Approximating nonstationary ph(t)⧸ph(t)⧸1⧸c queueing systems

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 k1 + 3k1k2 differential equations, where k1 is the number of phases in the arrival process and k2 is the number of phases in the service process, compared to the k1 + ck1k2 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.