Towards Better Multi-class Parametric-decomposition Approximations for Open Queueing Networks

Methods are developed for approximately characterizing the departure process of each customer class from a multi-class single-server queue with unlimited waiting space and the firstin first-out service discipline. The model is Σ(GI i / GI i )/1 with a non-Poisson renewal arrival process and a non-exponential service-time distribution for each class. The methods provide a basis for improving parametric-decomposition approximations for analyzing non-Markov open queueing networks with multiple classes. For example, parametric-decomposition approximations are the Queueing Network Analyzer (QNA). The specific approximations here extend ones developed by G. Bitran and D. Tirupati (1988). For example, the effect of classdependent service times is considered here. With all procedures proposed here, the approximate variability parameter of the departure process of each class is a linear function of the variability parameters of the arrival processes of all the classes served at that queue, thus ensuring that the final arrival variability parameters in a general open network can be calculated by solving a system of linear equations.