Approximating nonstationaryPh(t)/M(t)/s/c queueing systems

Nonstationary phase processes are defined and a surrogate distribution approximation (SDA) method for analyzing transient and nonstationary queueing systems with nonstationary phase arrival processes is presented. Regardless of system capacityc, the SDA method requires the numerical solution of only 6K differential equations, whereK is the number of phases in the arrival process, compared to theK(c+1) Kolmogorov forward equations required for the classical method of solution. Time-dependent approximations of mean and variance of the number of entities in the system and the number of busy servers are obtained. Empirical test results over a wide range of systems indicate the SDA is quite accurate.This research was partially funded by National Science Foundation grant ECS-8404409.