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Towards better multi-class parametric-decomposition approximations for open queueing networks

  • Approximate Techniques
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Abstract

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 σ(GT 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 Bitran and Tirupati [5]. 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.

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  1. AT&T Bell Laboratories, 07974-0636, Murray Hill, NJ, USA

    Ward Whitt

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  1. Ward Whitt
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Whitt, W. Towards better multi-class parametric-decomposition approximations for open queueing networks. Ann Oper Res 48, 221–248 (1994). https://doi.org/10.1007/BF02024659

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