service process, compared to the k 1 + ck 1 k 2 Kolmogorov-forward equations required for the classic method of solution. Time-dependent approximations of mean and standard deviation of the number of entities in the system are obtained. Empirical test results over a wide range of systems indicate that the approximation is extremely accurate.
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