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Towards better multi-class parametric-decomposition approximations for open queueing networks. (English) Zbl 0788.60116
Summary: 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 first-in-first-out service discipline. The model is $$\Sigma(GI_ i/GI_ i)/1$$ 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 used in the Queueing Network Analyzer (QNA). The specific approximations here extend ones developed by G. R. Bitran and D. Tirupati [Manage. Sci. 34, No. 1, 75-100 (1988; Zbl 0636.60101)]. For example, the effect of class-dependent 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.

MSC:
 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research 90B15 Stochastic network models in operations research
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