Summary
An analysis is given of multiple phase service facilities of which queueing networks are special models, for the case of a service discipline to be denoted as generalized processor sharing. Under this discipline requests are served simultaneously with a rate depending on the phase and the number of requests present here. The model is of a very general type, its analysis is given for arbitrary routing matrices and absolutely continuous required service time distributions. The mathematical technique used is that of the supplementary variable. Generalisations of known results for closed and open networks are obtained and new results about the average sojourn time of a request in the system are derived, in particular for requests with given route and given processing times at the nodes of the route. Some basic results about reversed processes and departure processes are discussed. For a special but important model the workload is discussed.
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Cohen, J.W. The multiple phase service network with generalized processor sharing. Acta Informatica 12, 245–284 (1979). https://doi.org/10.1007/BF00264581
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DOI: https://doi.org/10.1007/BF00264581